THE SEARCH FOR EXTRA-SOLAR TERRESTRIAL PLANETS:

TECHNIQUES AND TECHNOLOGY

Proceedings of a Conference held in Boulder, Colorado,

May 14-17, 1995

Editedby

J.M.SHULL University ofColorado, Boulder, Colorado, U.S.A.

H. A. THRONSON, Jr. University ofWyoming, Laramie, Wyoming, U.S.A. andNASA Headquarters, Office ofSpace Sciences,

Washington, DC, U.S.A.

and

S.A.STERN Southwest Research Institute, Boulder,

Colorado, U.S.A.

Reprinted from Astrophysics and Space Science Volume 241, No. 1, 1996

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-94-010-6453-8 ISBN 978-94-011-5808-4 (eBook) DOI 10.1007/978-94-011-5808-4

Cover photo: Jmage of the Earth--Moon system taken from the Galileo spacecraft during its flight to Jupiter. The detection of Earth-like planets around other stars is an exciting long-range goal

for 21 st -century astronomy. Photo credit: NASA.

Printed on acid-free paper

AlI Rights Reserved @1997 Springer Science+Business Media New York

Originally published by Kluwer Academic Publishers, New York in 1997 Softcover reprint ofthe hardcover lst edition 1997

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,

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TABLE OF CONTENTS

J.M. SHULL, H.A. THRONSON, Jr. and S.A. STERN / Preface 1

J.P. KASTING / Planetary Atmosphere Evolution: Do Other Habitable Planets Exist and Can we Detect Them? 3

G.W. WETHERILL / Ways that Our Solar System Helps Us Understand the Formation of Other Planetary Systems and Ways that it Doesn't 25

1. SCHNEIDER / Photometric Search for Extrasolar Planets 35 w.n. COCHRAN and A.P. HATZES / Radial Velocity Searches for Other

Planetary Systems: Current Status and Future Prospects 43

P. CaNNES, M. MARTIC and J. SCHMITT / Demonstration of Photon-Noise Limit in Stellar Radial Velocities 61

H.A. McALISTER / Aspects of Astrometric Searches for Other Planetary Systems 77

M. SHAO / Astrometric Detection of Earth-Like Planets with OSI 85

S. CASERTANO, M.G. LATTANZI, M.A.C. PERRYMAN and A. SPAGNA / Astrometry from Space: GAIA and Planet Detection 89

M. SHAO / Ground-Based Interferometry 105

w.J. BORUCKI, E.W. DUNHAM, D.G. KOCH, W.D. COCHRAN, J.D. ROSE, D.K. CULLERS, A. GRANADOS and J.M. JENKINS / FRESIP: A Mission to Determine the Character and Frequency of Extra-Solar Planets Around Solar-Like Stars 111

A. LEGER, J.M. MARIOTTI, B. MENNESSON, M. OLLIVIER, J.L. PUGET, D. ROUAN and J. SCHNEIDER / The Darwin Project 135

P. DASCH / Public Involvement in Extra-Solar Planet Detection 147

Index 155

PREFACE

J. MICHAEL SHl:LLJ , HARLEY A. THRO:\SOX, JR. 2, A:'>D S. ALAN STER:\3

I University of Colorado, Dept. of Astrophysical. Planetary, &. Atmospheric Sciences

2 University of Wyoming and KASA Headquarters, Code SR

3 Southwest Research Institute, Boulder Office

On May 15-17. 1995, three Rocky Motultain research institutions hosted a confererJce to dis­cuss the scientific basis, teclmological options, and programmatic implications of a large-scale effort to find and study Earth-like planets outside the Solar System. Our workshop attracted

scientists, erJgineers, space agency administrators, and the public media to discuss and debate the most promising teclmological options and opportunities. Major programs and proposals to search for and study exo-planets were preserJted and discussed. In addition, our meeting c0-

incided ·with NASA's "roadmap" study for the Exploration of Neighboring Planetary Systems (~"'\PS). Our meeting was the first international confererJce on this subject, affording an op­portunity for several members of this study to participate in the debates over new technologies.

Our meeting proyed to be timely. Shortly thereafter, in late 199·5 and early 1996, two groups of astronomers annotulced the first discoveries of planetary companions to nearby stars. using high-precision radial velocity measuremerJts to detect the gravitational reflex motion of the star. The first three detections include a Jupiter-mass companion to the solar-like star. 51 Pegasi, and two remarkable objects of mass at least 2.3 and 6.5 Jupiter masses arotuld the stars 47 Ursae :Majoris and 70 V"rrginis, respectively. A.s is common "ith new discoveries, many more have followed; extra-solar planets now number at least terJ.

The papers preserJted in this book prmide the currerJt early status of the search for e. .. ctra-solar planets. What sort of objects are we looking for in planetary atmospheres and planetary-system architectures? \\ bat techniques are currerJtly feasible, both from the grotuld and in space? How can interferometers be optimized to di.scern faint planets in the glare of their parerJt stars? We also made an e:x.-plicit effort to include the media at our confererJce, including a panel di.scussion on Progmmmaiic Directions for the Future, recognizing that the public is an essential partner in this effort. The book concludes "ith a cogerJt article on the role of public and media involvement in this quest, an activity likely to be both lerJgthy and expensive.

The papers in this volume just. scratch the surface of the planetary-search technologies that "ill be applied over the coming decade. Most searches "ill invoh'e studies of radial-velocities, photometric variations, and direct imaging. However, the tulbiased distribution of planet masses may first be characterized by grotuld-based monitoring of thousands of stars for gra,itational micro-lensing by planetary systems. lltirnately. imaging and spectroscopy may be done in the infrared, using large interferometers in space. possibly the most promising candidate technique at this time. However, since the most successful techniques cannot easily be predicted for the

Astrophysics and Space Science 241: 1-2, 1996. © 1996 KJuwer Academic Publishers.

2

long-term, the scientific funding agencies should rely on a variety of techniques. And, because the ent.erprise may require a long "attention span", a thirty-year effort by some estimation;;, the public and their go\'ernments should be prepared for a step-by-step approadl with appropriate milestones.

The results of such an enterprise are likely to be both spectacular and profound. The detec­tion and study of Earth-like planets outside our Solar System will be one of the great scientific, technological, and philosophical events of our time. :\0 scientific activity is more likely to cap­ture as strongly the public imagination and support. The outcome, either positive or negative, will have a profound effect upon our understanding of the Universe and our place v.ithin it. Furthermore, the facilities proposed to undertake this program may be eJ..-pected to be powerful general purpose astronomical obsenatories. At the same time, it is possible that no scientific enterprise will be more technically challenging, as it appears that such a program ",ill require sensitive operation of large optical S}'stems in space. \\ ith these motivations. we convened this conference and collaborated to produce this book.

To support this conference, we benefitted from the financial support of our institutions. \\e take this opportunity to thank: the Center for Astrophysics & Space A.stronomy (University of Colorado); the Department of Physics & Astronomy CCniyersity of \Vyoming): and the South­west Research Institute. For help at the meeting, we thank our local organizing committee, particularly Kachun Yu. Janet Shaw provided valuable computer-systems help at \anous stages of the enterprise. We also thank our colleagues at both :\ASA and ESA for their encouragement and tlleir attendance at the meeting. The help of \Yes Huntress (:\A5A) and Serge Volonte (ESA) was especially welcome in setting the visionary tone of our meeting.

Alan and Carole Siern with children

PLANETARY ATMOSPHERE EVOLUTION:

Do Other Habitable Planets Exist and Can We Detect Them?

JAMES F, KASTING Department of Geosciences

Penn State University, University Park, FA 16802

Abstract. The goal of this conference is to consider whether it is possible within the next few decades to detect Earth-like planets around other stars using telescopes or interfer­ometers on the ground or in space, Implicit in the term "Earth-like" is the idea that such planets might be habitable by Earth-like organisms, or that they might actually be inhab­ited. Here, I shall address two questions from the standpoint of planetary atmosphere evolution. First, what are the chances that habitable planets exist around other stars? And, second, if inhabited planets exist, what would be the best way to detect them?

1. Climate stability on the Earth

A planet must satisfy a number of conditions in order to support life as we know it. It must have water, carbon dioxide (for photosynthesis), and other volatile compounds (e.g., ones containing N, P, and S) available at its surface. It must have sufficient mass to hold onto an atmosphere, and it must be in an orbit that is stable over long periods of time. It also needs to have a stable climate that is, at the very minimum, conducive to the continued presence of liquid water. Liquid water is required by all known organisms during at least part of their life cycle and should be considered as a fundamental requirement for life elsewhere. It may be, of course, that some extraterrestrial life form does not require water but, if so, we would have little idea of what to look for or where it might exist. The practical search for habitable planets and for extraterrestrial life should be based on life forms that we know are possible, that is, on organisms that are basically similar to those on Earth.

Climate stability is often taken for granted here on Earth. The geologic record shows that liquid water has existed for at least 3.8 billion years (b.y.) of the Earth's 4.6 b.y. history and that life has been around for at least the last 3.5 b.y (Schopf 1983). But it is not really obvious why this should have been the case. During the last 4.6 b.y., the Sun's luminosity has increased by some 40%, according to stellar evolution models (Fig. 1). This conclusion is considered to be robust because the luminosity increase occurs as a direct consequence ofthe fusion of hydrogen into helium and the attendant increase in the density of the Sun's core. Sagan and Mullen (1972) showed that, all other factors being equal, this change in solar luminosity would imply that

Astrophysics and Space Science 241: 3-24, 1996. © 1996 Kluwer Academic Publishers.

4 JAMES F. KASTING

the mean surface temperature of the Earth was below the freezing point of water prior to about 2 b.y. ago. Their finding is corroborated in Figure 1, which shows calculations of the Earth's effective radiating temperature, Te ,

and mean surface temperature, T s , made with a one-dimensional, radiative­convective climate model (Kasting et al. 1988; Kasting and Toon 1989). Te is calculated from the energy balance relation,

4 S O"Te = "4 (1 - A) , (1)

where S is the solar flux at Earth's orbit, A is the planetary albedo, and 0" is the Stefan-Boltzmann constant. Ts is computed under the assumption that the atmospheric C02 concentration remained constant at 350 parts per million and that the tropospheric relative humidity remained constant as well. The difference between Te and Ts represents the greenhouse effect, the magnitude of which increases with time because of an increase in the absolute abundance of water vapor.

Of course, no one really believes that Figure 1 represents the actual cli­mate evolution of the Earth. The fact that liquid water was present from very early on indicates that either the Earth's albedo was lower in the past or its atmospheric greenhouse effect was larger. The modern planetary albedo is about 0.3. Lower values are possible in the past if cloud cover was signifi­cantly reduced (Henderson-Sellers 1979; Rossow et al. 1982). However, this effect would likely have been compensated by an increase in surface albedo caused by ice and snow, unless other warming mechanisms existed (Kasting et al. 1984; Kasting 1989). A larger greenhouse effect is a more plausible solution. Sagan and Mullen (1972) suggested that higher concentrations of ammonia might have provided the necessary warming. This is now consid­ered unlikely because ammonia should have been rapidly photolyzed to N 2 and H2 (Kuhn and Atreya 1979; Kasting 1982). Methane is another possible early greenhouse gas (Kiehl and Dickinson 1987). However, its sources today are almost entirely biological; hence, it is unlikely to have been present at high concentrations on the prebiotic Earth, although it may have contribut­ed to the greenhouse effect during the late Archean, around 2.5 b.y. ago (Rye et al. 1995). The best candidate, though (for reasons described below), is C02, which could have kept global surface temperatures above freezing if it was present at levels of a few tenths of a bar, or about 1000 times its present concentration (Owen et al. 1979; Kasting et al. 1984).

Could atmospheric C02 concentrations have actually been 1000 times higher in the past? Although this may sound like a large amount, it is small compared to the "-' 60 bars of C02 tied up in carbonate rocks in the Earth's crust. This carbon interconverts with atmospheric C02 on time scales of mil­lions of years by way of the carbonate-silicate cycle (Fig. 2). Atmospheric C02 dissolves in rainwater, and the resulting weak acid dissolves silicate

PLANETARY ATMOSPHERE HABITABILITY

300r---,--------.---------r--------.-------~

:::.:::

5

.... c: Q) VI Q) L. c..

Q) 275 L.

Freezing Point of Water .9 o ....

::l ... <tI I. Q)

(!)

.~ .... <tI

Co E

Q) a:

~ 250 .8

L...--....J4~---~3-----2l::----......L..----""""'-O·7

Billions of Years Before Present

~ VI o J: E ::s ...J L. <tI '0 (J)

Figure 1. Diagram (Kasting and Toon 1989) illustrating the faint young Sun problem for Earth. Solid curve is solar luminosity relative to today's value, as calculated by Gough (1981). Dashed curves represent effective radiating temperature, Te , and mean global surface temperature, T" as calculated by a one-dimensional climate model, assuming constant atmospheric CO2 fixed relative humidity, and no cloud feedback.

rocks on land. The bypro ducts of silicate weathering, which include calci­um ions (Ca++), bicarbonate ions (HC03), and dissolved silica (Si02), are taken up by streams and rivers and carried to the ocean. There, organisms use them to make shells of calcium carbonate (CaC03). Other organisms make shells out of silica. When the organisms die, they settle into the deep ocean, and some of their shells are preserved as carbonate and opal (sili­ca) sediments on the seafloor. The seafloor, however, is not static; it slowly spreads out from the mid-ocean ridge spreading centers as part of the global plate tectonic cycle. At certain plate boundaries, the seafloor is subducted, and its carbonate-rich sediment load is carried downwards with it. The high temperatures and pressures encountered at depth cause calcium carbonate and silica to recombine into silicate minerals, releasing C02 in the process. This C02 eventually makes its way back to the surface and is released into the atmosphere by volcanos, completing the cycle.

6

land

Ca5103 + 2 CO2 +H20 weathering Ca++ + 2 HCOi + si02

JAMES F. KASTING

THE CARBONATE-SILICATE CYCLE

Ocean

Ca+++2 HCOi

- + CaC03 t CO2 + H20

CaC03 + 5102 melamorphlsm Ca5103 + CO2 ..

Figure 2. Schematic diagram of the carbonate-silicate cycle, which controls atmospheric C02 concentrations over time scales in excess of one million years.

The carbonate-silicate cycle just described provides a natural explanation for why atmospheric C02 levels should have been higher in the past (Walker et al. 1981). If the early Earth actually had been frozen as a result oflow solar luminosity, silicate weathering would have ceased and volcanic C02 would accumulated in the atmosphere. Eventually, the greenhouse effect would have become large enough to melt the ice, restoring the normal hydrologic cycle of evaporation and precipitation, and allowing silicate weathering to proceed. Conversely, if the Earth were to become significantly warmer, the rate of silicate weathering would increase, atmospheric C02 levels would fall, and the climate would begin to cool. So, a planet like Earth that has a large carbonate rock reservoir and an active plate tectonic cycle also has a built-in negative feedback system that tends to stabilize its climate within the liquid water regime.

If one accepts the argument given above, one may then invert the logic of the faint young Sun paradox and use the predicted variation in solar lumi­nosity, along with known climatic constraints, to estimate the atmospheric C02 concentration at different times in the Earth's history (Fig. 3). The

PLANETARY ATMOSPHERE HABITABILITY

10 :-0. ::::::::~: .:

: : :

: : : : :

:

I

30% Solar flux .reduction (ODC)

10.J

10-4 4.5 3.5

,=> earth

~:,.

::::~ Huronian glaciation (5-20°C)

..ate Precambrian

1~-20 DC)

~~"

;§ "i

Terrestrial -: . C3 photosynthesis

~~'

2.5 1.5 0.5

lime before present (Ga)

7

103 :J ~ -c 0

10 2 .~

'E fl c 0 ()

10' .. 0 ()

::::v

Figure 3. Atmospheric CO2 concentrations required to offset decreased solar luminosity in the past (Kasting 1992). The vertical bars represent periods of glaciation. The arrow near 0.4 Ga marks the lower limit of CO2 for C3 photosynthesis (about 150 ppm).

shaded area on the graph represents the range of atmospheric C02 concen­trations that are consistent with the geologic record (Kasting 1987; Kasting 1993). The vertical bars at 2.5 b.y. ago and 0.65 b.y. ago represent periods of glaciation. During these times the C02 concentration could neither have been too low (because the oceans would have frozen) nor too high (because the glaciers wouldn't have existed). The suggested upper limit on atmo­spheric C02 at 4.5 b.y. ago is 10 bars. This value comes from considering the nature of the carbon cycle on a hypothetical ocean-covered early Earth (Walker 1985). Much of Earth's carbon could have been in the atmosphere in this case because silicate weathering would have been inhibited by the absence of exposed land surfaces and because the planet would have lacked stable continental platforms on which to store carbonate rocks. The mean surface temperature of a primitive Earth with a 10-bar C02 atmosphere has been calculated to be about 85°C (Kasting and Ackerman 1986). On the other hand, if weathering of impact debris removed significant amounts of C02 (Koster van Groos 1988), then the early atmosphere could have been

8 JAMES F. KASTING

much thinner and cooler. We don't really know whether the early Earth was hot or cold.

2. Limits on climate stability: Habitable zone around the Sun

The negative feedback mechanism described above may have stabilized the Earth's long-term climate but it does not operate on all planets. One has only to look at Venus and Mars to find examples of planets that are either too hot or too cold to support either liquid water or life. Venus' mean surface temperature is Ts ~ 730 K, whereas Ts ~ 218 K on Mars. The reasons why these planets failed to remain habitable are understood in general terms, if not in detail.

Let us first consider Venus and ask what went wrong in this case. Venus may well have been much more Earth-like in the distant past, perhaps even to the point of having liquid water flowing on its surface (Kasting 1988). Although some early models of planetary formation suggested that Venus might have formed dry because of its more interior position in the solar nebula (cf., Lewis and Prinn 1984), this now seems unlikely for several rea­sons. First, modern theories of planetary formation (e.g., Wetherill 1985, 1986) suggest that there was significant mixing between different zones of accretion, so some planetesimals formed near Earth's orbit should have been incorporated into the growing Venus. Furthermore, many of Earth's volatiles may have been supplied by cometary bombardment between 4.5 and 3.8 b.y. ago (Oro 1961; Chyba 1987, 1989; Owen et al. 1992). If so, Venus would almost certainly have been veneered with volatiles at the same time. (The same argument applies, although less compellingly, if the volatiles were brought in by rocky planetesimals from the asteroid belt region.) Additional evidence for the presence of water on early Venus is provided by the high D jH ratio in the Venusian atmosphere, which is about 150 times that of Earth's oceans (Donahue and Hodges 1992, and references therein). After years of debate concerning the significance of this measurement (Donahue et al. 1982; Grinspoon 1987, 1993), it has finally been demonstrated that this requires a high water abundance on early Venus (Gurwell 1995). (The high D jH ratio results from preferential loss of H compared to D from the top of the planet's atmosphere. Gurwell showed that a high initial water abundance is required even in the presence of continued input of water from impacting comets.)

If Venus did have a lot of water at one time, where did it all go? The favored answer is that it was lost because of the development of either a "runaway" or "moist" greenhouse (Kasting 1988 and references therein). A moist greenhouse differs from a runaway greenhouse in that liquid water is present at the planet's surface during the time that water is lost. Both

PLANETARY ATMOSPHERE HABITABILITY

l~r-~~--r-~~--r--'~--'--r-.r-o

1600

~ 1400 G

5 1200 iii ; 1000 Q.

E

Stratospheric,,.------- ----------------- 1

H20 "/'

c CD

C o u ...

I

: Critical : point

o 0-m

10-2 > .. 41

.! 800 G U 600 ~

~(oceans " evaporate)

iii ~

10--4 .g ... ~ 400

,,' Ts .. ' ---- Eany Present earth Venus , 200

41 ~ a.

Present ~ venus 10-6 ~

, en O~~~--~~--~~~--~~--~~~ .S 1.0 1.2 1.4 1.8 2.0

Solar constant relative to present earth

9

Figure 4. Diagram illustrating the "moist" and "runaway" greenhouse effects, adapted from Kasting (1988). The solid curve represents mean global surface temperature as a function of solar flux. A I-bar, N2 - 02 atmosphere is assumed. The dashed curve shows the stratospheric H20 mixing ratio. The oceans are lost for 8/80 > 1.1.

models have wet stratospheres, which allow hydrogen to escape rapidly to space. These concepts are illustrated in Figure 4, which shows what would happen if one were to move the Earth closer to the Sun. As the solar flux, 5, hitting the top of the atmosphere increased relative to its current value, 50, Ts would increase slowly at first, and then very rapidly at 5/50 ~ 1.4 (solid curve). For 5/50 > 1.4, the Earth would be in a runaway greenhouse state, that is, the oceans would vaporize entirely and Ts would rise to '" 1500 K, or even higher if additional sources of opacity were present. Ts is unlikely to have exceeded 1700 K, however, because the surface would have melted and water would have dissolved in the magma. Once the oceans had vaporized, the water would be lost as a consequence of photodissociation followed by escape of hydrogen. The oxygen left behind would eventually react with reduced minerals on the surface and with reduced volcanic gases.

If one were to move the Earth inwards more slowly, something slightly different would occur. The increasing surface temperature would cause a modest increase in the water vapor abundance in the lower atmosphere and a huge increase in water vapor in the stratosphere (dashed curve). Indeed, the stratosphere would become water-dominated for 5/50 > 1.1. This is the moist greenhouse. Water would be lost in the same manner as described above, but the ocean would still be present until near the end of this pro­cess. It should be noted that the quoted solar flux limits assume zero cloud feedback. Negative cloud feedback, which is quite plausible, could cause the

10 JAMES F. KASTING

moist greenhouse and runaway greenhouse limits to occur at higher solar fluxes.

The calculations shown in Figure 4 can be used to define the inner edge of "the habitable zone (HZ) for our present Solar System. A conservative (pessimistic) estimate is that Earth would become uninhabitable if the solar flux were to increase by 10%. The solar flux falls off as the inverse square of the distance from the Sun, so a conservative distance estimate for the inner edge of the HZ is rv 0.95 AU. This is the same inner-edge position as determined in an earlier study by Hart (1978), but it occurs for a different reason. (Hart's model predicted that a runaway greenhouse would develop at this distance.) Note that a moist greenhouse planet would not become uninhabitable immediately; rather, it would do so on the time scale for hydrogen loss, which is several hundred million years at current rates of solar EUV output (Kasting and Pollack 1983).

The outer edge of the HZ is somewhat trickier to calculate because the reasoning is more complicated. We argued earlier that atmospheric ·C02

should accumulate as a planet's surface temperature falls. So, if one were to move the Earth farther away from the Sun, the C02 concentration ought to rise in such a manner as to compensate for the decrease in the incident solar flux. This reasoning led Kasting et al. (1988) to conclude that the outer edge of the HZ might be determined by orbital stability: a planet could not remain habitable for very long if it were too close to the orbit of Jupiter. But they overlooked the fact that, if the atmosphere becomes too cold, C02 will start to condense and form clouds. This should have two principal effects on climate (Kasting 1991): (1) the planetary albedo should increase; and (2) the tropospheric lapse rate should decrease in the region where the clouds are forming. (High, cold C02 ice clouds might also contribute to the greenhouse effect, as do cirrus clouds on Earth, but the amount of warming is expected to be minimal because C02 ice is a poor absorber of infrared radiation except near 15 /Lm.) The albedo change is difficult to calculate quantitatively because it depends on such factors as fractional cloud cover, cloud thickness, and cloud optical properties, none of which can be determined by a one-dimensional climate model. Indeed, it is difficult to determine these factors in a three-dimensional model! The second effect, however, can be simply parameterized by assuming that the lapse rate follows a moist adiabat. The heat given off by condensing C02 causes the lapse rate to be shallower than it would be in the absence of condensation. A similar change in lapse rate occurs on Earth because of the condensation of water vapor.

When the lapse rate change caused by C02 condensation is included in a one-dimensional climate model, the magnitude of the greenhouse effect is reduced in some circumstances. This effect is illustrated in Figure 5, which shows Ts for Mars as a function of surface pressure and solar luminosity. The

.--.. :.::G '-"

I:J::l 0::: ;:J 260 E-< < 0:: I:J::l 0... ;::g I:J::l E-<

I:J::l 220 u

< ~ 0::: :::> \.Zl

180 0.001

PLANETARY ATMOSPHERE HABITABILITY

S/So = 1

0.8

-----------~ ",/

========-=--_ _________ 0 0 .. 7:'/ ./

0.01

Saturation,...-''''-

0.1

" .... , ....

SURFACE PRESSURE (bar)

11

10

Figure 5. Mean global surface temperature for Mars (Kasting 1991) as a function of surface pressure and relative solar luminosity, 5150. Here, So represents the present solar flux at Mars' orbit, 343 W 1m2 • Dashed curve shows saturation vapor pressure for CO2 .

atmosphere is assumed to consist entirely of C02 and H20. For S / So = 1, the effects of C02 condensation are minimal: Ts increases monotonically as the surface pressure is increased. At low solar luminosities, however, there are limits on both the amount of C02 that can exist in the atmosphere and the maximum surface temperature that can be reached. The maximum value of Ts is 0 DC for S / So ~ 0.85. This creates a problem in explaining the apparent climatic warmth of early Mars because the Sun should not have reached this luminosity until about 2 b.y. ago (Gough 1981), whereas the climate appears to have been warm prior to 3.8 b.y. ago. Squyres and Kasting (1994) offered some suggestions on how to resolve this dilemma. At least some of the surface features indicative of running water (the valley networks) may have been formed using geothermal heat to keep water in the liquid state.

This same process of C02 condensation can be used to define the out­er edge of the habitable zone. For an Earth-like planet, the "maximum greenhouse" limit (that is, the limit just described for Mars) occurs at

12 JAMES F. KASTING

S/So = 0.36, which corresponds to an orbital distance of 1.67 AU. This limit is not firm, however, because we neglected the effect of the C02 clouds on the planet's albedo. A more conservative approach is to define the outer edge of the HZ as the point where CO 2 condensation begins, which is at S/So = 0.53 or 1.37 AU. Thus, a minimum estimate for the width of the present HZ is 1.37 AU - 0.95 AU or '" 004 AU. Preliminary calculations (not yet published) with a latitudinally-resolved, energy balance climate model indicate that C02 cloud cover becomes ubiquitous at orbital distances just over 104 AU, so the conservative approach appears justified. On the other hand, the possible presence of reduced greenhouse gases in a planet's atmo­sphere could extend the habitable zone outwards, at least during the early part of a planet's history. Perhaps this could explain the climate of early Mars (Sagan and Chyba 1991). But it would not be wise to count on the presence of reduced greenhouse gases in defining the habitable zone, because they should largely disappear once a planet's atmosphere becomes 02-rich.

3. Continuously Habitable Zone around Sun and other Stars

The position of the HZ is defined for only a single instant in time. As the Sun's luminosity increases, the boundaries of the HZ should shift outward. Following Hart (1978), we define the continuously habitable zone, or CHZ, as the portion of the HZ that remains habitable over some finite time interval, b.t. If we take b.t = 4.6 b.y., then the conservatively estimated CHZ for our own Solar System extends from 0.95 AU to 1.15 AU. (An optimist would take Venus and Mars as defining the boundaries, in which case the CHZ would extend from 0.72 AU to 1.52 AU.) The inner edge of the CHZ is the same as that of the present HZ because the Sun is now brighter than it was earlier in its history. The outer edge of the CHZ is derived by dividing the current value of S/So (0.53) at the outer edge of the HZ by 0.7 (the relative solar luminosity 4.6 b.y. ago) and then applying the inverse square law. Our minimum estimate for the width of the 4.6-b.y. CHZ is 0.2 AU, or about 3 times the width estimate by Hart (1978). Although this may sound relatively narrow, one should remember that this estimate is extremely conservative, so the actual CHZ could be significantly wider. One should also bear in mind that the mean planetary spacing in the inner Solar System is about 004 AU. If planets exist around other solar-type stars, and if their spacing is similar, the chances of finding a planet within the 4.6-b.y. CHZ is roughly 0.2 AU /004 AU or 50%.

How do these numbers change for stars that are different from the Sun? Calculations bearing on this question are described by Kasting et al. (1993a). The results are summarized in Figure 6, which shows the instantaneous HZ for various stars at the time when they first arrive on the main sequence. The

PLANETARY ATMOSPHERE HABITABILITY 13

spacing of planets in our own Solar System is shown for comparison. The climatically-defined HZs of different stars have roughly the same apparent width if distances are expressed on a logarithmic scale. So, if planets around other stars are spaced logarithmically, as in our Solar System, the chances of finding one within the HZ should be roughly the same, about 50%. Although the problem of planetary spacing is far from resolved, orbital stability con­siderations (Lissauer 1995) suggest that this assumption is reasonable. The three-planet pulsar system (Wolszczan 1994) does not exhibit logarithmic spacing, but it would be a mistake to make too much of this. The innermost planet is much smaller than the other two, and three planets are, in any case, not enough to allow one to draw useful conclusions about planetary spacing.

The fact that different stars have HZs of comparable logarithmic width does not mean, however, that all stars have equal potential for harboring inhabited planets. Stars much more massive than the Sun evolve very rapidly and live out their main sequence lifetimes quickly. Thus, while their HZs may be quite wide, their CHZs are relatively narrow or, to express it another way, relatively short-lived. Such early type stars also emit large amounts of UV radiation and have strong winds (high mass-loss rates) that may inhibit planetary formation. Recent calculations (Sheldon 1995; Kasting et al. 1996) indicate that the high UV fluxes might be offset by the development of an extra-thick ozone screen on planets orbiting such stars.

Stars much less massive than the Sun are not likely to harbor habitable planets because their HZs lie within the tidal-lock radius (Fig. 6), which means that their potentially habitable planets are likely to develop syn­chronous rotation. The tidal-lock radius is proportional to MI/3, where M is the stellar mass; the HZ boundaries vary approximately as M 2 .25 (because low-mass stellar luminosity varies as M 4.5 for stars of type between about FO and K5.) Synchronous rotation is a potentially fatal problem for planetary habitability because a planet's entire atmosphere, or at least its H20 and C02 could condense to form a large ice cap on the dark side. Such a disaster does not necessarily have to occur; if the planet's atmosphere is sufficiently dense, enough heat might be transported to the dark side to keep it warm. (Venus is a good example: although its day length is very long, 117 Earth days, its surface temperature varies by less than a degree from the dayside to the nightside.) It is not clear, however, that such a dense atmosphere is compatible with habitability. A second way in which planets might avoid the tidal locking problem is by becoming trapped in various orbital resonances, such as the 3:2 spin-orbit resonance that prevents Mercury from rotating synchronously.

14 JAMES Fo KASTING

10

A /

:::::::r: ...•... G. // ....

K / / SOLAR SYSTEM /

M / /

-------<:) 0.1 HZ -7-2 '--" if)

/ /

if) / « /

2 0.01 / / /

/ / ~ TIDAL LOCK RADIUS / /

/ / / /

/ /

0.001 / . / .. • JUPITER SYSTEM

0.001 0.01 0.1 10 100

DISTANCE (AU)

Figure 6. Diagram showing the zero-age-main-sequence habitable zone (Kasting et al. 1993a) for stars of different masses. The Jovian moon system is shown to illustrate that planets might be expected to form within the region bracketed by the dashed lines. The dotted line shows the tidal locking radius.

4. Atmospheric 02 Levels as an Indicator of Life

I shall switch now to my second topic, namely: If inhabited planets exist around other stars, how could we detect them? Note that I have used the word "inhabited", rather than "habitable." We should be able to identify potentially habitable planets simply by finding planets around other stars and determining their orbital distances. If a planet falls within a star's HZ, then it could conceivably be habitable. Of course, to actually be habitable it would have to satisfy various other criteria, some of which were mentioned earlier in this paper. In particular, we would hope to observe traces of H20 and C02 in the planet's atmosphere. This could potentially be done with a space-based interferometer, as discussed by other speakers at this conference (e.g., R. Angel).

But if we could do this much, we could at the same time go a step further and look for life itself. The detection method is the obvious one: Earth-based life creates 02 by the process of photosynthesis. As abiotic

PLANETARY ATMOSPHERE HABITABILITY 15

sources of 02 are generally small, detection of 02 in an extrasolar planet's atmosphere would be strong evidence for life. Owen (1980) suggested that 02 could be identified spectroscopically by looking for its A-band absorption at 0.76 j.Lm. As discussed elsewhere in this volume (see also Leger et al. 1993), this might be difficult to do in practice because planets are very dim at this wavelength compared to their host stars. However, 02 is acted upon photochemically to produce ozone (03), and ozone should be readily observable spectroscopically (see below). Before accepting such a detection as evidence for life, however, we would need to know how much 02 and 03 could be produced by abiotic processes. A brief discussion of this question follows.

The topic of abiotic 02 concentrations has been studied extensively in relation to the problem of the origin and early evolution of life on Earth. Although work on this problem dates back to the early 1960's, the prob­lem was first formulated correctly by Walker (1977), who realized that the hydrogen released by volcanism and by water vapor photolysis must be bal­anced by escape of hydrogen to space. The hydrogen escape rate, in turn, is limited by the rate at which hydrogen can diffuse upwards through the atmosphere (Hunten 1973). Hydrogen escape can also be bottled up at the escape level, or exobase, but this can only slow the escape rate below the diffusion-limited value. Because some of the escaping hydrogen is produced by H20 photolysis, oxygen is generated by this process.

The amount of 02 that could be produced abiotically can be estimat­ed using a one-dimensional photochemical model (cf., Kasting et al. 1979; Kasting et al. 1984). An up-to-date discussion of this problem is given by Kasting (1993). There, the problem of balancing the atmospheric hydrogen budget is reviewed, and it is pointed out that rainout of reduced and oxi­dized gases should be taken into account. Lightning-induced decomposition of C02 is also a potentially important source of 02 at low altitudes in such atmospheres.

Typical results from such a photochemical model calculation are shown in Figure 7. The results shown are for a 1-bar atmosphere with a C02 mixing ratio of 0.3. (The term "mixing ratio" has the same meaning as "mole fraction.") The calculated 02 mixing ratio peaks at about 50 km at a value of just under 10-3, or 0.1% by volume. This high-altitude peak is produced by photolysis of C02 followed by recombination of 0 atoms with each other and with OH to form 02

O+O+M ~ 02+M

O+OH ~ 02+H

(2) (3)

The "M" represents a catalytic third molecule, needed to conserve ener­gy and momentum. The hydroxyl radical, OH, comes from photolysis of H20. The 02 concentration decreases rapidly towards the surface as a con-

16 JAMES F. KASTING

60

50

E 40 -" w'

-§bo l-t: ...I « 20

10

0 10-9 10-8 10-7 10-6 10-5 10-4 10-3

VOLUME MIXING RATIO

Figure 7. Concentrations of various gases for a typical, abiotic early Earth model atmo­sphere (Kasting et al. 1984). The assumed surface pressure was 1 bar and the CO2 mixing ratio was 0.3. The bulk of the atmosphere was assumed to consist of N2.

sequence of reaction with reduced volcanic gases, catalyzed by radical species produced by H20 photolysis. Also shown in Figure 7 is a thin ozone layer formed between 30 km and 60 km. The total column depth of this layer is 7 X 1014 molecules cm -2, which is about 0.01% of the present globally­averaged value (0.32 atm cm or 8.6 X 1018 cm-2).

How robust is the conclusion that atmospheric 02 concentrations should be low for a lifeless planet? For Earth, our confidence in this conclusion is quite high. The reason is two-fold. First, the stratosphere is cold and dry, so that photolysis of H20 followed by hydrogen escape represents only a small source of oxygen, less than 1 % of the amount produced by photosyn­thesis followed by organic carbon burial. The same should have been true of the early Earth, even if it had a dense, C02 atmosphere like the one described above (Kasting and Ackerman, 1986). Second, the Earth has a relatively large internal heat source, which drives a vigorous plate tectonic cycle and causes extensive outgassing of reduced gases such as H2 and CO. The volcanic source of reduced gases should have been even larger in the past as a consequence of a higher geothermal heat flux and, possibly, a more reduced upper mantle (Kasting et al. 1993b). Higher solar UV fluxes in the past could have enhanced the 02 concentration in the upper atmosphere, but they should have had little effect on ground-level 02 concentrations (Canuto et al. 1982, 1983; Kasting et al. 1984; Kasting 1985).

Abiotically-produced 02 concentrations could be much higher on plan­ets for which the preceding criteria do not apply. For example, a Venus-like

PLANETARY ATMOSPHERE HABITABILITY 17

planet could build up a transient 02-rich atmosphere as a consequence of rapid water loss and hydrogen escape. 02 partial pressures of tens or hun­dreds of bars are theoretically possible in this case. (The partial pressure of a fully vaporized terrestrial ocean is 270 bars, 240 of which come from oxygen.) Such a planet should be readily identifiable by its position inside the inner edge of the star's HZ. In our own Solar System, Mars has a moder­ately 02-rich atmosphere (0.1% by volume) because it lacks volcanism and because it has a cold, dry surface that is not conducive to weathering. Calcu­lations by Rosenqvist and Chassefiere (1995) suggest that Mars-like planets with C02 - H20 atmospheres should be limited to less than 10 mbars of abiotically-produced 02. As discussed elsewhere (Kasting 1995), their cal­culation is limited to Mars-like planets because it neglects volcanism and weathering. Note that this limit is significantly higher than the upper limit on p02 for an abiotic Earth.

A general conclusion is that abiotic atmospheric O2 levels should be low except in certain pathological situations that can probably be identified on the basis of a planet's location within the HZ and on its size. If high levels of 02 were detected on an extrasolar planet, we would certainly want to investigate these possibilities, but we ought to be able to decide whether any of these pathological situations apply.

An alternative way of confirming a biological origin for 02, originally suggested by Lovelock (1965, 1978), would be to look for the simultaneous presence of a reduced gas such as methane or nitrous oxide. The (highly dise­quilibrium) coexistence of CH4, N20, and 02 in Earth's atmosphere is strong evidence for the presence of life. The main problem with this suggestion is that remote detection of CH4 and N20 in an oxygenic atmosphere would be difficult. The CH4 concentration in Earth's lower atmosphere is only about 1.7 ppm; N20 is even less abundant, rv 0.3 ppm. The concentrations of both gases decrease rapidly with altitude in the stratosphere; thus, their spectral signatures as observed from space are relatively faint. Both of these gases were actually observed by the near-infrared mapping spectrometer (NIMS) aboard the Galileo spacecraft, when it flew by Earth in December 1990, and this observation was hailed as a test of remote life detection (Sagan et al. 1993). Making these same measurements on an extrasolar planet would be difficult, however, because planets are relatively dim at the wavelengths studied (2 - 5 /Lm) and because the absorption features themselves are nar­row and weak. Thus, while such reduced gases might eventually be observed, this would probably only be done after the presence of 02 itself had already been confirmed.

Before leaving this section, it should be noted that the absence of 02 from a planet's atmosphere does not necessarily imply that the planet is unin­habited. Earth's atmosphere was 02-free until about 2 b.y. ago, although life, probably even photosynthetic life, has been around for at least 3.5 b.y.

18 JAMES F. KASTING

0.20

-~ 'E 0.16

t.> "-~

300K

'" '" 'E 0.12

~

'" 0.08 t.> t::

.!:! l:l t:l 0.04 0::

0 0 1800 2000

Wavenumber (em-I)

I I aJ 50 20 12.5 10 8 5

Wavelength (pm)

Figure 8. Outgoing infrared fluxes measured from Earth orbit by Nimbus-7 satellite (Liou 1992). Strong absorption features at 15 pm and 9.6 pm are caused by C02 and 0 3

respectively. Thinner curves show blackbody emission functions at different temperatures.

(Schopf 1983). Various mechanisms, perhaps the release of excess H2 and CO from a more highly reduced upper mantle (Kasting et al. 1993b), kept atmospheric 02 concentrations suppressed for more than 1.5 b.y. after life originated. Earth's atmosphere during that time may have contained vari­ous reduced gases (CH4, COS?) produced by biological activity, and these gases could potentially be identified by their spectral signatures. However, reduced gases can also be produced by volcanic activity, so the implications of such a detection would be more ambiguous than would the detection of 02. (Methane does not come out of volcanos today, but it might have been released by submarine volcanism in the past, particularly if the mantle was originally more reduced.)

5. The relationship between Atmospheric Oxygen and Ozone

Even though atmospheric 02 may be diagnostic of life, we would probably not want to look for 02 directly. For reasons discussed elsewhere in this volume, spectroscopic investigation of extrasolar planets is best carried out at infrared wavelengths where 02 does not absorb. An 02-rich atmosphere should contain ozone, however, and ozone has a strong characteristic spectral signature in the thermal infrared (Fig. 8). The 03 9.6 J.lm band is, along with the C02 15 J.lm band, one of the two most readily identifiable features in the IR emission spectrum of the Earth. As such, it should be possible to detect

PLANETARY ATMOSPHERE HABITABILITY 19

this feature in the spectrum of an Earth-like planet using a space-based interferometer/spectrometer of modest resolution. Leger et al. (1993) have already made the case that this is the best method by which to proceed in the search for extrasolar life.

How would the strength of the 03 9.6 pm absorption band depend on the atmospheric 02 concentration? This question has not been addressed, but

it would make a worthy topic of investigation. The depth and shape of the band should depend on the vertical distribution of atmospheric 03 and on the vertical temperature structure of the atmosphere. The temperature and ozone concentration are interdependent, so one would need to do a coupled photochemical/radiative-convective climate model calculation to find the answer.

The first part of this problem, namely, the dependence of ozone on the atmospheric 02 level, has been studied by numerous investigators (e.g., Rat­ner and Walker 1972; Levine et al. 1979; Kasting and Donahue 1980, and references therein; Leger et al. 1993). Figures 9 and 10 from Kasting et al. (1985) represent perhaps the most detailed such calculation. Figure 9 shows 03 vertical profiles for 02 levels of 10-5 to 1 PAL. ("PAL" means "times the present atmospheric level.") As one might expect, the ozone layer moves downwards and thins as the 02 abundance decreases. Ozone column depths corresponding to these profiles are shown in Figure 10. The surprising result of the calculation is the extremely weak dependence of 03 column depth on 02 for oxygen levels near the present value. This behavior, which was anticipated earlier by Ratner and Walker (1972), is a consequence of the pressure dependence of the ozone formation reaction

(4)

Low atmospheric 02 levels allow dissociating UV radiation to penetrate deeper into the atmosphere where the abundance of third-body molecules, M, is higher. Hence, 03 concentrations do not decrease as rapidly with decreasing O2 as one might otherwise expect.

6. Conclusion

In this paper, I have argued that habitable planets ought to be relatively abundant around stars in the spectral range FO to K5, provided of course that extrasolar planets do exist. The basic reason for optimism is that one can identify a powerful feedback mechanism, namely, the carbonate-silicate cycle and its effect on atmospheric C02 that ought to stabilize climate both on the Earth and on other Earth-like planets. This cycle should operate on any planet that has abundant water and carbon present on its surface and that is big enough, or young enough, to have active plate tectonics or some equivalent mechanism for recycling carbonate rocks.

20 JAMES F. KASTING

60

50

02 = 1 PAL

40

E "'" w' 0 :::) 30 I-;:: ...J <i

20

10

0 106 107 109 1010

03 DENSITY. cm-3

Figure 9. Ozone number density profiles as a function of atmospheric O2 level, as calcu­lated by Kasting et al. (1985).

Limits on the width of the habitable zone around various types of stars can be derived using one-dimensional climate models. These limits are not robust because it is difficult to parameterize the effects of clouds; however, one can show that the HZ is reasonably wide even for very conservative assumptions about cloud feedback. The same calculations can be used to determine the width of the CHZ around a star by taking into account the increase in the star's luminosity with time and the corresponding outward drift in the boundaries of the HZ.

The question of whether habitable planets exist around other stars will remain extremely speculative until observational evidence is obtained. The best method of addressing this question would be to construct a space-based interferometer/spectrometer that could obtain an infrared spectrum of an extrasolar planet. The presence of a well-developed absorption feature near 9.6 11m would indicate the presence of 03 and 02 and would, in most cases, be strong indirect evidence for the existence of extraterrestrial life.

PLANETARY ATMOSPHERE HABITABILITY

1020 ,-----,-----,-----,------,-----,-----,

i i

i

i

;" i

i

./ I

-- STANDARD MODEL --- KASTING AND DONAHUE (1980) _.- LEVINE et al. (1979)

1014~----~----~----~ ______ ~ ____ _L ____ ~

10-5 10-4 10-3 10-2 10-1 ATMOSPHERE OXYGEN, PAL

21

Figure 10. Ozone column depth as function of atmospheric 02 level. The solid curve corresponds to the vertical profiles shown in Fig. 9 (Kasting et al. 1985).

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22 JAMES F. KASTING

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24 JAMES F. KASTING

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George Wetherill

WAYS THAT OUR SOLAR SYSTEM HELPS US UNDERSTAND THE FORMATION OF OTHER PLANETARY

SYSTEMS AND WAYS THAT IT DOESN'T.

GEORGE W. WETHERILL Department of Terrestrial Magnetism Carnegie Institution of Washington

Abstract. Models of planetary formation can be tested by comparison of their ability to predict features of our Solar System in a consistent way, and then extrapolated to other hypothetical planetary systems by different choice of parameters. When this is done, it is found that the resulting systems are insensitive to direct effects of the mass of the star, but do strongly depend on the properties of the disk, principally its surface density. Major uncertainty results from lack of an adequate theoretical model that predicts the existence, size, and distribution of analogs of our Solar System, particularly the gas giants Jupiter and Saturn. Nevertheless, reasons can be found for expecting that planetary systems, including those containing biologically habitable planets similar to Earth, may be abundant in the Galaxy and Universe.

1. Introduction

An important characteristic of a healthy science is the extent to which the­ory, observation, and experiment stimulate and challenge one another. The search for extrasolar planets is now underway. A complementary theoretical component is needed. How much should we be able to predict about what will be found? The simplest, probably the most honest, answer would be simply "not much." I will try and go further than this.

What are the available resources for addressing this problem? First of all, we have the universality of physical laws, the properties of matter and the abundance of the chemical elements. In addition, we do have a large amount of information about our own Solar System, including the detailed meteoritic record of events and conditions early in its history (Kerridge and Matthews 1988). If the Solar System were a randomly chosen sample of one, this would be great. In that case, I would then be very worried about a model for the formation of planetary systems that predicted our Solar System to be an unusual one. Unfortunately, it's not a random sample, but one that is heavily biased toward having characteristics that permit the evolution of organisms that are interested in questions of this kind. Nevertheless, our Solar System is a useful natural laboratory to test theoretical models for internal consistency, which then can to some extent accredit them for use in exploration of the consequences of different initial conditions, and other circumstances, such as the failure of a planetary system to form gas giant analogs of Jupiter and Saturn. Finally, there is a growing body of observational and theoretical

Astrophysics and Space Science 241: 25-34, 1996. © 1996 Kluwer Academic Publishers.

26 GEORGE W. WETHERlLL

astronomical work concerning star and presumably plaent formation that provides a context into which a theory of planetary origin must fit. We are on the threshold of being able to obtain a much less biased sample.

2. Solar System Formation

So, despite the risks, let us start off by assuming our Solar System to be not unusual, and pay the price later for having done such a foolish thing. To what extent can we model Solar System formation? As a start one can assume that it is the end product of the evolution of a centrifugally supported disk of gas and dust and is formed during or shortly after the late stages of growth of our central star, the Sun. The total mass and initial mass distribution is fairly well constrained by the observed Solar System, augmented by the hydrogen and helium that must have originally been present in the disk. This leads to original disk masses of", 2% to '" 10% Me;) (depending on how efficient the planet formation process was, particularly in the outer Solar System). This estimate is neither inconsistent with astronomical theory and observation nor necessarily implied by them (Weidenschilling 1977). It is from this material that planets must form.

Anticipating the subsequent extension of the modelling to other plane­tary systems, it should be pointed out that there are two partners in the planet-forming process, the central star and the disk. They have a symbiotic relationship. The star couldn't shed its angular momentum and become a star if it weren't for the disk, and the disk couldn't exist if it weren't grav­itationally bound to the star. Extrapolation to other systems will require understanding the relative importance of the roles of each of these partners. If we knew that all disks were more or less alike, and similar to the one required to form our Solar System, then the extrapolation to stars of dif­ferent mass would be relatively easy, because the range of stellar masses, luminosities and evolution are rather well understood. Unfortunately, it is most likely that planet formation depends primarily on the very much less well known properties of the disk, and the role of the star is primarily to hold the disk together. For this reason, one should pay close attention to anything that is assumed about the nature of the disk. That's where the trouble is going to come from.

As people are probably tired of hearing me say, there are two ways to make anything: either you start with something big and break it into small­er pieces, or you start with little pieces and put them together to make something larger. Both of these approaches have been used in models of planet formation. For good reasons that I will not get into here, the former approach is not fashionable at present, and this discussion will consider only

OTHER PLANETARY SYSTEMS 27

the latter, in which planets are built from smaller objects, like a house is built from bricks.

At this point a confession must be made, the consequences of which are enormous. It must be explained that we have as yet no adequate model for the formation of the outer Solar System. In the rest of this section, only the formation of the Solar System interior to Jupiter will be considered. The penalty paid for having to do this will be discussed in § 4.

The formation of planets in this inner region is thought to occur in three

reasonably distinct stages:

(1) Non-gravitational coagulation of micron-size grains into successively larger bodies, all the way up to planetesimals rv 1 km in diameter (Wei­dens chilling 1977, Weidenschilling et al. 1989, Cuzzi et al. 1993). Despite serious work on this process, it is still not well understood. If planets are to form from dust grains, this process must have occurred. Furthermore, it must be a robust process, because it occurred over a wide range of thermal, chemical, and physical conditions, especially when the satellite systems of the outer Solar Systems are considered as miniature planetary systems.

(2) Gravitational accumulation of 1 to 10 km bodies in the presence of nebular gas up to bodies in the size range of the moon and Mars ("planetary embryos"). This problem has been treated in some detail by Wetherill and Stewart (1993) and by Weidenschilling and Davis (1995). It is found that runaway growth of these large bodies occurs rapidly (I"V 105 years at 1 AU) by low velocity « 1 km/sec) accumulation of neighboring material. This process scales with heliocentric distance and surface density in an expected and regular way.

(3) Growth of moon to Mars mass planetary embryos into final planetary systems. A large number (rv 500) of Monte Carlo simulations of this process interior to 3.8 AU have been published (Wetherill 1992, 1994). The param­eters used are those appropriate to our Solar System. The most restrictive of these are the assumption of the formation of Jupiter and Saturn in their present orbits (after 5 m.y. and 10 m.y., respectively).

In this work, gravitational perturbations resulting from close encounters are treated by the use of expressions obtained by Opik (1951). In addition, the effects of the Jupiter and Saturn resonances in the asteroid belt are introduced in an approximate way. Jupiter also removes bodies from the system that evolve into orbits with aphelia larger than 4.75 AU.

Despite its undoubtedly oversimplified nature, this model successfully leads to an assemblage of planetary systems of which our Solar System is a

28 GEORGE W. WETHERILL

rather ordinary member in a number of ways (Wetherill 1992). These include:

(1) Spontaneous evolution of the initial specific energy and angular momen­tum of the system into a cluster of final values that include the values of these quantities in our Solar System.

(2) A limited range of final total masses that include that of our Solar System.

(3) Spontaneous clearing of the asteroid belt of original bodies in about 1/2 of the simulations.

(4) The number, size, and position of the final planets.

(5) The eccentricity and inclinations of the final planetary orbits.

(6) Occurrence of giant impacts on the final planets at times and with sizes consistent with the impact theory of lunar origin.

(7) The distribution of the relative velocities of residual "test bodies" placed in the asteroid belt agrees with those observed in the present asteroid belt.

3. Extension of this model to other planetary systems.

In one way, the model described above (Wetherill 1992, 1994) is already a model for the formation of extrasolar planets. Because of the chaotic nature of the gravitational perturbations resulting from close encounters and of the perturbations by Jupiter and Saturn resonances, even when initial conditions are essentially identical, there is a range of final planetary configurations of purely stochastic origin. All of these can be thought of as potential extrasolar systems.

In addition, there will be a huge range of similar systems resulting from initial conditions that differ from those of our Solar System. Let's explore that range a little, and see what can be said about the sensitivity of the final planetary systems to different assumptions and initial conditions.

At first, we will make the assumption that these alternative planetary sys­tems have Jupiters and Saturns just like ours, even though there is observa­tional evidence that this is not always the case (Walker et al. 1995' Cochran and Hatzes 1993; March and Butler 1992). Different assumptions concerning Jupiters and Saturns will be considered later in § 4. All of the calculations

OTHER PLANETARY SYSTEMS 29

that will be mentioned are presented in much more detail elsewhere (Wether-ill 1995). .

In addition to this matter of Jupiter and Saturn, there are several ways in which the initial conditions of other planetary systems differ from ours. Perhaps the simplest but still very interesting one of these is the effect of varying the mass of the central star. .

It's not too hard to guess that the final planet configuration is insensitive to this variation. If one considers an initial surface density distribution of matter, bounded above and below by semimajor axes amax: and arnin, the initial total energy and angular momentum will be completely defined. If a max and amin are in the terrestrial planet region, and the distribution of matter evolves through the three stages of planetary growth described in § 2, both the energy dissipated as collisional heat, and the mass lost from the system will be small. If as a consequence two bodies of equal mass with low eccentricities are formed, equating the initial energy and angular momentum with those of the final bodies leads to a unique solution for the final semimajor axes of the bodies. This is just a matter of solving two algebraic equations with two unknowns. The result will be independent of the stellar mass, because this quantity appears as the same factor on both sides of the expressions equating the initial and final angular momenta and energies. The same is true for any ratio of the masses of the two bodies. With decreasing credibility this reasoning can be extended to more realistic cases in which the initial distribution includes the asteroid belt as well, in which case significant mass and angular momentum are lost from the system. Nonetheless, when the results of much more general calculations for stellar masses of 0.5, 1.0, and 1.5 MG are obtained, it is found that results are very similar (Figure 1).

These figures also show the range of the "habitable zone" of "Earthlike planets" (as defined by Kasting et al. 1993) for the first 109 years of the age of the system. This illustrates what is referred to as the "Goldilocks" problem by Rampino and Caldeira (1994). The planets of small stars tend to be too cold, those of large stars too hot, whereas those of one MG are just right. Actually, for stars as large as 0.5 MG , about 10% of the final bodies may be habitable, and even more if small (rv 1027 g) bodies can retain an atmosphere at this distance from the Sun. Similarly, as seen in Figure Ie, a few habitable planets can be formed in the habitable zones of a 1.5 M0 star. But for larger and smaller stars, habitability is likely to be precarious.

This insensitivity of the result to the stellar mass is a harbinger of things to come. It turns out the characteristics of planetary systems are determined almost entirely by the nature of the disk. Except insofar as there may be a causal or stochastic correlation between the properties of the star and those of the disk, the disk dominates the evolution of the planetary system.

30

20

Ul 15 ::a ~ 0

NO 10

[j) [j)

'" ::a 5

0

20

U1 15

~ 0

" 10 0

::: [j) (f)

~ 5

0 0

GEORGE W. WETHERILL

STELLAR MASS= 1.0 SOLAR MASSES

COMPOSITE OF 23 SIMULATIONS

INNER EDGE=O.45 AU; SURFACE DENSITY OC (l/a)

SURFACE DENSITY (SOLlDS)=6.2 GRAMs/eM'

HZ ,

", "

"

", .... "- . , ..... : .

, ",

0 2 SEMIMAJOR AXIS

STELLAR MASS= 1.5 SOLAR MASSES

COMPOSITE OF 25 SIMULATIONS

Ul ::a ~ 0

" 0

::: [j) [j)

'" ::a

(AU)

20

15

10

5

3

INNER EDGE=0.45 AU; SURFACE DENSITY OC (l/a)

SURFACE DENSITY (SOUDS)=6.2 GRAMS/CM'

, , l ". . ~ .

i; 0° ".,..

,N : ••• :-

, .. ",

:a". of

HZ

2 3 SEMIMAJOR AXIS (AU)

HZ COMPOSITE OF 23 SIMULATIONS

SURFACE DENSITY=6.2 GRAMS/CM'

INNER EDGE=O.45 AU

" J,

" . .. " . . -.. -'

~

: ' .... 2 3

SEMIMAJOR AXIS (AU)

1 --:J

...j ,

1

Figure 1. Distribution of final planets for 23 simulations in which the stellar mass was varied at a constant disk solid matter surface density, equal to that found appropriate for a planetary system resembling our Solar System (Wetherill 1992). The points represent the totality of the bodies larger than 1026g at the end of the simulation. The distribution of planets is similar for all three stellar masses: 1.0 M8 (Fig. la), 0.5 M8 (Fig. Ib), and 1.5 M8 (Fig. lc). The habitable zone (HZ) is centered near the region in which the largest planets are found; for M. = 0.5 M8 , the HZ is interior to the highly populated region. For M. = 1.5 M8 , the habitable zone is exterior to the highly populated zone.

OTHER PLANETARY SYSTEMS 31

Although it may seem surprising, this is likely to be true even for temper­atures in the preplanetary nebula. In the present Solar System, the surface temperatures of the planets are in large measure determined by the solar flux at their heliocentric distance. If this were the case in the presolar disk, the temperatures in the meteorite source regions would be far too low to be com­patible with the meteoritic evidence for thermal fractionation of the moder­ately volatile elements at 1200 - 1400K (Palme and Boynton 1993, Larimer and Wasson 1988). Temperatures calculated for viscous accretion disks are also too low to satisfy these observational constraints (Ruden and Lin 1986, Ruden and Pollack 1991). Sufficiently high temperatures are found for a

disk accretional model dominated by compressional heating (Boss 1995a,b). In this model, the disk temperatures are nearly independent of the stellar mass, but are strongly dependent on the disk mass.

Another way of varying the initial conditions is to assume different surface densities of solid matter in the inner Solar System. It is conceivable, even likely, that in nature there are wide variations in this quantity.

It turns out that when the surface density varies, the number and posi­tion of the final planets is nearly the same, but the mass of the planets is roughly proportional to the surface density. Depending on the unknown frequency of various values of the surface density, it may be expected that there should exist planetary systems in which all the terrestrial planets are the size of Mars or smaller (taking "-' 109 years to grow), or in which ter­restrial planets several times the mass of Earth are expected. Such massive terrestrial planets could provide curious sights to those who will observe extrasolar planets: some relatively small planets with atmospheres of cap­tured gas from the disk, extending further than the distance of the moon, and containing several percent or more of the total planetary mass, as has been proposed for an early Earth entirely formed in the presence of nebular gas (Hayashi et al. 1979).

4. Jupiter, Destroyer of Worlds

In the previous section, the rash assumption was made that extrasolar plan­etary systems had Jupiters and Saturns in the same place as our Solar Sys­tem. There is beginning to be observational evidence against this (Marcy and Butler 1992, Walker et al. 1995, Cochran and Hatzes 1993). Further­more, no dynamical theory seriously predicts that they should be there, even though this may primarily reflect a weakness on the part of the theorists.

When one looks in detail into what is actually going on in the evolution that resulted in the results shown in Figure 1, it turns out that the paucity of large final planets beyond about 1.5 AU is caused by two things:

32 GEORGE W. WETHERILL

40 ...-. en

~ HZ 30

t:l

!;; 0 ....

20 -....; ,. . en . . . " . ,. ~

. .' . . ~.: . . . . . , . . .. . -.- .

10 .' ... . 0

0 1 2 3 4 5 SEMlMAJOR AXIS (AU)

Figure 2. Planetary systems without outer planets. One solar mass central star, solid matter surface density same as Fig. 1.

(1) Planetary embryos in the asteroid belt perturbed one another into a commensurability resonance with Jupiter, or into the Saturn-Jupiter secular resonance V6.

(2) This then caused a chaotic increase in eccentricity that resulted in the body crossing the orbit of Jupiter and being ejected from the Solar System. It is also likely that eccentricities were high enough to cause many of them to fall into the Sun (Farinella et al. 1994).

It then follows that if Jupiter and Saturn were at different heliocentric distances, the resonances would also be in different places and the evolu­tion of the inner Solar System could be quite different. Or if "Jupiter" and "Saturn" were much smaller or non-existent, massive rocky planets could flourish in the desolate region of our Solar System known as the asteroid belt (Figure 2).

5. Where do we go from here?

It is not hard to imagine that, as the competence of theoreticians improves, and cheaper, faster, better computers become available, that models of plan­et formation will evolve that are more or less able to predict the distribution, properties, and general chemical composition of all the planets in extrasolar

OTHER PLANETARY SYSTEMS 33

planetary systems, provided that the initial distribution of dust and gas are known, and the role of the central star in ultimately removing the gas from the system is understood.

But all this won't come about by theory alone. As stated at the out­set, a continuing dialogue must take place between theory, observation, and experiment. "Ground truth" in the form of a gallery of pictures and data of observed extrasolar planetary systems will occupy a central place in this achievement. One day, the outcome of this quest will be summed up in a simple qualitative statement that will be understood by everyone. It may tell us that worlds like ours are nearly as many as stars in the sky, or that they are so rare that we will cherish even more "this fragile Earth, our island home." Or maybe just something somewhere in between.

Acknowledgements

I wish to thank Scheherazade Moghadam Dunlap for her mastery of Kluwer Latex and type-setting of this ms. This work was supported by NASA grants NAGW-3928 and NAGW-1969.

References

Boss, A.P.: 1995a, "Proximity of Jupiter-like planets to low-mass stars." Science 267, pp. 360--362.

Boss, A.P.: 1995b, "Evolution of the Solar Nebula II. Thermal structure during nebula formation". Astrophy. J. 417, pp. 351-367.

Cochran, W.D. and Hatzes, A.P.: 1993, "McDonald Observatory Planetary Search: a high precision stellar radial velocity survey for other planetary systems". In Planets Around Pulsars (J.A. Philips, S.E. Thorsett, and S.R Kulkarni Eds.), Astron. Soc. Pac. Conf. v. 36, pp. 267-274.

Cuzzi, J.N., Dobrolvolskis, A.R, and Champney, J.: 1993, "Particle-gas dynamics in the midplane of a protoplanetary nebula". Icarus 106, pp. 102-134.

Farinella, P, Froeschle, Ch., Froeschle, c., Gonczi, R, Hahn, G., Morbidelli, A., and Valsec­chi, G.B.: 1994, "Asteroids falling into the sun". Nature 371, pp. 314-317.

Hayashi, c., Nakazawa, K. and Mizuno, H.: 1979, "Earth's melting due to the blanketing effect of the primordial dense atmosphere". Earth. Planet. Sci. Let. 43, pp. 22-28.

Kasting, J.F., Whitmire, D.P., and Reynolds, RT.: 1994, "Habitable zones around main sequence stars". Icarus 101, pp, 108-128.

Kerridge, J.F. and Matthews, M.S.: 1988, Meteorites and the Early Solar System, Eds., Univ. of Arizona Press, Tucson.

Larimer, J.W. and Wasson, J.T.: 1988, "Refractory lithophile elements". In Meteorites and the Early Solar system (J.F. Kerridge and M.S. Matthews, Eds.), Univ. of Arizona Press, Tucson.

Marcy, G.W. and Butler, RP.: 1992, "Precision radial velocities with an iodine absorption cell". Publ. Astron. Soc. Pac. 104, pp. 270-277.

Opik, E.J.: 1951, "Collision probabilities with the planets and the distribution of inter­planetary matter". Proc. Roy. Irish Acad. A54, pp. 165-199.

34 GEORGE W. WETHERILL

Palme, H. and Boynton, W.V.: 1993, "Meteoritic constraints on conditions in the Solar Nebula. In Protostars and Planets III (E.H. Levy and J.1. Lunine, EeLs.), Univ. of Arizona Press, Tucson.

Rampino, M.R. and Caldeira, K: 1994, "The Goldilocks Problem: climatic evolution and long-term habitability of terrestrial planets". Am. Rev. Astron. Astrophys. 32, pp. 83-114.

Ruden, S.P. and Lin, D.N.C.: 1986, "The global evolution of the protosolar nebula". Astro­phys. J. 375, pp. 740-760.

Ruden, S.P. and Pollack, J .B.: 1991, "The dynamical evolution of the protosolar nebula". Astrophys. J. 375, pp. 740-760.

Walker, G.A., Walker, A.R., Irwin, A.W., Larson, A.M., Yang, S.L.S., and Richardson, D.: 1995, "Absence of Jupiter - mass comparisons to nearby stars". Icarus 116 pp. 359--375.

Weidenschilling, S.J.: 1977, "Aerodynamics of solid bodies in the solar nebula". Mon. Not. R. Acad. Sci. 180, pp. 57-70.

Weidenschilling, S.J., Donn, B., and Meakin, P.: 1989, "Physics of planetesimal formation". In The Formation and Evolution of Planetary Systems (H.A. Weaver and L. Danly, Eds.), Cambridge Univ. Press, Cambridge.

Weidenschilling, S.J., and Davis, D.R.: 1995, "Multi-zone modelling of planetary accretion: updated results". Lunar and Planetary Sci. XXVI, pp. 1479-1480.

Wetherill, G.W.: 1992, "An alternative model for the formation of the asteroids". Icarus 100, pp. 307-325.

Wetherill, G.W.: 1994, "Provenance of the terrestrial planets". Geochim. et Cosmochim. Acta 58, pp. 4513-4520.

Wetherill, G.W.: 1995, "The formation and habitability of extrasolar planets". Submitted to Icarus.

Wetherill, G.W. and Stewart, G.R.: 1993, "Formation of planetary embryos: Effects of fragmentation, low relative velocity, and independent variation of eccentricity and incli­nation". Icarus 106, pp. 190-209.

Audience at the Boulder meeting

PHOTOMETRIC SEARCH FOR EXTRASOLAR PLANETS

J. SCHNEIDER CNRS, Observatoire de Paris, 92195 Meudon, France

schneider@obspm·fr

Abstract. The searches for extrasolar planetary systems by different methods based on the photometric monitoring of stars are reviewed. The search for extra-solar planets is, more or less consciously, the first step toward the search for other Mlnds in the Universe. A rational approach leads to the search for planets where structures with high complexity can emerge. In absence of any positive indication, it is safer to start this search by looking for planets within the "habitable zone" around main sequence stars where liquid water can be present. Of course, even if this future goal would fail, the detection of terrestrial planets would contribute to the characterization of other planetary systems and would constitute an interesting astrophysical goal by itself.

1. What are we looking for? Inner versus outer planets

In the solar system, there are two types of planets. Inner planets, defined as having a semi-major axis a smaller than ~ 2 AU, are solid and have radii Rp of the order of one Earth radius Rffi. Outer planets, defined as being further away, are much larger (Rp ~ 10Rffi ) and massive (Mp ~ 90Mffi). There must be a correlation between the location of a planet and its size, due to the relation

_ (1 - A)1/4 (R*)1/2 Tp- M xT* X -

v 2 a (1)

giving its temperature Tp as a function of its location and the star's tem­perature T* and radius R*. Indeed, giant planets being mainly made of hydrogen, they would not form if they would be too close from the central star because the hydrogen would be blown up by stellar winds. The habit­able planets zone, defined as having a temperature of about 300 K, lies in the zone of inner planets. Thus if one wants to detect habitable planets, one must be able to detect inner planets. Unfortunately, tradit.ional astromet­ric and spectroscopic methods fail to detect such tiny planets, as has been stressed for instance by the TOPS report (1992). Other methods are more likely to detect Earth-like planets, namely the micro-lensing and the pulsar monitoring (Wolszczan 1994). But, although micro-lensing may possibly be able to detect half a dozen Earths per year (Tytler 1995), one would get only (undoubtly useful) statistical information on the frequency of Earths in the Galaxy and the characteristics of individual planets discovered by this method, being at a distance of several kiloparecs, could not be investigated any further. In particular it would give no information on the atmosphere

Astrophysics and Space Science 241: 35-42, 1996. © 1996 Kluwer Academic Publishers.

36 J. SCHNEIDER

of the planet. In this respect, it is more interesting to search for planets around near-by stars. As for the timing method, for Earth-like planets it works only with pulsars, an environment probably hostile for life (although not completely ruled out as far as only thermal conditions are considered) - see also § 3 below. There are finally space projects based on IR interfer­ometry (Leger et al. 1995a,b) or optical imaging (Schneider 1995), but they are likely to be launched only within a couple of decades. There is then one method left, the ocultation method which can not only detect Earth-like planets, but also gives useful information on the planet in case of success.

2. The occultation method

2.1. GENERALITIES

I focus here on planets having a temperature of about 300 K, named "ter­restrial" planets, irrespective of their distance to the star. From Eq. (1) this gives the following condition on the planet distance to the star:

a - (R*) X (~)2 AU - R0 5770K

(2)

where 5770 K represents the Sun temperature. The detection of a transit requires three conditions:

1. The orbital plane of the planet must be correctly oriented: for random orientations, the geometric probability is

(3)

For a Jupiter around a solar-type star its value is 10-3. Since, in addition, the star must be photometrically monitored over at least one entire orbital revolution of the planet, this makes the occultation method very inconvie­nient for the random search of Jupiters. For an Earth, this probability is 0.5%, rendering the method more attractive since, in addition, the period of orbital revolution being shorter, the rate of events is higher.

2. The duration of the transit for a terrestrial planet is

D = 13 (R* )1/2 X (MM* )-1/2 X T*K hours R0 0 5770

(4)

Around a G-type star the duration is 13 hours. The exposure time must be shorter than this duration.

3. The photometric precision must be better than the depth of the occul­tation.

(5)

PHOTOMETRIC SEARCH FOR EXTRASOLAR PLANETS 37

The measurement of TJ and of the time span between two transits would give the radius and the distance to the star of the planet, and thus indirectly its temperature. For a terrestrial planet around a solar-type star this depth is 10-4. This small number and the rather low probability for a correct geometric orentation given by Eq. (3) make the occultation search rather difficult from the ground. Let us therefore try to improve this situation.

2.2. DWARF STARS

A first improvement is obtained for the occultation depth, 'f}, if the star is a dwarf (Schneider, Chevreton, & Martin 1990). For a radius of 0.2 R~)l TJ is 0.25% from Eq. (5). This number is to be compared with a ten times better photometric precision obtained by Gilliland & Brown (1992). In addition, dwarf main sequence stars are cool, so that the planet distance to the star is significantly smaller, giving a higher probability of correct orientation for its orbital plane. The geometric probability for a 3,000 K star with radius 0.2 R0 is, from Eqs. (1-3), PG = 2%: one would need to monitor only 50 dM's to detect one terrestrial planet. Furthermore, a being smaller, the occultation rate is higher: one occultation each 5 days in our example!

2.3. ECLIPSING BINARIES

One can make a step further by preselecting stars for which the orbital plane of the planet is likely to contain the line of sight: these are close eclipsing binaries, the planet being in orbit around the system (Schneider & Chevreton 1990). It is highly probable that the orbital plane of the planet is very close to plane of the binary system, as shown by Schneider & Doyle (1995). Indeed, if the protoplanetary disk initially does not lie in the binary plane, the combined action of the differential precession of the orbits of dust grains and of the dissipation of friction perpendicular to the binary plane would force the planes to become identical. If nevertheless there would still be a slight tilt left between the two planes, the precession of the plane of planetary orbits would force occultations to occur with 100% probability every half precession period (Schneider 1994). Also there are in the present case two occultations per transit event since the star is double; the shape of the double transit is strongly constrained by the (well determined) parameters of the binary system, namely its separation and its ephemeris (Schneider & Chevreton 1990).

One may ask whether the planetary orbits around binary stars are stable or not. Several numerical simulations have shown that there is indeed as stability as soon as the planet distance to the system is 3 times larger than its separation (see for instance Kubala et al. [1993], Pendleton & Black [1983], and references therein). The only question presently left is: can planet form

38 J. SCHNEIDER

in a protoplanetary disk submitted to the non-static and non axi-symmetric gravitational potential of a close binary? This question has yet never been investigated quantitatively.

3. Timing in eclipsing binaries

In addition to provide a configuration where the the geometric probability of occultation reaches 100%, eclisping binaries offer another way to detect surrounding planets, namely the accurate timing of their eclipse minima. If a planet is orbiting around a binary system, the binary itself orbits around the center of mass of the triple system at a distance a X (Mp/M**) where M** is the mass of the binary. The distance to the observer is modulated by that amount and the time of arrival of the light at the eclipse minima is itself modulated, with an amplitude

tJ..T = - X -- = 2 - -- -- sec a Mp ( a ) ( Mp ) (M**)-l c M** AU MJup M8

(6)

The measurement of this amplitude and of the modulation period would give the mass and the distance to the star of the planet.

For a terrestrial planet, the amplitude tJ..T is at most 10-2 sec., probably below the precision reachable for the timing of eclipse minima. Thus, this method is only suited for the search for J upiters.

4. Present observations and programmes

Another way of preselecting the orientation of the orbital plane of the planet is to choose stars with candidate protoplanetary disks viewed edge-on. This was first suggested by Schneider & Chevreton (1990) for the star (3 Pictoris. In an archival search in photometric data for this star, Lecavelier des Etangs et al. (1995) have found a drop in luminosity which could be explained by the transit of a giant planet with 2 Jupiter radii at a distance of about 10 AU from the star. In addition to this event, systematic searches are conducted or planned from the ground or proposed as space missions.

4.1. PRESENT OBSERVATIONS: THE TEP NETWORK

One can combine the advantages of eclipsing binaries and of dwarf stars presented in § 2.2 and 2.3. and take eclipsing pairs of dM stars as targets. One such candidate is the system CM Dra whose characteristics, taken from Lacy (1977), are shown in Table 1.

PHOTOMETRIC SEARCH FOR EXTRASOLAR PLANETS 39

Table I Summary of the eM Draconis System Parameters Relevant to

Planetary Detection (Data from Lacy 1977)

Parameter Primary Secondary

Binary Orbital Period 1.26838965

(days ± 0.0000001)

Radius (solar radii) O.252±O.O08 0.235±0.007

Mass (solar masses) 0.237±0.009 0.207±0.O08

Effective Temperature (K) 3i50±100 3150±100

Orbital Inclination (degrees) 89.82±0.05

Binary Semi-major Axis 1.75±0.03 2.01±0.O7

(a sin i in solar radii)

The relevance for planet detection of this system has been investigated by Schneider & Doyle (1995). Chevreton et al. (1995) have set a dedicated net­work, called TEP (Transits of Extra-solar Planets) of small to medium size telescope located in Crete, at the Observatoire de Haute Provence, in the Canary Islands, at the Rochester Institute of Technology, at Lick Observato­ry and at the National Observatory of Korea. The observations have started in May 1994 and are planned for several years. Jenkins et al. (1996) have shown that with the best photometric precision reachable from the ground, an Earth-like planet can be detected by a monitoring with a complete cov­erage of a few months. It should be noted that our systematic monitoring of CM Dra sould also be useful for the search for Jupiters by timing of the eclipse minima, as we estimate that our precision for individual eclipses is about 10 sees.

Another project, the LONEOS project (Lowell Observatory Near Earth ObectS) essentially dedicated to the search for asteroids passing near the Earth, could also have as a secondary objective the system search for Jupiter transists in M stars (Howell 1994).

4.2. SPACE PROJECTS

The systematic search for terrestrial planets by a dedicated space mis­sion was first proposed by Borucki et al. (1988, 1996). In the following, I describe a similar project, STARS, presently under consideration at the European Space Agency under the responsibility of M. Fridlund (the read­er can see a description of STARS on the World Wide Web at the URL

40 J. SCHNEIDER

http://astro.estec.esa.nl/ SA -general/Projects/Stars /intro.html from which part of this presentation is taken). It is aimed at providing an empirical framework to gain fundamental new insights into the physics of stellar objects and their evolution (equation of state, opacity of stellar material, energy and angular momentum transport by convection and by waves).

In order to reach its scientific objectives, the STARS mission will utilize a telescope with 0.5 m 2 collecting area to observe a number of 10 - 20 field of views for more than one month. The payload consists essentially (as far as our purpose is concerned) in an array of four 1024 X 2048 CCD arrays in the focal plane of a telescope having a diameter of 0.8 m and a FOV of 90 arcmin.

The observations will of course also detect all kinds of variability in stars that have amplitudes larger than the approximately 0.8 ppm necessary for detecting solar type acoustic oscillations in the nearest open clusters, and a major programme studying of the order of 20,000 stars over a nominal 2 year life time is expected.

If the last three years of the mission are dedicated to a search for Exo­planets, the spacecraft will remain pointed towards the same position for the whole 3 years, thus also providing a long term study of the micro-variability in up to 100,000 stars.

Detecting Telluric Planets with STARS:

Since the star must be monitored continuously in order not to miss the transit, the strategy of the mission would be the following: after the accom­plishment of the main objectives of STARS, an extra three years would be devoted to the monitoring of about one thousand stars in a suitably choosen field:

During the first year we would gather occultation "candidates". In the second year we would have another transit, giving us a determination of the orbital period of the candidate. It would serve to make the prediction of the time of occurrence ofthe third transit. During the third year, the observation of a third transit would be the confirmation of the planet detection.

We are now studying the implementation and the feasibility of this goal, mainly with respect to: (1) the number of stars to be monitored; and (2) the photometric precision. Monitoring 3000 stars should yield about 30 transit events if other stellar systems are similar to the Solar one. Then, either a detection of such a number of events or their non-detection would be informative.

For STARS to make a transit detection, it has to overcome the instrument noise, photon noise, and "astrophysical" noise. The consideration of the first two leads to a maximum stellar distance, depending upon the spectral type,

PHOTOMETRIC SEARCH FOR EXTRASOLAR PLANETS 41

of typically 500 pc for G V stars. The last contribution to the noise is unknown at the required accuracy except in the case of the Sun.

A key point to validate transit candidates is the possibility to make checks as the transits repeat with the planet revolution. The minimum number of transit observations is three, the period being determined by the first two events and the occurrence of the third one predicted. This requires a continuous observation of the same star field for three years. Assuming a stellar limb darkening similar to the Sun's, telluric exo-planets with sizes similar to the ones of the Earth and Venus, a preliminary estimate points to 5a detections of transits in front of 16 G V or K V stars and 25 M V stars.

It should be noticed that we do not know what is to be found. The pre­ceding estimates are rather conservative because larger telluric exo-planets are possible, and present indeed around pulsar PSR B1257+12, especially if stars with metallicity higher than the Sun's (up to 4 times in the Sun vicin­ity) are studied. They would lead to larger signals and therefore a larger sample of stars can be studied in a given neld.

An observing strategy could be to dedicate the first two years of the STARS mission to stellar seismology (also providing, automatically, the required information about the astrophysical variability - "astrophysical" noise - of stars on timescales of 10 hours). Then, if the Observatory is still working and the intrinsic stability of stars with spectral type close to the solar one sufficient, ESA could decide to have the instrument monitor con­tinuously a selected field for three extra years, searching for planet transits.

5. Conclusions

It is reasonable to design large-scale projects aimed at the detection of ter­restrial extra-solar planets, such as the DARWIN project. Given that such projects cannot be launched before a decade or two, it is worthwhile, in the meantime, to take every opportunity to detect terrestrial planets with projects which are more modest but, either have already started such as TEP or other ground-based proposals, or are ready for launch such as FRESIP or STARS. Since past experience has shown that the process of discovery is sometimes non-linear and full of surprises, it is worth investigating the occultation method which has the advantage to rest on ready technologies.

References

Borucki W., Allen L.E., Taylor W.S., Young A.T and Schaefer A.R.: 1988, 'A photometric Approach to Detecting Earth-Sized Planets', Bioastronomy - The Next Step, G. Marx Ed., Kluwer, p. 107.

Borucki W.: 1995, 'The FRESIP Mission', These Proceedings.

42 J. SCHNEIDER

Chevreton M., Deeg H.J., Doyle L., Freire P, Herpe G., Jenkins J., Kylafis N., Lee W.B., Martin E., Nikov Z., Paleologou E., Schneider J., Sterken G, Toublanc D., Vesque J.: 1995, 'TEP' (Transits of Extrasolar Planets): A Network for the Photometric Search for Terrestrial Extrasolar Planets', contributed paper at this meeting.

Gilliland R1. and Brown T.M.: 1992, 'Limits to CCD Ensemble Photometry Precision and Prospects for Asteroseismology', PASP 104,582.

Howell S. B.: 1994, 'CCD Time-series photometry of Astronomical sources', IAU Sympo­sium 167, The Hague.

Jenkins J.M., Doyle 1.R and Cullers K.: 1995, 'A Matched Filter Method for Ground­Based Sub-Noise Detection of Terrestrial Extrasolar Planets in Eclipsing Binary Sys­tems: Application to CM Draconis', Icarus 119.244.

Kubala V., Black D. and Szebehely V.: 1993 Celestial. Mech. 56, 51 Lacy GH.: 1977, 'Absolute Dimensions and Masses of the Remarkable Spotted dM4e

Eclipsing Binary Flare Star CM Draconis', Ap.J. 218, 444. Lecavelier des Etangs A., Deleuil M., Vidal-Madjar A., Ferlet R, Nitschelm G, Nicolet

B. and Lagrange-Henri A.M.: 1995, '(3 Pictoris: Evidence of light variations', Astron. and Astrophys. (in press)

Leger A., Mariotti J.M., Puget J.M., Rouan D., and Schneider J.: 1995 'How to Evidence Primitive Life on an Exo-Planet? The DARWIN Project', in Proceedings of th' e First International Conference on Circumstellar Habitable Zones, L.R Doyle (Ed), Tra' vis House Publications, Menlo Park, CA, in press.

Leger A., Mariotti J.M., Mennesson J.B., Ollivier M., Puget J.L., Rouan D. and Schneider J.: 1995 'Could we search for Primitive Life on Extra-Solar planets in the near future? - The DARWIN project - " submitted to Nature and these proceedings

Pendleton YJ. and Black D.G: 1983 'Further Studies on Criteria for the Onset of Dynam­ical Instability in General Three-body Systems', AJ 88, 1415

Schneider J.: 1995, 'SCODETEP: A Class of Mission Concepts for the Detection and Study of Terrestrial Extrasolar Planets by Coronographic Imaging in Space', paper presented at this meeting and submitted to Journal of Geophysical Research (Planets).

Schneider J., Chevreton, M. and Martin, E.: 1990, 'New efforts in the search for extrasolar planets', in 24th ESLAB Symposium, B. Battrick ed., ESA SP 315, p. 67.

Schneider J and Doyle 1.: 1995, 'The Search for Terrestrial Extrasolar Planets by Occul­tations: the Case for CM Draconis', in press in Planetary and Space Science

Schneider J. (1994), "On the Occultations of a Binary Star by a Circum-Orbiting Dark Companion", Planet. Space Sci. 42, 539.

Schneider J. and Chevreton M.: 1990, 'The Photometric Search for Earth-sized Extrasolar Planets by Occultation in Binary Systems', Astron. Ap. 232, 251.

TOPS (Toward Other Planetary Systems): 1992 NASA Report, Lunar and Planetary Insti­tute Publication, Houston, Texas.

Tytler D.: 1995, 'Detection of Terrestrial Planets by Microlensing', paper presented at this conference.

Wolszczan A.:1994, 'Confirmation of Earth-Mass Planets Orbiting the Millisecond Pulsar PSR B1257+12', Science 264,538.

RADIAL VELOCITY SEARCHES FOR OTHER PLANETARY

SYSTEMS:

Current Status and Future Prospects

W. D. COCHRAN and A. P. HATZES McDonald Observatory

The University of Texas at Austin Austin, TX 78712 USA

Abstract. Measurement of variations in the radial velocities of stars due to the reflex orbital motion of the star around the planetary-system barycenter constitutes a powerful method of searching for substellar or planetary mass companions. Mter several years of patient data acquisition, radial-velocity searches for planetary systems around other stars are now beginning to bear fruit. In late 1995 and early 1996, three candidate systems were announced with Jovian-mass planets around solar-type stars. The current paradigm for low-mass star formation suggests that planetary systems should be able to form in the circumstellar disks surrounding young stellar objects. These newly discovered systems, and other discoveries which will soon follow them, will test critically our understanding of the processes of star- and planet-formation. We review the techniques used in these radial-velocity searches and their results to date. We then discuss planned improvements in the surveys, and the prospects for the next 20 years.

Key words: Planet Detection ~ Radial Velocities

1. Introduction

The detection of planetary systems around other stars has been one of the great challenges of contemporary astronomy. If our Sun is indeed typical of other stars of similar mass and age, then we should expect planetary systems to be plentiful around nearby solar-type stars. The presence of a planet gravitationally bound to a star will shift the center-of-mass (barycenter) of the system away from the center of the star. The star and all planets in the system will then orbit the system barycenter. Because the star is much more massive than the planets, its orbit around the barycenter will be very much smaller and slower than the orbits of the planets. However, because of the enormous difference in detected fiux between the star and planet, ground­based searches for planetary systems around other stars have traditionally had to rely on the indirect detection of the planets by using the starlight to measure this gravitational influence of the planet on the star. Astrometric searches attempt to measure the position of the star in the plane of the sky by determining the offset of the star from other adjacent stars in the field. Radial velocity searches determine the line-of-sight velocity of the star by measuring the Doppler shift of the stellar spectrum. In both types of

Astrophysics and Space Science 241: 43-60, 1996. © 1996 Kluwer Academic Publishers.

44 w. D. COCHRAN AND A. P. HATZES

searches, the goal is to be able to detect changes in these measurements as a function of time as the star orbits the planetary system barycenter. Very careful high-precision observations must be obtained over an orbital period in order to infer the presence of the unseen planet.

2. What do Radial Velocities Tell Us?

If we assume circular orbits (which is probably a good assumption for plan­etary systems), then the observed radial component of the velocity of the star around the system barycenter is given by:

V* = mp sin iorb G(M* + mp)

M*+ mp a (1)

where M* and mp are the masses of the star and planet, a is the orbital radius, and iorb is the inclination of the orbital plane to the plane of the sky. The period of the orbit P is given by Kepler's third law (as revised by Newton):

(2)

If we now combine these two equations, we find the observed stellar orbital velocity and the period are related by

V _ (27rG) 1/3 mp SIll Zorb * - P (M* + mp)2/3 .

(3)

In radial velocity surveys, the observable quantities are V* and P. From these, and an educated guess at M* from its spectral type, we can calcu­late mp sin iorb, which then gives us a lower limit on the planetary mass mp.

Determination of the actual value of mp requires measurement or estima­tion of iorb, the inclination of the orbital plane. In principle, it is possible to estimate iorb from observations of the star itself. By analyzing the profiles of stellar photospheric absorption lines, one can measure Vr sin irot, the pro­jected stellar rotational velocity, where irot is the inclination of the stellar rotational axis to the line of sight. If one can also measure the stellar rota­tional period (e.g., from Ca II Hand K line photometry) and estimate the stellar radius, then one can independently determine the stellar equatorial rotational velocity V, and solve for i rot . This procedure has been done for a number of stars (Doyle, 1988; Doyle, Wilcox, and Lorre, 1984). This value of i rot may be used as a rough estimate of iorb, the inclination of the planetary orbital plane. In our solar system, the solar equator is inclined to the ecliptic by 7.25°.

~

'i ., ..s p '0 0 Qi > 0 :0 0

0::

RADIAL VELOCITY SEARCHES

10

0

-10

~ ~

_20~~ __ ~~ __ -L __ ~ __ ~~ __ -L __ ~ __ ~~ __ -L __ ~ __ ~i

1960 1970 1980 1990 Year

2000 2010 2020

45

Figure 1. The radial velocity of the Sun with respect to the solar system barycenter, as viewed from the direction of the vernal equinox.

The velocity of our Sun around the solar-system barycenter (mostly due to Jupiter) averages about 12.5 m s-l. Figure 1 shows the radial velocity of the Sun as would be measured by an observer in the direction of the vernal equinox. We see immediately that Jupiter dominates the signal, with a small modulation due to Saturn. The radial velocity semi-amplitude of the Sun due to each of the planets is given in Table I. In addition, the fifth column of Table I gives the astrometric perturbation on the Sun as measured at a distance of 10 parsecs. The solar reflex velocity due to four of the planets is shown in Figure 2. The diagonal lines show the velocity that these planets would have if they were at different distances from the Sun, in accord with equation 1.

It is important to note from equation 3 that the radial velocity signal is independent of the distance to the star. There is no bias toward nearby stars as is the case for astrometric detection, or for direct imaging or interfer­ometry. This means that radial velocities are particularly useful for making unbiased, distance-independent surveys of the frequency of planetary sys­tems as a function of stellar mass, age, metallicity, rotation, or magnetic activity. Radial velocities do have a selection effect for planets close to the star. This arises partly from the a- 1/ 2 dependence of the observed veloc­ity on the orbital semi-major axis. However, the real limit now seems to

46 W. D. COCHRAN AND A. P. HATZES

Table I Radial Velocity Signals of the Planets

Planet Mp R P 8* at 10 pc V* (MJ) (AU) (years) (mas) (ms-1 )

Mercury 1. 74E-4 0.387 0.241 6.4E-6 0.008 Venus 2.56E-3 0.723 0.615 1.8E-4 0.086 Earth 3.15E-3 1.000 1.000 3.0E-4 0.089 Mars 3.38E-4 1.524 1.881 4.9E-5 0.008

Jupiter 1.0 5.203 11.86 0.497 12.4 Saturn 0.299 9.54 29.46 0.273 2.75 Uranus 0.046 19.18 84.01 0.084 0.297

Neptune 0.054 30.06 164.8 0.156 0.281 Pluto 6.3E-6 39.44 247.7 2.4E-5 3E-5

2

1.5

~

'i (f)

5 ~ 5r '" .Q Q) I > en a .Q

-.5

-1

-1 -.5 a .5 1.5 2 log Semimajor Axis (AU)

Figure 2. The radial velocity semi amplitude of the Sun due to planets of the masses of Jupiter, Saturn, Uranus, and Earth. The diagonal lines show the heliocentric distance dependence of the solar reflex velocity.

be the time-span of the observations. The detection of radial velocity vari­ability can, in theory, be made with observations covering at least half of an orbital period. If the planetary orbit is nearly circular, then the velocity curve is approximately sinusoidal and is easy to identify. High eccentricity

RADIAL VELOCITY SEARCHES 47

orbits, however, often give velocity curves that are fiat for large portions of the orbit. The problem of measuring accurately the orbital period requires observations over more than one period. Black and Scargle (1982) discuss the difficulties of decoupling the planetary perturbation from the nonplanetary stellar motion in astrometric observations. They discuss in some detail the coupling of planetary orbital motion and stellar proper motion. In particular, the demonstrate that an insufficient time span of astrometric observations can easily lead to a serious misestimation of the amplitude and period of the planetary astrometric perturbation. Similar problems exist for radial velocity measurements. The observed radial velocity perturbation will be superimposed on any other observable stellar accelerations. In particular, if the star has a distant stellar companion, then the observed velocity signal will be the combination of the orbital accelerations due to both the plan­et and the stellar orbital motions. Since the stellar orbit will be of a much longer period, it can often be approximated by a constant acceleration over a planetary orbital period. If this stellar acceleration is not taken into account in the analysis, a spurious period and velocity amplitude will be determined.

3. Detectability of Planetary Systems

Ground-based observational searches for extra-solar planetary systems are virtually always pushing the limits of the available technology. Individu­al observations will often have uncertainties comparable to or larger than the signal being sought. In addition, the expected orbital periods of Jovian planets in orbit around solar-type stars will probably be comparable to the duration of an observing program to search for such objects. Thus, a survey for extra-solar planets must be designed to detect a low-amplitude signal in the presence of noise with only a few orbital periods of data at best. While most of the statistical tools already exist, it is useful to examine critically the problem of analysis and interpretation of data from a survey for extra-solar planetary systems so that data from current surveys may be interpreted in an unambiguous manner, and new surveys may be optimized in their search strategies and methodologies. The analogous problem of astrometric detec­tion of extra-solar planets was considered in detail by Black and Scargle (1982).

If we assume circular orbits for simplicity, the measured signals in a radial velocity survey for extra-solar planetary systems are essentially the irregu­larly spaced time series:

(4)

where Xo is the amplitude of a signal of frequency Wo and phase </>, and R( ti) is the error of measurement i taken at time ti. All of the results will

48 W. D. COCHRAN AND A. P. HATZES

also apply for the more general case of nonzero eccentricity. The first-order problem of planet detection is to determine that a periodic signal does indeed exist within the data stream X(ti). Such a periodic signal could arise from a number of causes. These would include orbital motion due to a companion object, stellar pulsation, stellar rotation, or unremoved periodic systematic measurement errors. After the existence of such a true stellar signal has been established, we would like to determine the frequency (w), amplitude (Xo), and phase (<p) of the signal to a level of precision that will help identify the cause of the periodic variation in velocity. If the cause might be orbital motion, the next step is to determine the system parameters to a high level of precision, i.e. we would like to solve the orbit.

Most of the high-precision radial velocity planet detection programs are achieving a '" 3 - 15 m s-l in a single measurement. Thus, the expected signal amplitude for a Jupiter- or Saturn-mass planet is comparable to the error bars of each data point. However, we must never confuse the uncer­tainty in a single measurement with the amplitude of 1:1 signal which may be detected in a time series of measurements as described in equation 4. In the following sections we will derive the relationship between these quantities.

3.1. THE PERIODOGRAM

The classical technique to analyze time series of observations which may contain periodic signals is Fourier analysis. For unevenly sampled data, the discrete Fourier transform,

No

FTx(w) = LX(tj) exp( -iwtj) , j=l

may be used to calculate the classical periodogram (Deeming, 1975),

1 2 Px(w) = No IFTx(w)1

1 No No L X(tj) exp( -iwtj)

j=l

2

~o [q: Xj co, wi j)2 + (~>j ,in wij )2]

(5)

(6)

Scargle (1982) and Horne and Baliunas (1986) have introduced a slightly modified definition of the periodogram which has a much better defined statistical behavior than the standard definition:

1 {[:LjXjCOSW(t j - T)r [:LjXjsinw(tj - T)f} Px(w) = - - - + - - ,(7) 20'5 :LjCOS2w(tj - T) :Ljsin2 w(tj - T)

RADIAL VELOCITY SEARCHES

where

I:. sin 2wtj tan(2wT) = .... J

LJj cos 2wtj

49

(8)

Here, ao is the total variance of the data, including the variance due to the periodic signal. This definition of the periodogram (equation 7) gives a function which looks very much like the classical periodogram (equation 6), but has some very useful statistical properties. A detailed analysis of this periodogram is given by both Scargle (1982) and by Horne and Baliunas (1986). The properties of most relevance to detection of extra-solar planetary

systems are summarized below. . The most useful property of the periodogram is that for a signal which is

pure noise, the power at a given frequency level is exponentially distributed. If we measure Px(w) in units of ao, and let Z = Px(w) then the probability of finding Z between z and z + dz is

Pz(z) dz = Pr(z < Z < z + dz) = exp( -z) dz , (9)

and the probability that the observed power at some frequency is greater than some value z is

Pr(Z> z) = exp( -z) . (10)

This property gives us a convenient means of estimating the probability that a given periodogram peak is the result of random noise or is indeed a true signal.

3.2. FALSE ALARM PROBABILITY

The periodogram Px( w) is often very noisy. What is the probability that some peak in the periodogram is just a random noise spike and not a true signal? We would like to define a periodogram power level Po such that any claimed detection of a signal exceeding Po will be wrong only some small fraction, say F, of the time. This is given by

Po = -In [1 - (1 - F)l/N] . (11)

The total variance of the observed signal is

(12)

where a r is the random portion of the total variance, i.e. the precision of an individual measurement. As more data are obtained, the power due to noise,

(13)

50 W. D. COCHRAN AND A. P. HATZES

remains constant. However, the total power at the signal frequency is

NoXg No ( 2a;)-1 PN(WO) = 2Xg + 4a; = 2 1 + x;f . (14)

This power increases as more data are obtained. Let us then define the periodogram signal-to-noise ratio as ~ = X6!2a;. We can now express the false alarm probability F in terms of No and ~ as

F-l- l-e 2" • _

[ _ No (1+,,-1)-1] Ni

(15)

where Ni = No/2 is the number of independent frequencies searched for the maximum. For a given number of data points, No, we can use this relationship to determine what power signal/noise f, = X;f/2a; (and thus what ar) is needed for any desired false alarm probabilities. Conversely, for a given value of ar, we can determine the number of measurements No necessary to detect a system with a given Xo with the desired false alarm probability. This is shown is Figure 3, where f, is plotted as a function of the number of independent observations No for false alarm probabilities ranging from 1.0% to 0.001%.

Inspection of Figure 3 shows that we do not really gain much information about the possible presence of a low-amplitude periodic signal in the data until we have about 30 independent measurements. We can detect a system with Xo = ar at about 45 observations for F = 1%. If we double the number of independent observations to about 90, the false alarm probability drops to 0.001%. Systems in which Xo < ar can be detected quite reliably given a sufficiently dense sampling over the orbital period.

3.3. SPECTRAL LEAKAGE

The finite total interval covered by the data will give rise to a periodogram containing significant sidelobes - or leakage of power to nearby frequencies. The finite size of the interval between samples causes leakage to distant frequencies. If the data are evenly sampled, the phenomenon of aliasing will cause leakage of power from high frequencies to low frequencies. Spectral leakage is generally examined and characterized by calculating a "window function", which describes the sampling of the data,

(16)

RADIAL VELOCITY SEARCHES 51

1.5 F=0.001

- - - - - - - - - - F=0.0001

F=0.00001

N b

N

.5~ N'-.... 0

C-O' ~ .Q

t -.5 ~

60 80 100 120 140

Figure 3. The power signal-to-noise ratio as a function of the number of independent observations No spaced over the orbital phase for a variety of false alarm probabilities F.

3.4. DETECTION STRATEGIES

To avoid possible erroneous claims of planet detection, we need to set the false alarm probability fairly low, and clearly state this probability. We sug­gest the adoption of F ::; 0.001 as necessary for the announcement of the "detection" of an extra-solar planetary system. There is an obvious tradeoff between the false alarm probability, F, and the detection efficiency. If we set F to a very low value, we may miss some real planetary systems. How can we work around this problem?

3.4.1. Maximize the signal-to-noise ratio. Recall that we have shown that the total power at the signal frequency is

NoXo No 2aT 2 ( 2)-1 PN( wo) = 2X;r + 4a; = 2 1 + X;r (17)

All high-precision programs have all worked very hard to reduce aT' We may still see some modest improvements there in the future, but it will be difficult to achieve aT < 1 m s-l in the immediate future (Butler et al. 1996). One can then increase PN(WO) by increasing No, Le_ take more data.

52 W. D. COCHRAN AND A. P. HATZES

3.4.2. Average the data. If we can heavily average the data, we can maximize the detection efficiency without harming the false alarm probability. This is because averaging the data will decrease the effective random noise level ar, and thus increase the power signal-to-noise ratio~. Of course, one should not average to the point where the Nyquist frequency becomes lower than the signal frequency.

3.4.3. Tailor the window junction. One can adjust the contributions of the sidelobes (and thus the amount of spectral leakage ) by applying a time-domain window to the data. To do so, you multiply the data values by a function w( t) which is 1.0 over most of the data, but goes smoothly to 0.0 at the ends. A "cosine bell" is commonly used, but there are other choices. This avoids the introduction of false frequencies necessary to reproduce discontinuities at the ends of the data stream.

A second method of tailoring the window involves judicious selection of the times of the observations. For a large number of programs, this is not always practical. Our observing times (and thus window function patholo­gies) are often governed by the object coordinates, the phases of the Moon, the weather, and the whims of telescope allocation committees. Howev­er, in programs with dedicated (or semi-dedicated) telescopes, those using queue-scheduled facilities, or programs using facilities such as HST where observing time is precious and must be optimized, it may be possible to add data-window considerations as a scheduling constraint. The best example of window-tailoring is the sampling intervals chosen by the HST extragalactic distance scale key project (Freedman et al., 1994). This program needed to sample the light curves of Cepheid variables in as efficient a manner as possi­ble. They selected a power-law distribution of sampling within the total time interval available for obtaining data. This type of algorithm could easily be tuned for the problem of planet detection.

4. Radial Velocity Measurement Techniques

Stellar radial velocities are measured by determining the Doppler shift of the spectrum of a star, corrected to the solar-system barycenter. Classical radial velocity techniques rely on the wavelength calibration and stability of the spectrograph as well as observations of radial velocity standard stars to make the velocity measurement. The CORAVEL (CORrelation - RAdial -VELocities) program ofthe Geneva Observatory (Baranne, Mayor, and Pon­cet, 1979; Mayor, 1985; Duquennoy, Mayor, and Halbwachs, 1991) is a classi­cal large-scale radial velocity survey based on spectral cross-correlation tech­nique. The basic method was first suggested by Fellgett (1953), and the tech­nique was brought into widespread use by Griffin (1967). The spectrum of

RADIAL VELOCITY SEARCHES 53

the star is shifted with respect to a negative mask template spectrum in real­time in the spectrometer. The total transmission of light through the mask is measured as a function of spectral shift, giving the cross-correlation func­tion of the spectrum and the template. The center of the cross-correlation dip is taken to be the velocity shift of the object star with respect to the template spectrum. The entire system is calibrated onto a standard abso­lute radial velocity system by the observation of radial velocity standard stars. The Center for Astrophysics (CfA) survey (Latham, 1985) operates in a very similar mode, except the stellar spectrum is recorded digitally and the cross-correlation is done in software. This adds considerable flexibility to the data reduction process, premitting an optimal template spectrum for each star to be chosen during the data reduction process. With very careful attention to the observing and calibration processes, these techniques can give radial velocity precision of 200 - 300 m s-l. The principle limiting factor in these classical techniques, as discussed by Griffin and Griffin (1973), is the difference in illumination of the spectrograph optics by the object and com­parison sources. The wavelength comparison spectrum is general taken at a different time than the object spectrum, has a different beam illumination pattern and may follow a different path through the spectrograph. Murdoch, Hearnshaw and Clark (1993) went to great effort to control these sources of systematic error by using a fiber-optic feed to a carefully temperature­controlled spectrograph. They were able to achieve 55 m s-l characteristic random error for bright solar-type stars.

The secret to making high-precision measurements of stellar radial veloc­ities is to superimpose the velocity metric on the stellar spectrum during the stellar observation. Thus, any instrumental wavelength shifts due to seeing, entrance aperture illumination, or spectrograph or detector drifts will affect both the stellar and the wavelength standard spectrum equally. This can be accomplished in a variety of methods. Mayor and Queloz (1995) used "classical" cross-correlation techniques very similar to those used in CORAVEL in a special fiber-feb echelle spectrograph, Elodie, at the Obser­vatoire de Haute-Provence to obtain velocity precision of 13 m s-l. They do this by carefully controlling the spectrograph temperature and fiber-feeding the signal from a calibration source into the spectrograph simultaneous­ly with the stellar optical fiber. McMillan et al. (1994) use a tilt-tunable Fabry-Perot etalon in transmission as the independent velocity metric, and use a cross-dispersed echelle spectrograph to then separate the Fabry-Perot orders on their CCD detector. This system allows achievement of 10-15 m s-l precision for solar-type stars. An alternative method to achieve high veloci­ty precision is to pass the starlight through a gas absorption cell before the light enters a classical echelle spectrograph. This technique was pioneered by Campbell (Campbell and Walker, 1979; Campbell, Walker, and Yang, 1988; Walker et al., 1995) who used a HF cell on the Canada-France-Hawaii

54

f i r

.c I I

'iii ~ c <ll r c

~ <ll J > ~ .~

(i) II

a)

5188

W. D. COCHRAN AND A. P. HATZES

5190 5192

Wavelength (1)

5194

1 I

1 5196

Figure 4. Sample spectra using an h gas absorption cell. Panel (a) shows the absorption spectrum of the h cell (illuminated with white light) from 5187 A to 5197 A. Panel (b) gives the spectrum of a CMi A, without the h cell, and panel (c) shows the spectrum of a CMi A taken with the cell in front of the entrance slit to the spectrograph.

Telescope to achieve 10-15 m s-l precision in a 12-year survey of 21 bright solar-type stars. This technique has been extended independently by Mar­cy (Marcy and Butler, 1993) and by Cochran (Cochran and Hatzes, 1994; Kiirster et al., 1994), both of whom use an 12 gas absorption cell. The basic observational technique for gas absorption cell observations is illustrated in Figure 4. Panel (a) shows the spectrum of the 12 cell in the 5187-5197A spectral range. The 12 cell is permanently sealed and is temperature stabi­lized, giving a constant dense pattern of deep absorption lines to serve as the velocity metric. The middle panel (b) shows the spectrum of a typical program star (a Canis Minoris A) in the same spectral region. The lower panel (c) gives the spectrum of the star taken through the 12 gas absorption cell. Relative changes in the radial velocity of a star are determined from a time-series of observations such as those in Figure 4c. The velocities are measured by determining the shift of a pure 12 spectrum and a standard pure stellar spectrum (both corrected for the instrumental point-spread-function if necessary) required to best match the observed program spectrum through the h cell.

RADIAL VELOCITY SEARCHES 55

5. Planet Detection Results

The several high-precision radial velocity surveys operated for many years before suddenly producing interesting results. The first hints of low-mass companions to solar-type stars came from the CfA survey, which detected possible low-mass companions to HD114762 (Latham et al., 1989), HD140913 (Stefanik et al., 1994), and HD29587 (Mazeh, Latham, and Stefanik, 1996). All three of these stars are G dwarfs which are IAU radial velocity standard stars. HD114762 has m2 sin iorb of about 9 Jupiter masses, while HD140913 and HD29587 have minimum companion masses of 0.046 and 0.061M0 respec­tively. Mazeh et al. conclude that, if they assume a flat mass-ratio distribu­tion, they can reject the hypothesis that there are no substellar companions in their survey to a high level of confidence. Thus, at least one (and possi­bly all) of these objects is probably substellar. The CaRAVEL survey has also found three spectroscopic binaries with F or G dwarf primaries and with minimum secondary mass less than 0.1 M0 (Duquennoy and Mayor, 1991). From this, they infer that (8 ± 6)% of F and G dwarfs should have companions of 0.1 M0 or less.

The CFHT survey (Walker et al., 1995), which has now concluded, did not find any sub stellar companions in its sample of 18 stars. They placed upper limits of 1-3 Jupiter masses on possible planetary companions in 10-15 year period orbits around most of its program stars.

In October 1995, Mayor and Queloz(1995) made the stunning announce­ment of a possible low-mass companion to the star 51 Pegasi. They reported a radial velocity variation with an amplitude of 59 m s-l and a period of 4.23 days. This orbital period would correspond to a semimajor axis of about 0.05 AU, or 1/8 the distance of Mercury from the Sun. The mass function of 0.91 X 10-10 M0 corresponds to a minimum companion mass of about 0.5 Jupiter masses. Mayor and Queloz (1995) discuss and reject possible other sources of the radial velocity variability for this star, such as pulsation or rotation of stellar spots across the face of the star. The common paradigm for planet formation does not easily allow for such massive planets to form so close to a star (Boss, 1995), because it has been thought that water con­densation is necessary for the formation of giant planets. Lin et al. (1996) suggested that the planet may have originally formed much farther away from the star, and then slowly spiraled toward the star due to tidal forces in the protoplanetary disk. Guillot et al. (1996) demonstrated that planets would indeed be stable at that distance from a star, and that a 1 Jupiter­mass planet would lose about 0.5% of its mass due to stellar EUV radiation over the main-sequence lifetime of 51 Peg.

In January 1996, the Lick Iodine Planet Search announced the detection of radial velocity variations in 70 Virginis (Marcy and Butler, 1996) and 47 Ursae Majoris (Butler and Marcy, 1996) which imply the presence of

56 \\'. D. COCHRX\ X\D :\. P. 1l:\TZES

Table II Detections of Possible Planetary Companions to Stars

Star Period I\: lnpsmi a e

(Days) (ms- 1 ) (:-'IJupller) (At; )

HDl14762 83.91 617 9 0.38 0.38

HDl-10913 1-18.1 1920 46 0.,55 0.55

HD29587 1473. 1130 61 2.53 0.31

51 Peg 4.23 53 0.5 0.05 ~O,O

70 Vir 116.7 318 6.6 0.43 0.40

47 UMa 1090 45.5 2.39 2.1 0.03

Sun (Jupiter) 1332 G ! 1.!J ' Q ;).1 DD.]

planetary mass companions to these stars. The orbital solution to the 70 Vir velocity variations gives a minimum ('ompanion mass of 6.6 Jupiter masses. an orbital period of 116.7 da~;s. (,ccentricity of 0.-10. and a semi major a;'us of about 0.-13 At'. These orbital characteristi(,s seem to be quite similar to the companion to HDll,1762 fOlllld b:; Latham et al. (1989). The radial \'elocity variations found in -l7 l'\la han' a 2.98yr period and a velocity semi-amplitude of -l5 .. ) m s-1. yielding an orbital solution with m2 sin iorb = 2.39Jupiter masses and low e(,centricity (r = 0.0:3).

The detections of possible extrasolar planets as of February 1996 are shown in Table .s. :\one of the planets around other stars resemble Jupiter. which had been regarded as the archetype. The objects in this table seem to divide into t\VO categories: those with low eccentricity and those with large eccentricity. It is somewhat tempting to regard this possible dynami­cal difference as indicative of their formation mechanism. Thus. one might claim that the low eccentricity. low mass objects are "giant planets" and the objects with higher mass and eccentricity are "brown dwarfs". In this scheme, a giant planet would be an object formed according to our stan­dard model of the formation of .Jupiter. in which rock and ice particles in a protoplanetary disk accumulate into planetesimals. These planetesimals then grow larger by collisions until a planetary core is formed . .If this core reaches a critical mass of 10 - 20 Earth masses while there is significant gas left in the disk, then it can accrete an extensive atmosphere and become a giant planet such as Jupiter (Pollack, 1984). On the other hand, a brown dwarf is, by definition, an object which is formed in the same manner as a star is formed, but with a mass too low (:S 0.07 M 0 ) to ignite fusion reac­tions in its core. The assignment of "planet" or "brown dwarf" based on the eccentricity follows from the observation that a large number of binary star systems have large eccentricity, and that the planets in our solar system all have low eccentricity probably resulting from their formation in a dissipative disk. However, we must be very cautious in this crude taxonomy. It is imp os-

RADIAL VELOCITY SEARCHES 57

sible to know the formation mechanism of the object from radial velocity observations. Marcy and Butler (1996) proposed the designation of "super planets" for objects between about 5 and 20 Jupiter masses. However, this really begs the question of the origin of these bodies. Clearly, many more systems must be discovered in order to understand the diversity of planetary systems. Additional theoretical work is necessary in order the formation and evolution of these systems.

6. Future Prospects

After many years of hard work and frustrations, planets have finally been discovered around other nearby stars. We now finally understand that our solar system is not unique, and is not even the result of some very rare circumstances. Planetary systems do indeed seem to be a common natural result of the process of star formation. The systems discovered thus far are all planets more massive than Jupiter in orbits considerably smaller those of the giant planets in our own solar system. That such planets were the first detected is undoubtedly the result of a strong selection effect in radial velocity surveys that favors the detection of short-period orbits with large velocity amplitude. The systems with planets such as Jupiter will be discov­ered when the surveys have had sufficient time baseline to detect planets at larger distances from the star. Clearly, radial velocity surveys must continue over the next decade in order to discover the whole spectrum of planetary systems which can be formed. In order to do so, and to discover possible second planets in systems, radial velocity precision of 1-3 m s-l will be nec­essary. This level of precision will also permit detection of "failed Jupiters" at 5 AU. These are object such as Uranus and Neptune which have attained their critical planetesimal core mass of 15-20 Earth masses too late in the evolution of the nebula to accrete a significant amount of gas from the pro­toplanetary disk before it was dispersed.

Achievement of this measurement precision is possible now. Butler et al. (1996) discuss the requirements for attaining radial velocity precision of 3 m s-l. They show results from the Keck HIRES spectrograph which demon­strate 3.2 m s-l rms radial velocity precision over a 5.5 hour interval. The major task now is to control the long-term systematic errors to the sub-m s-l level in order to maintain this 3 m s-l precision for a decade-long time base­line .. It is quite possible to believe that this can be achieved on a large sample of solar-type dwarfs in new surveys over the next 10-15 years. An expanded survey should entail a cooperative and coordinated effort among many different independent programs to survey a total of at least 1000 stars in the northern and southern hemispheres down to V magnitude of 9 or 10. There are several possible ways to conduct this survey. The new genera-

58 W. D. COCHRAN AND A. P. HATZES

tion of large-aperture telescopes with high-resolution spectrographs (VLT, RET, Keck-1) will allow very high SIN observations of stars to be obtained extremely quickly. These telescopes can be used for surveys of several hun­dred stars with a modest investment of observing time. Another alternative is to dedicate a modern 3-meter class telescope to a high-precision radial velocity survey. The large amount of observing time available on a dedicat­ed telescope would compensate for the smaller aperture.

These new expanded ultra-high precision radial velocity surveys are vital to our understanding of the process of planetary system formation. These surveys will enable us to move from the present regime of planet detection into the regime of planetary system characterization. They should conclu­sively answer the question of what types of planetary systems can form around nearby stars. We will determine the frequency of planet formation and the properties of planetary systems as a function of stellar mass, metal­licity (age), rotation, magnetic field, or any other measurable property of the star. This will give us significant new insight into the physics of planetary system formation.

7. Conclusions

The discovery of planetary systems around nearby solar-type stars using radial velocity techniques is radically changing our understanding of the pro­cess of planetary system formation and evolution. Radial velocity surveys of nearby stars provide a powerful technique to detect sub-stellar (brown dwarf) and planetary mass companions to a large sample of solar-type stars. Current high-precision ground-based radial-velocity surveys have demon­strated that they have already achieved the precision level necessary to detect Jupiter-sized planetary companions at 5 AU distances from the stars, in addition to the more massive planets already discovered much closer to the stars. Most main-sequence G, K, and M stars are suitable for radial­velocity planet searches. Intrinsic stellar variability seems to be at a level below the signal due to a Jupiter-mass companion. Routine measurement precision is now improving to about 3 m s-l, and may well improve to 1-2 m s-l with higher resolution spectrographs. If 1 m s-l precision can indeed be achieved, then objects of Uranus-Neptune mass can be detected. Greatly expanded sample sizes (1000 stars) sampled at 1-5 m s-l will provide exciting new insights on the process of planetary system formation.

RADIAL VELOCITY SEARCHES 59

Acknowledgements

We would like to thank R. S. McMillan and G. W. Marcy for a number of informative discussions. This work was supported by NASA Grant NAGW-3990.

References

Baranne, A., Mayor, M., and Poncet, J. L.: 1979, 'CORAVEL - A New Tool for Radial Velocity Measurements', Vistas in Astronomy 23, 279.

Black, D. C. and Scargle, J. D.: 1982, 'On the Detection of Other Planetary Systems by Astrometric Techniques', Astrophysical Journal 263, 854.

Boss, A. P.: 1995, 'Proximity of Jupiter-Like Planets to Low-Mass Stars', Science 267, 360.

Butler, R P. and Marcy G. W.: 1996, 'A Planet Orbiting 47 Ursae Majoris', Astrophysical Journal, Letters to the Editor 464, L153.

Butler, R P., Marcy, G. W., Williams, E., McCarthy, c., and Vogt, S. S.: 1996, 'Attaining Doppler Precision of 3 mis', Publications of the ASP ,in press.

Campbell, B. and Walker, G. A. H.: 1979, 'Precision Radial Velocities with an Absorption Cell', Publications of the ASP 91, 540.

Campbell, B., Walker, G. A. H., and Yang, S. L. S.: 1988,'A Search for Substellar Com­panions to Solar-type Stars', Astrophysical Journal 331, 902.

Cochran, W. D. and Hatzes, A. P.: 1994a, 'A High Precision Radial-Velocity Survey for Other Planetary Systems', Astrophysics and Space Science 212, 281.

Deeming, T. J.: 1975, 'Fourier Analysis with Unequally-Spaced Data', Astrophysics and Space Science 36, 137.

Doyle, R R: 1988, 'Progress in Determining the Space Orientation of Stars', in Bioas­tronomy - The Next Steps, G. Marx Ed. (Kluwer), 101.

Doyle, R R, Wilcox, T. J., and Lorre, J. J.: 1984, 'The Space Orientation of Stars', Astrophysical Journal 287, 307.

Duquennoy, A., Mayor, M., and Halbwachs, J.-1.: 1991, 'Multiplicity among solar type stars in the solar neighbourhood. I. CORAVEL radial velocity observations of 291 stars', Astronomy and Astrophysics, Supplement Series 88, 28l.

Duquennoy, A. and Mayor, M.: 1991, 'Multiplicity among solar type stars in the solar neighbourhood. II. Distribution ofthe orbital elements in an unbiased sample', Astron­omy and Astrophysics 248, 485.

Fellgett, P. B.: 1953, Optica Acta 2, 9. Freedman, W. 1., Hughes, S. M., Madore, B. F., Mould, J. R, Lee, M. G., Stetson, P.,

Kennicutt, R C., Turner, A., Ferrarese, L., Ford, H., Graham, J. A., Hill, R, Hoessel, J. G., Huchra, J, and Illingworth, G. D.: 1994, Astrophysical Journal 427, 628.

Griffin, R F.: 1967: 'A Photoelectric Radial-Velocity Spectrometer', Astrophysical Journal 148,465.

Griffin, R and Griffin, R: 1973, 'On the Possibility of Determining Stellar Radial Velocities to 0.01 km/sec', Monthly Notices of the RAS 162,243.

Guillot, T., Burrows, A., Hubbard, W. B., Lunine, J. 1., and Saumon, D.: 1996, 'Giant Planets at Small Orbital Distances' Astrophysical Journal, Letters to the Editor 459, L35.

Horne, J. H., and Baliunas, S. L.: 1986, 'A Prescription for Period Analysis of Unevenly Sampled Time Series', Astrophysical Journal 302, 757.

Kiirster, M., Hatzes, A. P., Cochran, W. D., Pulliam, C. E., Dennerl, K., and DObereiner, S.: 1994, 'A Radial Velocity Search for Extra-Solar Planets Using an Iodine Gas Absorption Cell at the CAT+CES', ESO Messenger 76,51.

60 W. D. COCHRAN AND A. P. HATZES

Latham, D. W.: 1985, 'Digital Stellar Speedometry', in Stellar Radial Velocities, A. G. D. Phillip and D. W. Latham Ed., (L. Davis Press: Schenectady NY USA), 2l.

Latham, D. W., Mazeh, T., Stefanik, R. P., Mayor, M., and Burki, G.: 1989, 'The Unseen Companion of HD114762: A Probable Brown Dwarf', Nature 339, 38.

Lin, D. N. c., Bodenheimer, P., and Richardson, D. c.: 1996, 'On the origin of the low mass companion to 51 Pegasi', Nature 380, 606

Marcy, G. W., and Butler, R. P.: 1993, 'Precision Radial Velocities with an Iodine Absorp­tion Cell', Publications of the ASP 104, 277.

Marcy, G. W., and Butler, R. P.: 1996, 'A Planetary Companion to 70 Virginis', Astro­physical Journal, Letters to the Editor 464, L147.

Mayor, M.: 1985, 'Cross-Correlation Spectroscopy with CORA VEL' , in Stellar Radial Velocities, A. G. D. Phillip and D. W. Latham Ed., (L. Davis Press: Schenectady NY USA), 35.

Mayor, M., and Queloz, D.: 1995, 'A Jupiter-mass companion to a solar-type star', Nature 378,355.

Mazeh, T., Latham, D. W., and Stefanik, R. W.: 1996, 'Spectroscopic Orbits for Three Binaries with Low-Mass Companions and the Distribution of Secondary Masses near the Substellar Limit', Astrophysical Journal ,in press.

McMillan, R. S., Moore, T. L., Perry, M. L., and Smith, P. H.: 1994, 'Long, Accurate Time-Series Measurements of Radial Velocities of Solar-Type Stars', Astrophysics and Space Science 212, 271.

Murdoch, K A., Hearnshaw, J. B., and Clark M.: 1993, 'A Search for Substellar Compan­ions to Southern Solar-Type Stars', Astrophysical Journal 413, 349.

Pollack, J. B.: 1984, 'Origin and History of the Outer Planets: Theoretical Models and Observational Constraints', ARAA 22, 389.

Scargle, J. D.: 1982, 'Studies in Astronomical Time Series Analysis. II. Statistical Aspects of Spectral Analysis of Unevenly Spaced Data', Astrophysical Journal 263, 835.

Stefanik, R. P, Latham, D. W., Scarfe, C. D., Mazeh, T., Davis, R. J., and Torres, G.: 1994, 'The Unseen Companion of HD140913: Another Brown Dwarf Candidate', Bulletin of the AAS 26, 931.

Walker, G. A. H., Walker, A. R., Irwin, A. W., Larson, A. P., Yang, S. L. S., and Richard­son, D. c.: 1995, 'A Search for Jupiter-Mass Companions to Nearby Stars', Icarus 116, 359

David Tytier (L) and Nick Woolf (R)

DEMONSTRATION OF PHOTON-NOISE LIMIT IN STELLAR RADIAL VELOCITIES

P. CONNES, M. MARTIC and J. SCHMITT Service d'Aeronomie du CNRS, Verrieres-le Buisson, 91371, France

Abstract. We have measured apparent fluctuations in stellar radial velocities with the ELODIE fiber-fed crossed-dispersion spectrograph and the 193-cm telescope of Observa­toire de Haute-Provence. Within one given night, the fluctuations consist of two terms which may be sorted out. The first comes from imperfect scrambling of the stellar beam; the second arises from photon noise and agrees closely with our published calculations. So far, scrambler noise dominates for bright stars, but a perfect scrambler could be built by combining adatative optics and a single-mode fiber. The photon-noise results confirm that PSfXi1~L np;.D£,u,J:YJ RearrbiuJ!orwJ t.b£'Jadiab. velocitv. t.ecbJROl}B .may. he j=)emented with relatively small telescopes for a large number of stars. Consequences for the detection of "astrophysical noise" are discussed.

1. Introduction

In several papers (Connes 1985, 1992) we have discussed a proposed tech­nique for extrasolar planetary searching from the gravitational signature detected through radial-velocity (RV) variations. Our approach differs from that of the presently-operational searches, for which a recent review is avail­able (TOPS 1992). Here we shall briefly summarize the two main concepts in the proposal, which are independent of (but compatible with) each other.

The first was "absolute accelerometry," a technique intended to remove the severe difficulties arising from the changes in Earth velocity, which are greater than 100 times the hoped-for residual error level; in a typical case, these changes would cause the stellar lines to shift over 20 CCD pixels, while the line centers must be pinpointed to better than 1/3000 pixel error. The problem is a particularly troublesome one because no laboratory simulation is feasible, hence no relevant-accuracy velocity calibration is ever available for the spectrograph. We have pointed out (Connes 1986) that ignorance of these effects has led to the "discovery" of a revolving solar core, through misinterpretation of an apparent 13-day periodicity in solar radial veloci­ties, which had remained coherent over several years. Actually, this was an artifact from the Earth motion. The analogy with possible future detection of spurious planets is complete.

In the absolute technique the stellar lines are compared to a shifting refer­ence: the channelled-spectrum from a variable path FP interferometer. The lines from the Fabry-Per~t (FP) and star track each other, but do not move relative to pixels to which they are locked; the spectrograph acts merely as a null detector for which no calibration is needed. The burden of measuring

Astrophysics and Space Science 241: 61-76, 1996. © 1996 Kluwer Academic Publishers.

62 P. CONNES ET AL.

the wavelength shifts is transferred to that of tracking the FP spacing: this is done with two lasers, one tunable and one stabilized, and recording the beat frequency. Development has been proceeding at a slow pace; partial tests on the Sun and laboratory sources have been reported (Connes 1992). Suitable FP interferometers and tunable diode lasers have long been com­mercial, but are too expensive for the available funding. Hence the major part of the effort has been building our own substitutes, a frustrating situ­ation. A further report solely on lasers would be, by itself, of little interest to astronomers.

The second concept was that of a well-defined ultimate photon-noise limit in RV measurements, to be treated here in Part 2. The conclusion from the computed curves of photon-noise RMS error versus stellar magnitude was that planetary systems could be detected around a large number of stars with CCD-equipped crossed-dispersion spectrographs, using relatively small telescopes. The main difficulty would be reducing systematic errors to the same level; hence the need for the absolute technique.

For planetary detection through absolute accelerometry we proposed in 1985 a dedicated spectrograph, which would have been somewhat compara­ble to the recently-completed AFOE (Brown et al. 1994); no support was obtained. However, in March 1995, we were able for the first time to use the general-purpose ELODIE spectrograph on the 193-cm telescope at Obser­vatoire de Haute Provence (OHP). Without lasers and/or tunable FP, the observations were not a preliminary test of absolute accelerometry. They were only intended to check various sources of errors in spectrograph oper­ation and the feasibility of detecting stellar oscillations. Of main interest to our program was a verification of photon-noise error, to be reported in Parts 3 and 4.

Present planetary searches put either a FP etalon or a gas cell in the beam, which removes most of the effects of spectrograph instabilities. How­ever, the photon-noise RV limit is much increased; this is an important point for a valid comparison, but it will be treated elsewhere. Absolute accelerom­etry (and the observations described here) do not suffer from this limitation, the reference beam being separate, but they require the use of so-far imper­fect "scramblers" (Part 5). The possible detection of "astrophysical noise" will be treated in Part 6.

2. The Computed Photon-Noise Limit

A photon-noise limit is a vague concept unless the base hypotheses are spelled out; one observer's limit may not apply to another's technique. We have published a complete treatment (Connes 1985) giving an ultimate lim-

STELLAR RADIAL VELOCITIES 63

ntensity

. . ~"""""""""R'G"""""""''''''''''''>l Wavelength

Figure 1. Left: single absorption line case. Right: complex spectrum of arbitrary shape, within range RG.

it. Only the starting point and main equations in simplified form will be given here.

Let us recall first a standard result. If we observe an emission or absorp­tion line (Figure 1) in which the wavelength FWHM is W, and if N photo­electrons are collected from the line profile during one exposure, the RMS wavelength error on the line-center position over many exposures will be

(1)

where ](1 and ](2 are numerical coefficients on the order of unity; ](1 is a function of the line shape, and ](2 of the measuring procedure. If the line finesse is F = Ao/W, then the RMS velocity error may be written

~V; _ C](1](2 1 rIllS - F VN (2)

This result is simple and convenient, but it is not applicable to complex spectra with overlapping lines, which is the case for stars in the spectral ranges where much of the RV information is present. Our approach is more systematic, and provides a result that is both general and optimal.

We consider a spectrum of arbitrary shape within a spectral range RG. No lines are needed for the argument. We take infinitesimal spectral slices of width dA, and we integrate their contributions to the final Doppler-shift estimate while taking into account photon counting; this treatment extracts from the spectrum all the RV information. Let ( ) denote an average over the range RG, and let I(A) be the spectral intensity, normalized to have

64 P. CONNES ET AL.

(I(A)) 1. Let M(A) = (A/I)(dI/dA), with I(A) > o. We next define a numerical "quality factor", Q, characteristic of the spectral profile within range RG. In the pure photon noise case, Q is given by

(3)

A slightly different formula for Q applies if detector noise predominates. The final RMS photon-noise velocity error is

C

~Vrms = Q y'N '

where N is the total number of photoelectrons collected from RG.

(4)

Within a program devoted to stellar RV changes, a "reference" spectrum h(A) will be recorded at a epoch EI, when the velocity is VI; M(A) and Q will be computed from h(A). Next, the star will be observed at epoch E2, with velocity V2 and the recorded spectrum will be h(A). From hand h the measured velocity change will be given by

C V2 - VI = Q2 ([h(A) - h(A)]M(A)) . (5)

This algorithm uses the same optimal procedure and insures that the above­defined ~ Vrms error is obtained. However, unlike the more common cross­correlation, it is accurate only if the line shift remains very small relative to pixel width (which is the case for absolute accelerometry). The function M(A) plays a role analogous to that of the physical mask in CORAVEL-type spectrometers; hence we call it the "mask function". It may be artificially modified at will, for example to select only wanted lines.

Altogether, the RV error may be predicted from two independent fac­tors, Nand Q. The quantity N involves stellar magnitude, atmospheric and instrumental transmission, detector efficiency, and exposure time. The quantity Q involves spectral type and spectrometer resolution. If the instru­mentallineshape FWHM is small relative to W, we reach a "theoretical" Q which cannot be exceeded; if not, the actual Q is easily computed from the recorded spectrum, as degraded by convolution. Both computations were performed from numerical atlases of the Sun, Arcturus, Procyon, and Sir­ius. For the Sun, the highest finesse F is roughly 60,000, and the highest Q factors, about 40,000, are found in the near UV.

From these Q factors, RMS photon noise curves versus magnitude for a given telescope size and exposure time were computed. The case of an ideal instrument outside the atmosphere provided the minimal conceivable error, at least from the spectral ranges available in the atlases. The crossed­dispersion CCD spectrograph is the only device that may approach this lim­it; various assumptions about transmission, resolving power, spectral range, and CCD readout noise were introduced for describing "practical" cases.

STELLAR RADIAL VELOCITIES 65

A simplified version of the noise-magnitude diagram will be given here in Figure 9.

3. Observations

The ELOD1E spectrograph has been built by the same team responsible for the well-known CORAVEL; a full description is given by Baranne et al. (1995). This a fiber-fed spectrograph within a stable temperature-controlled environment. The fiber input accepts a 2" diameter image. The 100 X 400 mm, 743-angle, 31 grooves mm-1 echelle is cross-dispersed by a Carpenter prism-grating; up to 65 echelle orders are usable, from 389 to 681 nm. The 1024 X 1024 CCD, with 25 X 25 fLm pixels, is liquid-nitrogen cooled; readout noise is about 10 e- RM8. The measured instrumental line shape (1L8) FWHM corresponds to 2.2 pixels, and to a resolving power R = 45,000 at the center of the orders. It is mainly fixed by fiber and pixel size, with only a minor increase due to aberrations and diffraction. The pixel velocity­width is 3100 m s-1, and the FWHM is 6820 m s-1. The highest measured overall efficiency has been 1.2% electrons per incident photon outside the atmosphere, but 0.7% is an average value for OHP seeing.

For our March 1995 observations, the channelled spectrum from a fixed FP was introduced, because such a spectrum gives the best-possible ref­erence. All pixels are used, just as for the star, and the highest possible reference Q is obtained. For absolute accelerometry, ELODIE will require several adaptations which are not yet available. In particular, one must opti­cally switch the FP and stellar beam through the same fiber, so that the same pixels are used for both. The present setup is shown in Figure 2. A some­what ancient FP etalon with invar spacers was used; temperature changes were recorded with less than 10-3 K error. Temperature stabilization within 10-2 K provided maximum 10-8 spacing instability.

Since the etalon thermal time constant was greater than 1 h, the corre­sponding velocity error of 3 m s-1 appeared only as a slow drift. Pressure was maintained below 0.1 mb by a liquid nitrogen trap. Etalon thickness was 6 mm; fringe spacing varied from 4.6 to 3.1 pixels from 600 to 400 nm. The reflectivity was about 0.3, hence the finesse was only 2.5.

Two kinds of recordings were made: FP /FP spectra, with FP light on both fibers, and star/FP spectra. The outputs of both fibers were displaced by a few pixels in the direction of cross dispersion. Orders for both spectra alternate over the CCD; exposures are simultaneous. For extraction of the one-dimensional spectra (each corresponding to one echelle order) from the two-dimensional CCD images, we relied on the regular ELOD1E software; for the computation of RV, we used our own algorithm.

66

CASSo FOCUS

P. CONNES ET AL.

FIBER2

SPECTRO

FIBER3

FIBERl

Figure 2. Optical system. FP: Fabry-Perot etalon; Tg: tungsten-halogen lamp. CASS FOCUS : Cassegrain-focus optical commutator: either fibers 1 and 2 both transmit FP bearns, or one transmits a star beam and the other an FP beam.

In order to get meaningful RMS error figures within a few hours, and also to check the suitability of ELODIE for studying stellar oscillations, we planned a large number of short exposures (60 s) on a given star. No preliminary tests of the procedure could be made (a cardinal sin). While most individual spectra proved correct, long sequences were almost always interrupted by electronic failures of unclear origin. Out of 8 more-or-less usable nights, we salvaged only one presentable 7-hour star/FP sequence.

4. Results

4.1. FP IFP SPECTRA

A few sequences were recorded, and the least-perturbed one (252 60-s expo­sures) is shown in Figure 3. The lost time from CCD readout, extraction of the spectra, and computation of RV was 40 s, hence the cycle time was 100 s and the sequence took about 7 h. The diagram presents spurious-RV curves relative to a previously exposed reference spectrum. They are com­puted from a single echelle order centered at 522 nm; the range RG = 5.6 nm.

For both fibers we find slow drifts of the order of 50 m s-l and "fast" fluctuations of a few m s-l amplitude. The first arise mostly from thermal changes of the spectrograph elements, and the second from internal air con­vection. However, these effects (fast or slow) are almost the same for both fibers. The slow trend in the difference curve, which is independent of any

'" E

~~

STELLAR RADIAL VELOCITIES 67

30

-30

-60

TIME s

Figure 3. Apparent radial velocities with FP beams on both fibers. Spectral range 5.6 nm at 522 nrn. Recording time 7 h.

FP drift, shows that the two-fiber setup does not compensate fully for spec­trograph drift, an expected result. The fast residuals (0.9 m s-1 RMS) come mostly from photon noise.

4.2. STAR/FP SPECTRA

4.2.1. Data The star 't/J UMa (V = 3.3, Kl III) was selected because its spectrum was close to that of Arcturus and because it could be observed all night. First, a I-min exposure reference spectrum was recorded on March 12. Figure 4 shows one typical order. The star mask functions and quality factors are found to agree well with the Arcturus-atlas results. Next, a sequence of 245 similar 60-s exposures with 100-s cycles was recorded. The total observation time was 24,500 s, and the total exposure time was 14,700 s (about 4 h). The elevation increased from 46 to 89, then decreased to 58. The overall average efficiency was 0.7%. Intensity fluctuations for order 40 will be found in Figure 6; a large part of the fluctuations arose from changes in seeing, but we did not have separate checks of transparency and seeing, nor of guiding errors. We did record the autoguider corrections, which apart from one brief guider failure show no clear correlation with intensity, nor with radial velocity errors.

4.2.2. Narrow Spectral Range RV Results Compared with Theory Here we use a narrow range near 520 nm, not because it gives the best results, but because this is the longest wavelength in the Arcturus atlas. Above 520 nm, we cannot make a direct comparison with the Connes (1985) predictions.

til

E >­t­o o

68

toxro' ,---------~~-

0.8XlO'

0.6xlO' !

O.4xlO' 11,."wMlI/Il/III~iI!III~~\~I~~~~ 02x1O'

P. CONNES ET AL.

PIXEL NJMlER

Figure 4. Typical echelle order; I-min exposure on 1./J UMa plus FP; 1024 pixels, 5.6-run range centered at 520 run. Mter order extraction but without corrections for flat-field, bad pixels and echelle blaze. Apparent oscillations in FP spectrwn are a sampling effect.

-100

ill -300 >

0.8x105 O.9x105

TIME s

Figure 5. Measured RV change on 1./J UMa compared with the Earth contribution (smooth curve). Two adjacent orders (40, 41) are shown for 245 100-s cycles with 60-s exposures.

Only the (star-FP) RV curves will now be given. We have stressed that our V2- VI algorithm is inaccurate when lines move across the pixels (which is the case here); since we are not demonstrating absolute accelerometry, all curves have been recalibrated against the earth velocity through multiplication by a constant factor.

Figure 5 presents the RV from two adjacent echelle orders, and the Earth velocity. Residual differences are illustrated in Figure 6. First shown is the

STELLAR RADIAL VELOCITIES 69

~ 0 OFFERENCE (40-4~

~ -25

::~ 70000 75000 80000· 85000 ------;90000=-------'

Figure 6. Lower panel: Mean-intensity fluctuations on 1/J UMa (one echelle order, arbitrary units). Upper panel: Apparent RV fluctuations, as in Fig. 5, but on more expanded scale, and difference between the mean of the two orders and Earth velocity, showing scrambling noise plus drift, and 2nd-order fit. Two curves give difference between both orders, show­ing pure photon noise. Arrow indicates peak due to guider failure (during 5 exposures); reduction of intensity is minimal, but velocity error is large.

difference between the sum of the two orders RV's and that of Earth-motion. The low-frequency error may be accounted for by etalon and spectrometer drifts. Both factors are unimportant, at least for our long-term program: absolute accelerometry does not need an etalon, and uses commutation of the star/FP beams in the same fiber. However, the fast fluctuations are relevant. They come from imperfect stellar-beam scrambling by the present fiber; let us describe them as "scrambler noise" ,just as we speak of "detector noise." The RV curves are found to be almost the same for a single order, or for an average of several orders, a clear sign of systematic (non-photon) errors. The RMS residual relative to a 2nd-order fit is 6.2 m s-l; as shown below, this figure clearly exceeds photon noise. Scrambler noise may also contribute a low-frequency drift-like term, but we have no evidence.

Figure 6 also presents the difference between the RV's for the two orders. The greater part of the above fluctuations was common to both and has vanished; the residual pattern is stationary, with 5.3 m s-1 RMS. Of course the photon and detector noises were not common and have been added by taking this difference. Since the noise-power contribution of both orders is about equal (same Q, same N), the RMS RV error for each order observed alone would have been 5.3/-)2 or 3.7 m s-1, which must be compared with

70 P. CONNES ET AL.

photon-noise predictions. For both orders, the number of electrons/pixel (averaged over the spectrum, and over the 7-h sequence) was about 26,000. Since there are 1024 pixels, we get N = 2.6 X 107 electrons for the 5.6-nm range RG. For both orders, Q was about 15,000; from the Part II theory, we compute a 3.9 m s-1 RMS error.

To summarize: with a V = 3.3, K1 III star, 193-cm telescope, 0.7% effi­ciency, 45,000 resolving power, 3100 m s-l pixels, within a 5.6 nm range centered at 520 nm, for 60-s exposures, a 3.7 m s-1 RMS fluctuation has been recorded after removal of systematic errors.

This figure agrees well with the prediction of photon-noise from an opti­mal procedure (Connes, 1985 and Part 2). It would be reduced, in a pre­dictable manner, by an increase in photon number from any cause (exposure time, telescope size, etc.). Still, for a given star, telescope, spectral range and exposure, it might only be improved (also predictably) by a more effi­cient and/or higher resolution spectrometer. However, in the present set-up, another error arises from scrambler noise, which has given a 6.2 m s-1 RMS difference relative to Earth motion. This figure is not reduced by an exten­sion of spectral range, nor would it be by any gain in photon number, e.g. from a larger telescope; on the other hand, for increasingly fainter stars, it would soon become hidden by photon noise. Since velocity noise from poor scrambling arises from beam motions and distorsions within the spectrom­eter, it is proportional to ILS velocity-width (all other things being equal). Hence it would be automatically reduced by an increase in spectrometer resolving power; the present figure of R = 45,000 is dearly rather low for our intended program. Moreover, improved scramblers will be discussed in Part 5.

4.2.3. Extension to a Wide Spectral Range As stressed above, the absolute fluctuations are not reduced in the present data by averaging RV's from several orders. At least at V = 3.3, they are scrambler-noise limited even for a single order. In order to illustrate the reduction of photon-noise errors from a wide spectral range, Figure 7 presents the difference between two groups of21 orders each (odd and even). From the measured Q and N, an optimal weighting scheme could be defined; this has not yet been done, and plain averages are used.

The RMS fluctuation level is now reduced to 1.8 m s-1 but the pattern is no longer stationary. There is slow drift, and fluctuations increase near the end. Taking the difference between orders is no longer sufficient for cancellation of systematic errors. Still, we get an upper limit for the RMS photon noise that is obtainable for the full spectral range (190 nm, from 443 to 632 nm). For one group of 21 orders, it would be 1.8/ y'2, and for the sum of both sets one gets DVrrns = 1.8/2 = 0.9 m s-1.

STELLAR RADIAL VELOCITIES 71

0.7><10 --- -O.BXW" - ------~----·-----~0.9~><1O=·--

ThE.

Figure 7. Apparent RV fluctuations, as in Fig. 6 upper curve, but from a 193 nm spectral range (443 to 636 nm). The difference between 2 groups of 21 orders each is shown; the sum is not, as it differs little from that in Fig. 6. Fluctuations increase at right is probably due to seeing degradation.

All above RMS figures are for 60-s exposures. In order to illustrate the error level obtainable from a 4-hour sequence (i.e., 2 hr 24 min integration time), Figure 8 presents the square root ofthe power spectrum ofthe velocity curves. The result shows that the detection of stellar-type oscillations is well within the capability of ELODIE or similar spectrographs if scrambler noise is reduced.

In Connes (1985) sets of curves of predicted photon-noise versus magni­tude for different spectral types were given, together with a full discussion. The above results confirm the theoretical predictions; however, one pro­posed "practical" curve was computed for 10 % efficiency, which now seems far too optimistic. An updated (and much-simplified) curve, based on the above DVrms = 0.9 m s-l, is given here in Figure 9. Scrambler noise could be represented (by an horizontal line); however, since the spectrum is not expected to be fiat, we could only compute a correct figure if we had a set of independent 1-h observations.

5. Scramblers: Brief Discussion and a New Proposal

The availability of scramblers has done much to bridge the gap between interferometers and slit spectrographs for precision radial velocities. How­ever, they are still not perfect. A brief discussion is in order. Thirty years ago, we demonstrated the use of a short light-pipe as a "scrambler" for an astronomical beam (Connes 1966). After optical fibers were discussed by

72 P. CONNES ET AL.

:::[443T~0636f11l~~~L 0'5m1S~ 4-HNfEGRAllON\~~ I E 0.3 PHOTON NOISE ! 02

0.1

o 0 0.001 0.002 0.003 0.004 0.005

FREQUENCY Hz

Figure 8. Spectrum of velocity curves (linear scales) from the first (and best) 4 hours of the '1j; UMa recording; artificial oscillations with 500-s period and known amplitude are added for calibration. Lower panel: sum of 42 orders, illustrating actual performance of ELODIE, as limited by scrambling noise. Upper panel: spectrum of the Fig. 7 difference curve, showing mostly photon noise; SNR would be improved by a further factor of 2 for the sum of all orders.

Angel et al. (1977) for connecting telescope arrays, plus some other appli­cations, we proposed their use as scramblers and presented the first tests (Connes 1980). This was done specifically for planetary searching. The idea was immediately adopted by K. Serkowski for his "velocity spectrometer" (Serkowski et al. 1980), then by others. A recent review is given by Heacox and Connes (1992).

Beam scrambling by a multi-mode (MM) fiber is a complex phenomenon; fiber defects, plus bends and stresses, playa major role, and no simplistic cylindrical model is adequate. There is no way of computing the output beam shape. In practice, it soon became clear that results were imperfect. Azimuthal scrambling is good, radial scrambling is poor. Moreover, while the beam cross section in the plane of the fiber output ("near-field") is largely stabilized against input-beam motions, the diverging beam ("far-field") is not. Hence we proposed the "double scrambler" in which two fibers are used in series (Connes 1985): a lens or set of lenses is interposed in such a way that each fiber "sees" the tip of the other at infinity. Unfortunately, no tests could be carried out at the time.

STELLAR RADIAL VELOCITIES 73

5 V MAGNITUDE 10

Figure 9. Predicted RMS velocity error from photon noise versus magnitude. Same format as in Fig. 10 of Connes (1985), but based on present results, in which systematic errors have not been totally removed; hence curve is an upper limit. Assumptions: Kl star; 1 m telescope; 1 h integration; 1% efficiency; 45,000 resolving power; 443 to 636 nm range.

The double-scrambler idea has since been independently developed by Brown (1989) who presents an RV curve similar to that of Figure 5. This result seems to be the most precise to date for a a time stretch of a few hours. The absolute fluctuations (after subtracting Earth motion) are not specified but the residuals from a low order polynomial are 1.1 m s-l RMS, much lower than ours, mostly we believe thanks to the double scrambler.

Laboratory tests have been reported by Hunter and Ramsey (1992). The device has since been incorporated within the AFOE spectrograph (Brown et al. 1994) with good results. However the efficiency so far is poor (about 0.2), for non-fundamental reasons. Moreover, the device should also be tried wi th a higher resolving power spectrometer. So far, there is no indication that any limit in velocity errors from scrambler noise has been reached.

Another solution, which cancels scrambler noise, will now be proposed. In contrast with the MM fiber, a single-mode (SM) fiber is a well-defined optical device with fully-computable properties (Jeunhomme 1983). The concept of "focal ratio degradation" , standard for MM fibers, is not applicable. An SM fiber acts as a perfect 8M spatial filter. For any feasible fiber length, all radiation modes, except the axial one, become undetectable due to large

74 P. CONNES ET AL.

attenuation. This is true not only for ideal fibers, but also for actual ones irrespective of surface errors, bending, and so on. All cross sections of the output beam are quasi-Gaussian and preserve no memory of the input beam geometry. Hence a SM fiber behaves as an ideal scrambler. For this reason (plus some others), we proposed its use for astronomical interferometry, and there are now several experiments underway in the field (see above review).

A SM fiber may be almost perfectly matched to the Airy pattern at the focus of a diffraction-limited telescope, irrespective of its diameter. The accepted fraction of the flux is computable, and equal to 0.78 (Shaklan and Roddier 1988). Hence, it is a natural solution for a (perfect) space telescope. On the ground, with a telescope pupil smaller than the "Fried diameter", plus fast guiding, the same result applies; but this diameter (roughly 12 cm in the visible for 1" seeing) is too small to be useful.

The difficulty is solved by adding adaptative optics in front of the SM fiber. Such systems are complex, but three factors help to make the present proposal a relatively simple case: 1) bright stars only: energy for sensors will be adequate; 2) small telescopes only: number of actuators will be moderate; 3) residual errors will only reduce (slightly) fiber-input efficiency, and will not affect scrambling accuracy. Auxiliary advantages: spectrometer design is greatly simplified, since with a diffraction-limited beam a smaller grating and matching optics are adequate. Simultaneously, resolving power (hence Q factor) may be increased, and line profiles become accessible.

If we want it hard enough, scrambler noise is bound to vanish altogether, and performance of the slit-spectrograph will become photon-noise limited for stellar sources, just as it is for laboratory ones. As to cost for a planetary­search program, one may start comparing solutions such as a) going to the Keck telescope with a gas cell, or b) going to aIm-class telescope with adaptative optics. The point will be treated elsewhere.

6. Detection of Astrophysical Noise

The above discussion has left out one essential source of errors in RV plan­etary searches: line shifts from the stellar atmosphere itself. This is often called the "astrophysical limitation" and a short discussion is in order. In the worst-case scenario, an atmosphere might exhibit quasi-periodic pulsa­tions, with all lines shifting with the same phase- and velocity-amplitude and with stable profiles. If so, this atmosphere mimics the gravitational signature of a planet, and there is nothing spectroscopy can do about it. However, for all other conceivable cases, differential shifts and/or profile changes appear, and may be said to carry an "atmospheric signature." Is it detectable?

The astrophysical limitation has so far always been treated as an issue separate from all instrumental factors. But, such a limit is just as mean-

STELLAR RADIAL VELOCITIES 75

ingless a notion as a photon-noise limit if the methodological context is not specified; one observer's limit will not apply to another's results. Any technique constrained to just a few lines has little chance of detecting usable differential shifts. With a FP as a reference (plus a scrambler), one makes use of the entire spectrograph range, and all pixels are calibrated. No absorber is interposed in the beam, and wide-range stellar spectra are recorded in the most straightforward manner.

The spectroscopist is able to apply all standard tricks. In particular, he may measure profiles and/or sort out the lines in several different groups, selected solely from astrophysical criteria: he only needs to compute a sep­arate mask and to measure a separate V2 - V1 for each of them. The max­imum practical number of groups is limited by photon Joise alone; for a given star and long-term program (e.g., number of planned exposures), it may be estimated from our curves or equations. The same applies to mea­surement of line profiles through an increase in resolving power. A precise understanding of the photon-noise RMS velocity error is needed before any of these operations can be implemented. A technique that is optimal as far as photon-noise is concerned is ipso facto optimal for detecting any eventual stellar atmospheric signature.

The TOPS report (which does not list any of our references, nor those of Brown et al. 1994), fails to discuss photon noise and ignores scramblers and absolute accelerometry. The performance of presently-operating spec­trometers is not compared with any theoretically-attainable goal. Our own conclusion is that any prospective treatment of planetary detection from radial-velocities should not be confined to a presentation of "classical" tech­niques, and their extrapolation to larger telescopes.

Acknowledgements

We thank all members of the ELODIE team for their help, and P. Veron, Director of ORP, for his active interest. E. Pelletier and F. Lemarquis pro­vided the (highly complex) FP layers, and F. Chollet the Earth-velocity program.

References

Angel, J. R. P., Adams, M. T., Boroson, T. A. and Moore, R. L.: 1977, 'A very-large optical array linked with fused-silica fibers', Astrophysical Journal 218, 776

Baranne, A., et al.: 1995, 'ELODIE: a spectrograph for precise radial-velocity measure­ments', to be published

76 P. CONNES ET AL.

Brown, T.: 1989, 'High precision Doppler measurements via echelle spectroscopy', Astr. Soc. Pac. Conf. SeT. 8, 335

Brown, T. et al.: 1994, 'The AFOE: a spectrograph for precise Doppler studies', Publica­tions of the ASP 106, 1285

Connes, P. and Connes, J.: 1966, 'Near infrared planetary spectra by Fourier spectroscopy', JOSA 56, 896

Connes, P.: 1980, 'A proposed system for the detection of dark companions", in Ground­based techniques for detecting other planetary systems, eds. D. Black and W. Brunk, NASA Conf. Pub. 2124, p 197

Connes, P.: 1984, 'Absolute astronomical accelerometry', in Stellar radial velocities, ed. A. Davis, L. Davis Press, Schenectady, NY, fA U Coil. 88, p. 131

Connes, P.: 1985a, 'Absolute astronomical accelerometry', Astrophys. Sp. Sci. 110, 211 Connes, P.: 1985b, 'Absolute accelerometry: a new tool for planetary searching', in Search

for extraterrestrial life, ed. M. Papagiannis, fA U Symp. 112, D. Reidel Pub!. Co. Connes, P.: 1986, 'Solar core rotation: a down-to-earth view', in Seismology of the Sun

and Distant Stars, ed. D. Gough, D. Reidel Pub!. Co., p. 229 Connes, P.: 1994, 'Development of absolute accelerometry', Astrophys. Sp. Sci., 212, 357 Heacox, W. and Cannes, P.: 1992, 'Optical fibers in astronomical instruments', Annual

Review of Astronomy and Astrophysics 3, 169 Hunter, T. and Ramsey, L.: 1992, 'Scrambling properties of optical fibers and the perfor­

mance of a double scrambler', Publications of the ASP 104, 1244 Jeunhomme, J. B.: 1983, 'Single-Mode Fiber Optics', M. Dekker, NY Serkowski, K., et al.: 1980, 'The University of Arizona radial-velocity spectrometer', in

Ground-based techniques for detecting other planetary systems, eds. D. Black and W. Brunk, NASA Conf. Pub;. 2124,175

Shaklan, S. and Roddier, F.: 1988, 'Coupling starlight into SM fiber optics', Appl. Opt., 27,2334

TOPS Report: 1992; A Report by the Solar System Exploration Division, NASA

Jan Vrtilek (L), Ed Barker (e), and Shri Kulkarni (R)

ASPECTS OF ASTROMETRIC SEARCHES FOR OTHER PLANETARY SYSTEMS

HAROLD A. McALISTER Center for High Angular Resolution Astronomy

Georgia State University, Atlanta, Georgia 30303 Electronic mail: hal@chara.gsu.edu

Abstract. With precision potentially attainable to better than 1 milliarcsecond, ground­based astrometric techniques are capable of detecting Jupiter-mass planets around the nearest stars. This paper is intended not as a review of the relevant progress in astrometry but is instead aimed at pointing out some of the pitfalls inherent in very high precision relative astrometry.

1. Introduction

Relative astrometry employs the use of background stars to establish a frame of reference against which the motions of nearby stars are measured. This extremely powerful and effective approach has led to a wealth of knowl­edge regarding the parallaxes and proper motions of large numbers of stars. Numerous low-mass stellar companions have been detected in the reflex motions of stars (Lippincott 1978), and relative astrometry has for decades held out the possibility of detecting planetary companions to the nearby stars. The detection of a submotion in the proper motion and parallax resid­uals to Barnard's star by van de Kamp (1977,1982) and the ensuing scrutiny ofthose data are well known. Although the original perturbations announced by van de Kamp have not been supported by more recent observations, the case for low-mass companions for Barnard's star may still not closed (van Altena 1983).

The Barnard's star saga has demonstrated the pitfalls of attempting to deal with astrometric detections just above the noise level in the data. Indeed, it is widely recognized that astrometric methods hold great promise for detecting Jovian-mass planets with additional potential for the discovery of Uranian-type bodies. The detection of terrestrial mass objects is likely to remain beyond the ability of ground-based astrometry.

Increased accuracy will substantially increase the potential for ground­based astrometry to respond to the challenge of detecting other planetary systems. And yet the ground-based astrometric detection of even massive planets is likely to remain a few-a problem. Improvements in observational accuracy will inevitably be accompanied by an extension to larger distances from the Sun to provide a larger survey sample.

New levels of sensitivity also result in the detection of numerous other effects and phenomena that may themselves mimic a planetary detection.

Astrophysics and Space Science 241: 77-84, 1996. © 1996 Kluwer Academic Publishers.

78 HAROLD A. MCALISTER

The purpose of this paper is to identify some of these "nuisance" effects and to evaluate their magnitudes with respect to a possible planetary submotion. It will be shown that, at a level of astrometric accuracy of 100 f-1arcsec, certain of these effects substantially exceed the submotion induced by a massive planet.

2. Astrometry at the 100 f-1arcsec Level

For the purposes of this discussion, an attainable limiting accuracy of 100 f-1arcsec is assumed. This is a less than an order of magnitude gain in accura­cy over what is currently being achieved in the parallax program of the U.S. Naval Observatory using CCD imaging on the 61-inch astrometric reflector in Flagstaff. The practical limits to ground-based astrometry are ultimately set by atmospheric anisoplanatism, to which might possibly be added subtle refraction effeCts not now well understood. Isoplanatism is the underlying essence of binary star speckle interferometry, traditionally been employed over angular separations of well under one arcsecond. The importance of isoplanatism in larger angle relative astrometry has been recognized by G. Gatewood. Using CCD imaging of 15 cluster stars across a 2 arcmin field of view, Pravdo & Shaklan (1996) found differential image motion repeat­able to ±400 f-1arcsec (rms) after modest exposure times. It therefore seems not unrealistic to discuss an environment in which relative positions in an astrometric reference frame are measured at the 100 f-1arcsec level.

The semi-amplitude in arcseconds of the gravitationally induced reflex motion imposed upon its parent star by a planet is given by

ro, - M M -2/3p2/3d-1 u.* - p * pc , (1)

where Mp and M* are the planetary and stellar masses in units of solar mass, P is the planetary orbital period in years, and dpc is the distance in parsecs. U sing a conservative detection criterion of five times the limiting accuracy of a single observation, one could expect to detect a planetary system if

(2)

This is equivalent to a 5a detection of a Jupiter/Sun system from a distance of 10 pc. In reality, the ability to extract periodic signals from noisy data would result in higher signal-to-noise ratio detections than Sa, but for sim­plicity we consider a 500 f-1arcsec semi amplitude as the detection threshold. From an evaluation of Equation 1, it is apparent that Uranian planets in long-period orbits around the lowest mass stars would be detectable.

At this level of accuracy, it is essential to consider effects beyond the par­allax, proper motion and potential submotion associated with the program star. Two general classes of effects are present: those associated with the

ASTROMETRlC SEARCHES FOR OTHER PLANETARY SYSTEMS 79

observed objects themselves (classically called "cosmic" effects) and those associated with the observational process, i.e. instrumental effects. In this paper we consider only the cosmic effects as they can straightforwardly be identified and evaluated. These effects include:

1. Parallaxes and proper motions of the reference stars 2. Perspective secular acceleration of reference and program stars 3. Submotions induced by stellar companions to reference stars 4. Differential refraction effects on reference and program stars

Each of these effects is considered in the following sections.

2.1. PARALLAXES OF REFERENCE STARS

It is assumed that the reference stars will fall within the apparent magni­tude regime of mref = + 18 to + 19 mag and will be dwarfs with a mean spectral type of K5 and therefore an absolute magnitude of Mv = 7.3. These constraints will ensure reasonable availability of reference stars within small angular displacements from a program star. These stars would have a mean distance of 1,700 pc and a mean parallax of 600 J-larcsec or just larger than our minimum 50" detection for a planet. To drop the reference star parallax­es below the 100 J-larcsec level, and thereby bury them in the measurement noise, requires selecting reference stars at distances beyond 10,000 pc. A distance modulus of 15 magnitudes leads to a mean magnitude of +22.3 for a sample of K5 V reference stars. One would have to go as early as F5 V to maintain a mean sample magnitude of +18, but the numbers of such objects would be significantly reduced. The use of very distant late type giants would also lead to a reasonable brightness for the reference stars, but K giants are significantly rarer than K dwarfs.

We are led to conclude that the parallaxes of the reference stars are comparable in amplitude to a planetary perturbation in the program sta.r and therefore must be explicitly evaluated in the astrometric solution. The annual dependence of parallax is helpful to its isolation from detectable planetary orbital periods, which from Equation 1, will be in excess of five years. Spectroscopic parallax also forms a first-order input to the astrometric solution.

2.2. PROPER MOTIONS OF REFERENCE STARS

A star's proper motion (in arcsec per year) in terms of its parallax 7l' and tangential velocity VT is given by the well-known equation

7l'VT J-l = 4.74' (3)

80 HAROLD A. MCALISTER

For reference stars with 7r = 600 f-larcsec, a reasonable tangential velocity of 25 km s-l leads to f-l = 3.2 milliarcsec yr- 1 , or more than six times the amplitude of the planetary signal in a single year. Over a period of ten years, which might be a minimum duration goal for a planet search program, the proper motion of a single reference star, if unaccounted for, would accumulate to some sixty times the semi amplitude of a planetary submotion in the program star. In order to avoid the biasing of the program star signal with reference star proper motion, one must measure refere:n,ce star proper motions with high accuracy. Of special concern would be the careful weighting over time of the various reference star terms to ensure uniform contributions to the reference frame motion. One could imagine "turning up or down" the relative weights of say two reference stars such that their improperly evaluated proper motions would produce curvature in the reduced motion of the program star. Obviously, careful attention must be paid to the analysis of the proper motions of reference stars.

2.3. REFERENCE STAR SECULAR ACCELERATIONS

Secular acceleration effects resulting from changing geometric perspective with time exist in both proper motion and parallax. These effects are quite small and are given in arcsec yr- 1 by

2.05 X 10-6 V f-l7r (4)

(5)

In the case of reference stars having f-l = 6.3 milliarcsec yr- l , V = 25 km s-l, and 7r = 600 f-larcsec, one finds:

2 X 10-4 f-larcsec yr- l (6)

(7)

Perspective secular acceleration effects arising from reference star motions are thus insignificant and can be completely ignored because of the great distance of these stars.

2.4. PROGRAM STAR SECULAR ACCELERATIONS

While secular acceleration is of no consequence to the analysis of reference star effects, there is potential for its presence at a detectable level in the motions of nearby program stars. Consider the nearest stars (7r 2: 0.2 arcsec)

ASTROMETRIC SEARCHES FOR OTHER PLANETARY SYSTEMS 81

with moderate space motions (V ~ 20 km s-1). Evaluation of Equation 4 shows that the growth of 1::.11 to 100 l1arcsec would be encountered unless 11 ::; 0.61 arcsec yr-1 . This is a modest proper motion for a nearby star, and therefore secular acceleration in proper motion would be a common problem requiring inclusion in the astrometric solution.

To keep the parallax secular term from growing beyond 100 l1arcsec requires from Equation 5 that V ~ 125 km s-l. This is a large velocity and therefore secular acceleration in parallax would only be an occasional problem. As examples of these effects among two noteworthy nearby stars we consider T Ceti and Barnard's star. The 20-year accumulated effects are 1::.11 = 195 l1arcsec and 1::.7r = 30 l1arcsec for T Ceti, and 1::.11 = 23,000 l1arcsec and 6.7r = 600 l1arcsec for Barnard's star. Clearly one must worry about both effects in the case of the rapidly moving Barnard's star while only 6.11 is of concern for T Ceti. The necessity of including secular acceleration terms in the astrometric solution for a program star can easily be determined in advance. Thus, while the effect can be large, as in the case of Barnard's star, it will not come as a surprise.

2.5. DUPLICITY OF REFERENCE STARS

Mayor et al. (1992) have found that the duplicity frequency of K type stars is approximately 40%. One must therefore carefully consider the consequence of binaries among reference stars. As an example, we consider a binary comprised of stars of spectral type K5 + MO having a total mass of 1.2M8 and a mass ratio of 0.7. It can be shown that the "photo centric" submotion in such a system with a linear semimajor axis a and a parallax 7r is given by

Ctphot = 0.25 a7r . (8)

For Ctphot ~ 100 l1arcsec, one must begin to consider the effects of the submotion. And since in the case under consideration,

(9)

then all periods in excess of 0.5 yr for systems at a distance of 1700 pc (the average distance of the reference stars considered here) would contribute submotions approaching the threshold of detect ability. This would mean that the majority of the K-star binaries would be detected and that roughly one third of the reference stars would be binaries with submotions at the limit of detect ability. One would have to solve for orbital motions for all the reference stars as the binaries are not identified a priori.

Radial velocity monitoring would be helpful. In this particular example, the system would have a circular orbital velocity of

V = 31.8P-1/3 km s-1 , (10)

82 HAROLD A. MCALISTER

and for P 2:: 0.5 yr, one would encounter V :::; 40 km s-l. Such large velocities would encourage spectroscopic monitoring of reference stars to support the orbital solution in the astrometric reduction. Spectroscopically determined values of the orbital elements P, T, e, and w would be extremely valuable input to the astrometric solution for the binaries that will inevitably be found among the reference stars. However, this requires a lengthy spectro­scopic support effort on top of the primary astrometric program.

Binary systems among the reference stars pose a significant problem requiring additional observational overhead. Their consideration in the astro­metric solution also requires sufficient terms to account for all the geometric orbital elements. If such care is not taken, and if the reference star frame is small, one runs the great risk of falsely identifying a planetary sub motion in a program star on the basis of what is really a pedestrian binary reference star. Binary reference stars are particularly insidious because their periods overlap entirely with the range of periods likely to be detected for planetary systems.

2.6. DIFFERENTIAL REFRACTION EFFECTS

Atmospheric refraction increases with zenith angle z approximately accord­ing to the relation,

R ~ [58.3(tanz) - 0.067(tanz)3] arcsec, (11)

from which the differential refraction over a small change in zenith angle is approximately given by,

!::J.R ~ 58.3( sec2 z) (!::J.z) arcsec. (12)

At a zenith angle of 30°, one finds t1R = 78(!::J.z) arcsec. If z increases by 10 arcmin at Z = 30°, then t1R changes by 100 J-larcsec. Refraction therefore results in a measurable distortion of the reference frame that is very sensi­tive to zenith angle. It is also a wavelength dependent phenomenon, and the implications of color differences among reference stars and especially between the reference frame and the program star must be investigated. The amount of absolute refraction compared with the limiting sensitivity of 100-J-larcsec astrometry is, of course, enormous. One is led to wonder whether we under­stand refraction effects at this level to sufficiently well anticipate their effects. Are there anomalous terms in refraction perhaps produced by atmospheric "gravity waves" that might invade the astrometric solution? What about instrumental color effects coupling with refraction? Atmospheric refraction could be the least predictable of the effects considered here.

ASTROMETRIC SEARCHES FOR OTHER PLANETARY SYSTEMS 83

Table I Effects on Astrometric Searches for Nearby Planets

Effect Program Star Reference Stars

7r Up to 8,0000" 60"

6,7r Occasionally significant Insignificant

J.l Huge 300"

/:lJ.1 Occasionally significant Insignificant

Duplicity Must always Up to one-third will be be evaluated detectable binaries

Refraction and Must always Must always Color Effects be evaluated be evaluated

Instrumental Will be present HERE BE Effects (of unknown nature) THE DRAGONS!

3. Conclusion

The various effects briefly discussed above and their degree of influence on a program of 100-f.Larcsec astrometry aimed at detecting planetary systems among the nearby stars are summarized in Table I.

The ground-based astrometric search for other planetary systems has many advantages over other techniques. It utilizes relatively straightfor­ward and comparatively inexpensive instrumentation that requires no major developments other than a push in observational practices towards some­what higher accuracy than is now routinely achieved. Recent experiments have shown that a limiting accuracy of 100 f.Larcsec is a reasonable goal. To achieve this goal will require a long-term commitment to large amounts of observing time on large telescopes. This degree of access to large telescopes has never been granted to programs of astrometry, which traditionally have been carried out on relatively small telescopes dedicated to the task. If appro­priate telescopes time is made available for a long-term effort, astrometry will give well-defined results, both negative as well as positive, for stars in the solar neighborhood in terms of their possession of gas giant planets. For the nearest and lowest-mass stars, precise ground-based interferometry can look for Uranus-mass planets. In its regime of applicability, astrometry not only detects planets but also provides a determination of their mass in comparison with radial-velocity methods (which puts limits on planet mass-

84 HAROLD A. MCALISTER

es due to unknown orbital inclinations). While there appears to be no real hope that astrometry from the ground will be sensitive to terrestrial plan­ets, a successful ground-based effort will provide a reconnaissance for future space detection of terrestrial planets.

When the high accuracy imagined here is attained, extraordinary care must be given to the design of the observing program, the observing method­ology, and the selection of reference stars. The reduction of the astrometric material will be complex in order to accomodate all terms in the solution arising from the effects described above. The precise determination of these terms will require an adequate number of reference stars and large amounts of observing material. It would be wise to not rely upon a single astrometric search, and two programs would be advisable to avoid a repetition of the "Barnard's star syndrome".

This paper is intended to provoke some thought towards the proper reduc­tion of an astrometric reference frame in which nothing is standing still. It is presented in this conference because it is the author's observation that more thought has been given to the instrumentation required for precise astrom­etry than to the proper analysis of the data eventually to be provided by that instrumentation. History has shown us that the essence of astrometry is the identification and evaluation of systematic instrumental and cosmic errors. This challenge has never been more important as we move into new realms of astrometric precision.

References

Lippincott, S. L.: 1978, Space Sci. Rev. 22, 153. Mayor, M., Duquennoy, A., Halbwachs, J.-L., & Mermilliod, J.-C.: 1992, fA U Colloq. 135,

Complementary Approaches to Double and Multiple Star Research, eds. H.A. McAlister & W.I. Hartkopf, ASP Con/. Series, Vol. 32, p. 73.

Pravdo, S. H. & Shaklan, S. B.: 1996, Astrophysical lournal465, 264. van Altena, W. F.: 1983, Annual Review of Astronomy and Astrophysics 21, 131. van de Kamp, P.: 1977, Vistas in Astr., 20, 501. van de Kamp, P.: 1982, Vistas in Astr., 26, 141.

ASTROMETRIC DETECTION OF EARTH-LIKE PLANETS

WITH OSI

MICHAEL SHAO Jet Propulsion Laboratory, California Institute of Technology

Abstract. The Orbiting Stellar Interferometer (OSI) is a space-based astrometric interfer­ometer designed primarily for wide-angle astrometry. OSI is potentially capable of achiev­ing astrometric accuracies of", IJlas in narrow angle (10) astrometry. This paper discusses the implications for astrometric planet detection, specifically the detection of Earth-like planets around nearby stars. OSI has the potential to detect a limited number of planetary systems with Earths, if a number of technical problems are solved.

1. Introduction

Astrometry detects the presence of a planet by looking for the wobble of the star as the star and planet orbit about their center of mass. Because astrometry measures two coordinates of motion (versus radial velocity's one coordinate of motion) it has no undetermined orbital parameters such as orbit inclination. The astrometric signature of a Sun-Jupiter system is small compared to conventional astrometry with ground-based telescopes (or the HST) where accuracies of '" 1 mas (10- 3 arcsec) is possible. But the 0.5 mas amplitude of a Sun-Jupiter system at 10 pc is large compared to the 0.010 mas accuracies we expect with ground-based interferometers. In fact even Uranus-mass planets wit~O-year orbits (15 fLas = 15 X 10-6 arcsec) are easily detectable from the ground.

However an Earth-Sun system has a much smaller astrometric signature, 0.3 fLas, 1500 times smaller than Jupiter's signature. Additionally, for a solar­type star at 10 pc, 0.3 fLas is a motion that is only 0.03% of the diameter of the star. For comparison, star spots can shift the photocenter of the star by 0.1 - 0.2%, which is 3 - 6 times the size of the astrometric signature.

2. Number of Targets

If we ignore for now the star problem, we can estimate the number of Earths detectable for a given level of astrometric performance by conducting a com­puter search through the Gliese catalog of stars within 25 parsec. In search­ing for Earths, we assume that the Earth-like planet has a mass equal to the Earth and it is located a distance from the star such that the temperature of the planet would be the same as our Earth. The results of this search are summarized in Table 1. As can be seen, an accuracy of 1 fLas leaves very

Astrophysics and Space Science 241: 85-88, 1996. © 1996 Kluwer Academic Publishers.

86 MICHAEL SHAO

Table I Potential Target Stars in Astrometric Search

Astrometric Accuracy (fJas) Number of Targets

3 0 2 2 1 4

0.8 6 0.6 10 0.4 32 0.3 89 0.2 303 0.1 1167

few target for earth-like planets. The 1 /-Las prediction for OSI was based on the design of a 7m baseline space interferometer. We are currently exam­ining deployment technology developed by the Defense Department to fit a 20 meter interferometer into the launch shroud of a Delta-II rocket. With a 20m baseline, the potential narrow-angle astrometric accuracy is 0.3 fJas.

3. Systematic Error Models

Systematic errors in astrometric interferometers are directly related to the accuracy of the laser metrology used to monitor the geometry of the inter­ferometer. In the lab, we at JPL have demonstrated linear metrology with accuracy better than r'V 0.2 picometer. A laser 3D optical "truss" is used to measure the geometry of the instrument. An error propagation multi­plier (of value r'V 20) can be used to estimate the 3D accuracy from 1D measurement errors. The systematic error limit of a 20m interferometer is potentially 20 X 0.2 picometersJ20m. This is 2 X 10- 13 radians or r'V 0.04 /-Las; the corresponding 7 m interferometer has a potential accuracy of 0.1 /-Las. But this level of accuracy is so much higher than current technology (the Hipparcos mission has r'V 1 mas accuracy) that we don't really know what the true accuracy of the system will be in practice.

4. Star Spots

These levels of instrumental accuracy are also far smaller than the expected "astrophysical noise" due to star spots. A typical sunspot group occupies 0.001 ofthe surface ofthe Sun. At 10 pc, the presence of an 0.001 area spot at the limb of the sun will shift the photo center by 0.5 /-Las. Since the Sun rotates

ASTROMETRIC DETECTION OF EARTH-LIKE PLANETS WITH OS1 87

with a N 30 day period, if the Sun were observed from the pole, the presence of a planet with with a 30 day orbit would be astrometrically identical to a sunspot. It has been suggested that Fourier analysis can eliminate star spot rotation because planets have much longer orbital periods.

A couple of years ago, we would have said that we know planets have periods of 3 months to hundreds of years, and a I-month orbit would obvi­ously be a sunspot. But in the recent past, the astronomy community has been presented with evidence of planets with a 4 day orbit (51 Peg) and Jovian mass planets at distances from the star well inside the "ice conden­sation zone" where gas giant planets were not supposed to form. From an experimentalist's point of view it is best to devise an observation technique that does not depend on specific assumptions on how and where planets form. One partial solution to the star spot problem is two-color astrometry. Another solution is very high-resolution imaging.

4.1. HIGH-RESOLUTION IMAGING

The star spot is a problem only because the int~rferometer doesn't have the resolution to "see" the star spot. If a very high multi-pixel resolution image of the star were made, one could measure the center of mass of the star by looking at the edge of the star, ignoring the star spots. We can determine the location of the sun with much higher accuracy than 1/1000 of the diameter of the Sun. The edge of the Sun is measured with better than 0.003 arcsec accuracy, and the center of the Sun is easily known to better than one part per million. Resolving the stellar disk to 10 X 10 pixels may result in a factor of 10 improvement in astrometric accuracy due to star spots. For a solar type star at 10 pc, 10 pixels across the stellar disk implies a rv 500 meter baseline. Unfortunately such a long baseline is well beyond first-generation space interferometers.

4.2. TWO-COLOR ASTROMETRY

Star spots are areas of a star with high magnetic fields that interferes with convection of hot gas from the interior reaching the surface of the star. The spot is typically several hundred degrees cooler than the normal photosphere. Because the peak of the blackbody spectrum occurs in the visible part of the spectrum, a slight drop in temperature results in a large change in surface brightness. In the IR part of the spectrum, the surface brightness is only proportional to temperature. A 500 K temperature drop from 5700 K is a 15% change in surface brightness at 2.2 /Lm but a 36% drop at 0.55 /Lm. If the surface of the star can be modeled as a number of spots all at roughly the same temperature, the mei8urement of the position of the star at several wavelengths can be used to derive the true position of the star in the absence of star spots.

88 MICHAEL SHAO

In the above example, if we know the star spot was 500 K cooler, the apparent photo center is X = Xo + 0.15S at 2.2 f1m and the Y = Yo + 0.36S at 0.55 f1m. Measuring X and Y, the apparent position at two wavelengths, is sufficient to solve for both the true position Xo of the star as well as the position of the spot S. There is an error multiplier. The two-color position multiplies the random measurement noise by rv 5.

5. Summary

Astrometric detection of Earths with space-based interferometer is poten­tially possible for a significant number of nearby stars. But star spots are a major noise source that will require significant resources to overcome. One solution is a rv 500m interferometer to "image" the spots. Another is multi-color astrometry where accuracies a factor of rv 5 higher are needed to compensate the "error multiplier" incurred with multi-color observations. In this case, accuracy at the very limit of existing technology is needed to survey a substantial number of nearby stars for Earths. Astrometry however is the only known technique to measure the mass of the Earth-like planets.

Acknowledgements

The work described in this paper was performed at the Jet Propulsion Lab­oratory, California Institute of Technology under contract with NASA.

Panel discussion: left-to-right are Michael ShaD, Christ Ftadas, Robert Reasenberg, Roger Angel

ASTROMETRY FROM SPACE:

GAIA AND PLANET DETECTION

S. CASERTANO ESA/Space Telescope Science Institute

3700 San Martin Drive, Baltimore, MD 21218, USA

M. G. LATTANZI Osservatorio Astronomico di Torino

Strada Osservatorio 20,10025 Fino Torinese (TO), Italy

M. A. C. PERRYMAN Astrophysics Division, ESTEC

Noordwijk 2200AG, The Netherlands

A. SPAGNA Osservatorio Astronomico di Torino

Strada Osservatorio 20, 10025 Fino Torinese (TO), Italy

Abstract. The proposed baseline GAIA mission will be able to detect the astrometric signature of Jupiter-size planets around of the order of a million stars, using either global or narrow-angle astrometry. If the mission can realize the higher astrometric accuracy that photon statistics allows for bright stars, lower-mass planets (from Earth size to ten times larger) can be found around ten to a few hundred stars.

1. The GAIA mission concept and planet detection

GAIA (Global Astrometric Interferometer for Astrophysics) is a space-based astrometric mission currently being considered by the European Space Agen­cy for its Horizon 2000+ program, with a possible launch date around 2010-2015. The mission is intended as a survey of over 50 million stars, complete to V = 15 mag, with position and parallax accuracy of order of 10 /-las. Although the main goal of the proposed GAIA mission is a complete map­ping of the structure and kinematics of our Galaxy, its projected sensitivi­ty, accuracy, and coverage are such as to produce many valuable additional results, among which we will concentrate on its value in the search for extra­solar planets. Our discussion is mainly based on the detailed mission concept presented by Lindegren and Perryman (1995, 1996), although some possible modifications which would improve GAIA's capabilities for planet searches are also discussed.

The basic design consists of three imaging interferometers with a baseline of 2.45 m and primary apertures of 0.55 m each. The interferometers have a coherent field of view of about 1° each, positioned on the same great circle at separations of 54°, 78.5°, and 132.5°. The highest resolution is along the great circle containing the three fields of view, and the satellite spins so

Astrophysics and Space Science 241: 89-104, 1996. © 1996 Kluwer Academic Publishers.

90 S. CASERTANO ET AL.

as to scan that great circle in approximately 2 hours. The basic observing strategy is similar to that of Hipparcos, with a projected improvement of a factor of 100 in astrometric accuracy and sensitivity, and a factor of 1000 in the number of targets. The GAIA concept is currently in a dynamic state; see the proceedings of the recent Cambridge meeting (Perryman and van Leeuwen 1995) for a wealth of discussion of improvements and new ideas on science with GAIA, including the application to planet searches (Casertano et al. 1995).

A search for extrasolar planets would be accomplished with GAIA by the detection of the astrometric signature of a planet, as done from the ground (cf. Gatewood 1987). Detection involves observing the reflex motion of the star with respect to the barycenter of the star-planet system. The amplitude of this reflex motion depends on the orbital radius, the mass ratio, and the distance of the system. For a given mass ratio and distance, the astrometric signature grows with the orbital radius. Thus, more distant, slower-orbiting planets are easier to detect, a~ long as the orbit is sufficiently well~sampled during the length of the mission. In this regard, astrometric detection is com­plementary to the radial velocity method (see, e.g., McMillan et al. 1994), which is more sensitive to planets with small orbital radius and thus larger orbital velocity. A comparison of direct and indirect methods for planetary detection can be found in the TOPS report (Burke et al. 1993).

GAIA's projected accuracy and sensitivity are ideally matched to detect a large number of Jupiter-like planets around solar-type stars. GAIA should also be able to detect much less massive planets, down to a few Earth masses, around a few hundred stars. If technology advances are sufficient, Earth-like planets may in principle be detectable around 10-20 nearby stars.

A few extrasolar planets have now been detected from radial-velocity sur­veys, including a few around normal stars (Mayor and Queloz 1995; Marcy and Butler 1996; Butler and Marcy 1996) and around pulsars (cf. Wolszczan and Frail 1992). With continuing improvements, it is likely that Jupiter-like planets will also be found from ground-based astrometric studies in the next few years (cf. Pravdo and Shaklan 1996). Direct detection of giant planets is also possible from the ground in the next 5-10 years (see for example Burrows et al. 1995). Even so, space-based astrometrywith the precision of GAIA will push the search for planets into a new dimension. GAIA will improve the astrometric accuracy by a factor 50 at least-more for bright stars. This means a factor 50 in distance, or a factor over 105 in volume sur­veyed. Instead of a few cases, of order of 106 stars can be studied, making both the statistical properties (if planets are found) or the negative result (if none are) much more significant. Furthermore, astrometric detection yields complete information on the mass and orbital parameters of the planet. Thus, GAIA promises to find many such planets, with full knowledge of their mass and orbital parameters, and thus to provide very valuable infor-

ASTROMETRY FROM SPACE: GAIA 91

mation on the statistical properties of planetary systems and their formation process.

For simplicity, we restrict the following discussion to the case of a single planet orbiting a single star. Planets beyond the first will be more difficult to detect, and it will require much better signal-to-noise ratio. Binaries also create problems: the signature caused by a planet may be more difficult to identify in the presence of a much larger motion due to a stellar-mass com­panion, nor is it clear under which conditions planetary systems can form around non-isolated stars. We also assume that the orbit is well-sampled, and that there is no degeneracy with the parallax. We consider a planet "detectable" if the amplitude a of the astrometric signature (eq. 1 in § 3.1) is larger than three times the standard error alyr of the one-year normal point, namely the error accumulated in each coordinate of the star's posi­tion in one year of observations. We refer to this as the three-alyr criterion (eq. 2 in § 3.1). All the additional complications mentioned above can be sub­sumed into an "average detection probability", which will be a function of amplitude of the signature, orbital period, and mission parameters, and will reflect an average over properties such as ecliptic latitude (which determines the sampling law and the shape of the parallax ellipse), orbit inclination, eccentricity, and phase, and any other parameters that may be required to specify the orbit of the planet. Preliminary simulations appear to indicate that the three-alyr criterion may be somewhat conservative, which is appro­priate since there are numerous complications we do not consider. Because of all the uncertainties in both mission properties and detection process, the numbers presented here must be considered only as a first indication of GAIA's capabilities in the search for extrasolar planets.

2. Measurement accuracy

Individual observations of a star result in an image of its fringe system in the focal plane of one of the interferometers. The angular separation between this and other stars wIthin the same field of view can be determined by measuring the position of each star's fringe system. For stars observed by different interferometers, the basic angle between the interferometers must also be known to comparable accuracy; this information is crucial to the measurement oflarge-angle angular distances, and thus to GAIA's ability to perform global astrometry. While planetary searches can be performed within the scope of small-angle astrometry, the precision reached in this mode is ultimately limited by the availability of reference stars within the same field of view. The accuracy achieved in small-angle mode is comparable to what can be obtained in global astrometry with the conservative assumption that the baseline position remains constant to about 200 picometers (pm) (see

92 S. CASERTANO ET AL.

§ 2.2); this is adequate for Jupiter-like planets, but not for less massive objects. In global astrometry, the mode we will consider in the following, the accuracy obtained for a star is determined by both the error in measuring the position of its fringe system and the uncertainty in the basic angles at the time of the measurement.

2.1. PHOTON NOISE AND FRINGE MEASUREMENT

The ability to measure accurately the position of a star depends ultimately on the width and sharpness of fringe system and on the number of photons detected. For a well-sampled fringe system, the theoretical limit is shown by Lindegren (1978) to be f = )../( 41fX nnsv'N) , where X rms is the rms size of the aperture in the measurement direction. For two circular apertures of diame­ter D and with a central separation E, we have X rms = V(E /2)2 + (D /4)2; for the baseline GAIA parameters (E = 2.45 m, D = 0.55 m), X rms = 1.23 m (Lindegren and Perryman 1995, 1996). For ).. = 550 nm, this translates into a theoretical measurement accuracy of 7.3 mas/v'N.

However, this optimal measurement accuracy can only be achieved in the monochromatic case. For a Gaussian filter centered at 5500 A and 1500 A wide, the optimal measurement accuracy is about 12.0 mas/ VN, or a factor 1.6 worse. In addition, the requirement of optimal sampling may be difficult to achieve, since the central fringe is only about O'!04 wide and the field of view is 10 • In practice, this will probably cause a loss of accuracy of about 20-40% (see also Gai et al. 1995). In the following, we assume a "best reasonable" single-measurement accuracy of 16 mas/VN.

Since scans overlap partially, each "observation" of a star will consist of about 10 measurements, with a total integration time of 160 s. For a total collecting area 'of 0.475 m 2 per interferometer (2 apertures of 0.55 m diameter each) and a total system efficiency of 20%, a star with V = 15 would generate about 2.54 X 105 photons per observation, corresponding to a photon-limited measurement accuracy of the fringe position of 31. 7 fLas. The accuracy scales with the inverse square root of the flux. This accuracy is based on the photon statistics only, and does not take into account possible systematic effects, such as distortions in the optical system or in the detector, imperfection in the fringes, and so on. Many such systematic effects can be calibrated using closure methods, others will require careful consideration of how the system will eventually be built. However, the present treatment is adequate for an exploratory study.

2.2. BASIC ANGLE MEASUREMENT ACCURACY

The basic angles can be measured and monitored accurately over a full scan by making use of the 21f closure properties of the scan; the values of the

ASTROMETRY FROM SPACE: GAIA 93

angles have been chosen so as to optimize these closure properties. However, variations over shorter time scales need to be controlled by ensuring that the relative positions and shapes of all optical elements do not vary throughout the observation. The necessary sub-nm accuracy will probably be achieved by a combination of passive control and of laser metrology. For simplicity, we will summarize the accuracy with which the (relative) position of the baseline of each interferometer is known by a single number, the "baseline error" abase. For example, a baseline error of 1 nm translates into an error of 80 J-las in the relevant basic angle. While the main contribution to the baseline error will probably come from the relative position of the primary mirrors, any motion and/or distortion of an optical element can generate an effective baseline error.

Laser metrology has already achieved extremely high precision in the lab­oratory. Both the OSI team at JPL (Gursel 1993) and the POINTS team at efA (Noecker et al. 1993; Noecker 1995; Reasenberg et al. 1995a) have reported picometer-Ievel precision in relative measurements in a laboratory setting, where the limitation is fluctuations in air density in the path of the metrology laser beam. Such precision has ben reached over short (few wavelengths) variations in path length, which are appropriate to the GAIA design if a good active thermal control is included. (For comparison, Michel­son designs such as POINTS and OSI need to measure accurately much longer path lengths, because of the delay lines involved.)

However, the few pm error quoted refers to the precision and stability of a one-dimensional laser gauge measurement of a single optical path. Maintain­ing the accuracy of the interferometer baseline is much more complex, first, because the three-dimensional positions of many optical elements needs to be monitored simultaneously, and second, because of the possible differences between the optical path of starlight and of the laser gauge beams. Noecker (1995) lists a number of possible systematic errors for the POINTS mission concept. A similar study has yet to be carried out for the GAIA mission concept, but it is likely that controlling the interferometer baselines to a similar accuracy will prove similarly complex. Because of these uncertain­ties, it is difficult to give realistic figures for the baseline accuracy that will eventually be achieved. We consider two cases which probably bracket real­istic expectations: a "conservative" accuracy abase = 200 pm, which should be attainable relatively easily, and an "optimistic" accuracy abase = 20 pm, which probably will require significant investment in the technology of laser metrology early in the process. A baseline error of 200 pm translates into a basic angle error of 17 fLas per measurement, or about 5.3 fLas for a full observation (assuming that errors in successive passes are uncorrelated). A baseline error of 20 pm would translate into a basic angle error of 1.7 fLas per measurement, or 0.53 fLas for a full observation. Also, note that the accuracy specified by the "conservative" hypothesis can be achieved in narrow-angle

94 S. CASERTANO ET AL.

astrometry mode, and thus does not require any baseline monitoring for the purpose of planet detection.

Table I Photon and total error for single observation (10 exposures)

V mag Photon error Total error (flas) ( flas) {O"ba.se = 200 pm) (O"base = 20 pm)

0 0.032 5.3 0.53 1 0.050 5.3 0.53 2 0.080 5.3 0.54 3 0.126 5.3 0.55 4 0.20 5.3 0.57 5 0.32 5.3 0.62 6 0.50 5.3 0.73 7 0.80 5.4 0.96 8 1.3 5.5 1.4 9 2.0 5.7 2.1

10 3.2 6.2 3.2 11 5.0 7.3 5.1 12 8.0 9.6 8.0 13 12.6 13.7 12.6 14 20.0 20.7 20.0 15 31.7 32.2 31.8 16 50.3 50.6 50.3 17 79.7 79.9 79.7 18 126.4 126.5 126.4 19 200.3 200.4 200.3 20 317.5 317.5 317.5

2.3. TOTAL POSITIONAL ERROR; ONE-YEAR NORMAL POINT

In the absence of other significant systematic terms, the error of each position measurement is the combination of the photon error in the fringe position and the baseline error in the basic angle. In the "conservative" case, the fringe position error is more significant for V ~ 11 mag; in the "optimistic" case, fringe position error dominates for V ~ 6 mag. The combined full­observation errors for the two cases are given in Table I as a function of the brightness of the target.

The error in the one-year normal point, O"lyr, depends on the number of observations per year, which is a function of the ecliptic latitude: stars at high ecliptic latitude are observed more often. We assume a minimum of 6 observations per star per year. The error in each coordinate should then be approximately ..j276 = 0.58 times the single-observation error (the V2 at

ASTROMETRY FROM SPACE: GAIA 95

the numerator takes into account that each observation is one-dimensional, but two coordinates must be measured). The actual error will be somewhat larger, because of the errors in the measured parallax and proper motion; the contribution of these terms varies, and will impact the accuracy on different time scales in a different way. We adopt a factor 0.8 as a reasonable compromise. Therefore we estimate the error in the one-year normal point alyr to be 0.8 times the error listed in Table I, probably a conservative estimate especially at high ecliptic latitude.

3. Planet detection

As a survey mission, GAIA will be able to test for the presence of plan­ets around all stars within well-specified limits. We call "candidate" stars those around which a planet of given properties can be detected, if present. The number of candidate stars can be found from an understanding of the detection process and from the stellar luminosity function.

Detecting a planet around a candidate star requires a detailed study of the full time-series of observations of that star, similar to the solution for binary stars (Bernstein and Bastian 1995). Essentially, it requires extracting a significant periodic component, beyond that due to the parallax-which has a known period and shape-and modeling it in terms of a projected Keplerian motion. The ability to detect this motion obviously depends on its amplitude compared with the error in individual observations, but is likely to be a function also of ecliptic latitude, observing history, period, orientation, and phase of the orbit, as well as parallax and proper motion of the star. A complete simulation of the detection probability, as that carried out by Reasenberg et al. (1995b), should include the full detection process, from a simulated set of raw data through the solution for position, proper motion and parallax, and finally the fitting for the planet's properties.

Because of the exploratory nature of this study, we have adopted a more limited approach. We have identified a simple criterion, the three-alyr condi­tion, to define which stars are likely to be detected, and we have performed a limited set of simulations to verify that this simple criterion does in fact give reasonable answers. The criterion allows us to define a "maximum detection distance" for a given star-planet combination; from this, we can estimate the total number of candidate stars expected for a given set of planet prop­erties. We first discuss the three-alyr criterion, and then describe briefly the numerical simulations that justify it.

3.1. THREE-alyr CRITERION AND MAXIMUM DETECTION DISTANCE

The three-alyr criterion states that a planet is detectable if its astrometric signature, ex, which is half the maximum excursion of the star, is larger than

96 S. CASERTANO ET AL.

three times the error in the one-year normal point, O"lyr. This criterion is only useful in the average. Obviously, detect ability of individual planets will also depend on their orbital period, on the orientation and phase of the orbit, and on the time sampling obtained. However, on average, this is likely to be a conservative criterion, at least for planets whose orbits are well-sampled. This has been confirmed with simple numerical simulations (see § 3.2).

Let us see how the three-O"lyr criterion translates into a maximum distance at which a star-planet system of given intrinsic properties is detectable as a planet. The astrometric signature of a single planet of mass m p , orbiting at a radius Tp from a star of mass m s , which is at a distance D from the Sun will be

(1)

where the orbit is assumed circular (the maximum correction for an eccen­tricity e < 0.3 is less than 5%), Tp is measured in AU, and D is in pc.

For a given system, the astrometric signature decreases with increasing distance, while the measurement error increases as the star becomes fainter with increasing distance. Thus, we can define the "maximum detection dis­tance" Dmax as the maximum distance at which the three-O"lyr criterion for detection is fulfilled. Explicitly, given masses of star and planet, orbital radius, and absolute magnitude Mv of the star, the maximum detection distance Dmax is the solution for D of the equation

2.94 mp mra Tp = 3 X 0.8 [31.7 (D /10)lOo.2(MV-15)] 2 + O"£ase , { }1/2

mEB ms D 10 ,(2)

where the left-hand side is the astrometric signature a, and the right-hand side is thrice O"lyr (both in fLas), assuming a single-observation error of 31. 7 fLas for a star with V = 15 and a baseline error O"base. The factor 0.8 effects the conversion from single-observation measurement error to one-year nor­mal point, as discussed in § 2.3. In the following, we have assumed a relation between mass and absolute magnitude typical of main-sequence stars; a dif­ferent relation must be used for other evolutionary stages (giants, white dwarfs, etc).

3.2. DETECTION PROBABILITY AND SIMULATIONS

The three-O"lyr criterion can only be an approximate guide to planet detectabil­ity. In reality, the probability of detection is a function of both target physics (orbit size, orientation, phase, period, and so on) and mission parameters (such as life time and scanning law). One way of providing improved esti­mates of these detection probabilities for the GAIA concept is through

ASTROMETRY FROM SPACE: GAIA 97

Monte-Carlo simulations based on reliable models. A first step in this direc­tion has been attempted by simulating the detection process for a GAIA­like mission. The simulation consists of two separate parts: generation of the observations and analysis to identify the planets. So far, only a small fraction of the possible parameter space has been covered; the results give us con­fidence that the three-Ulyr criterion can be used as a reliable, conservative guide to planet detect ability.

3.2.1. Generating the observations The simulation code is an adaptation of that used by Galligani et a1. (1989) for the assessment of the astrometric accuracy of the sphere reconstruction in the Hipparcos mission. First, we generate a catalog of single stars randomly distributed on the sky; for the moment, parallaxes and proper motions, as well as magnitudes and colors, are drawn from simple distributions which do not represent any particular Galaxy model. Second, the satellite is made to sweep the sky according to a given scanning law; the spin axis precesses around the Sun at a rate of about 6.5 rev yr- 1 and with a constant angle of 43°. Stars that at any given time are "seen" within a strip 1° wide along the great circle being scanned are considered observed; a great circle is completed in about 2.5 hours. Basic measurements are the abscissae along a great circle, as GAIA, like Hipparcos, makes very precise measurements in one dimension only. The mission lifetime is set to 5 years and the scanning law is such that the number of basic observations per star is a function of ecliptic latitude.

The position of a star at a given time, as described by the combined effects of parallax and proper motions, is called here barycentric location and it has been described in Euclidean space. General relativistic effects, which will have to be considered in the future, are not taken into account. Finally, gravitational pertubations (Keplerian motions) induced by a nearby orbiting mass are added to the barycentric location resulting in the "true" geometric location of a target. Observations are generated by adding the proper astrometric noise to the true locations. The noise simulated is such that the typical yearly normal point (in the sense discussed above) has an accuracy of 10 fLas.

3.2.2. Astrometric Detection Detection here denotes a meaningful estimation, in the least squares sense, of all of the parameters describing the astrometric motion of a particu­lar star induced by a planetary-mass "companion" (eccentricity, semima­jor axis, inclination, period, initial phase, and so on). This is in contrast to "detection" criteria, in which only thresholding techniques are used to detect deviations from the astrometric signatures expected for a single star.

A preliminary simulation includes a sample of 23 stars distributed ran­domly on the sphere, each perturbed by a Jupiter-mass planets on a circular

98 S. CASERTANO ET AL.

orbit with a period of 2 years and amplitude such that the astrometric sig­nature a ~ 3CTlyr, where CTlyr is the rms error in the one-year normal point. In all cases, the three parameters characterizing the orbit (amplitude, peri­od and phase) can be retrieved correctly, and the convergence rate of the solution is high. When the signal to noise ratio aj CTlyr drops below 3, conver­gence appears slower, but we do not have a sufficient number of simulations to quantify this result.

Obviously, we need a more complete simulation, such as that carried out by the POINTS team (Reasenberg et al. 1995b )~including a blind test, non­circular orbits of arbitrary period and orientation, as well as independent solutions for parallax and proper motion~before we can be satisfied that our results are fully reliable. However, on the basis of our preliminary results, we conclude that the three-CTlyr criterion is sufficiently realistic, at least for orbits that are well-sampled, and provides a good (perhaps somewhat conservative) indication of which planets may be detectable.

4. N umber of candidate stars

The number of stars around which planets of given properties can be dis­covered can be estimated from the maximum detection distance, using the luminosity function observed for stars in the solar neighborhood. For each set of planet properties, identified by mass mp and orbital period P, and each absolute magnitude, Mv, the maximum detection distance can be com­puted from Equation (2), where the stellar mass ms is determined from the absolute magnitude using the mass-luminosity relation for main-sequence stars (see for example Mihalas and Binney 1981). The number of candidate stars is then obtained statistically from the main sequence luminosity func­tion, which we take from the lAS Galaxy Model (Bahcall et al. 1987). This luminosity function is derived from those of McCuskey (1966) and of Wie­len et al. (1983), with suitable separation into evolutionary sequences and density components. It has been used to represent successfully the observed properties of many different observations of nearby and distant star samples. It is certainly adequate for the present purpose. For distances smaller than 20 pc, the average stellar density predicted from the luminosity function should be replaced with the actual stars found, for example, in the Gliese catalog (Gliese 1969; Gliese & Jahreiss 1979) as significantly refined from the preliminary Hipparcos parallax results (Perryman et al. 1995). However, actual stars cannot properly be used unless the dependence of the detection probability on ecliptic latitude is assessed. This information will only be available after a full simulation of the planet search is carried out. There­fore, in this exploratory study, we consider only the average stellar density as determined from the luminosity function.

ASTROMETRY FROM SPACE: GAlA 99

,..... . a) aba.ellne = 200 pm b) aba.ellne = 20 pm 0

..s 103 103

(I)

0 ~ III

102 102 ~ fIl

:0 ~ .~ 10 10 ~ 0 (I) ~ Q)

"0 1

S 1

:::l S .--

'>< 0.1 0.1 to -5 0 5 10 15 -5 0 5 10 15 :::?1

Absolute V magnitude

Figure 1. Maximum detection distance as a function of the star's absolute V magnitude for conservative (left) or optimistic (right) baseline accuracy. The three lines refer to Jupiter-like (solid), Big-Earth (dashed), and Earth-like (dotted) planets respectively.

We consider three basic types of planets: "Jupiter-like", which have the same mass and orbital period as Jupiter; "big Earth", which have an orbital period equal to the Earth but a mass ten times larger, comparable to the rocky core of Jupiter; and "Earth-like", which are like the Earth in both mass and orbital period. Jupiter-like planets have the largest astrometric signature and are easiest to find; Earth-like planets have an astrometric signature smaller by a factor 1,500, and are very difficult to find. Big Earths are hard to find, but not as hard as true Earth-like planets. In each case, we keep the planet mass and orbital period constant as we change the mass of the star; this results in an astrometric signature that decreases as m;2/3 as the stellar mass increases. Different prescriptions, such as constant orbital amplitude and mass ratio, result in a different dependence on the mass of the star; the total number of candidate stars changes, but only slightly (about 20%).

The maximum detection distance is shown for the three types of planets in Figure 1a (conservative, abase = 200 pm) and Figure 1 b (optimistic, abase

= 20 pm). The number of candidate stars, estimated as described above, is shown in Figures 2a (abase = 200 pm) and 2b (abase = 20 pm). In each figure, the solid line corresponds to Jupiter-like planets, the dashed line to big-Earth planets, and the dotted line to Earth-like planets.

100 S. CASERTANO ET AL.

a) abasellne 200 pm b) aba.eline 20 pm

107 ~""""~~"""~ 107 ~"TT"""rr"TT"~

106

105

o 5

106

105

10

1 LLLLLLLL~~~~~~U 10 15 -5 o 5 10 15

Absolute V magnitude

Figure 2. Cumulative number of candidate stars as a function of the star's absolute V magnitude for conservative (left) or optimistic (right) baseline accuracy. The three lines refer to Jupiter-like (solid), Big-Earth (dashed), and Earth-like (dotted) planets respectively.

4.1. CASE 1: JUPITER-LIKE PLANETS

Jupiter-like planets have a relatively large astrometric signature-SOO }.las at 10 pc for a solar mass star. Even with the conservative baseline accuracy of 200 pm, Jupiter-like planets can be detected to over 200 pc for solar-type stars. For example, a solar mass star has V '"" 11 mag at 200 pc, thus an error on the one-year normal point of'"" 7 }.las. At that distance, the astrometric signature is about 25 }.las, over three times the one-year normal error. Since the maximum detection distance corresponds to relatively faint stars, for which the photon error is dominant, an improvement in the baseline accuracy does not increase the maximum detection distance significantly (Figure 1 b).

The total number of candidate stars is rv 8 X 105 for baseline accuracy 200 pm, and about a factor 2 larger for baseline accuracy 20 pm (Fig. 2). Both numbers may be slightly overestimated, by about 20%, because of the assumption of constant stellar density away from the Galactic plane. The large number of candidate stars promises a very clear answer to the ques­tion of the frequency of Jupiter-like planets and their distribution of their properties with respect to those of the central star. The detection margin is large enough that numerous multiple-planet cases should be observable as well.

ASTROMETRY FROM SPACE: GAIA 101

4.2. CASE 2: BIG-EARTH PLANETS

This case is somewhat artificial, and is included to bridge the gap of three

orders of magnitude between between the astrometric signatures of Jupiter­like and Earth-like planets. The orbital period is 1 year, and the mass of 10 Earth masses corresponds approximately to Jupiter's rocky core. The astrometric signature at 10 pc is about 3 IJ,as, a factor of 150 less than for Jupiter-like planets. As a consequence, such planets can only be detected around only nearby stars. Since such stars are typically (apparently) bright, the measurement error is dominated by the baseline error, and the two cases offer substantially different results.

The maximum detection distance is very small with the conservative base­line error (200 pm)-at most 5 pc for stars with Mv rv 12 mag (Fig. 1a), for a total of about 20 candidates. In the "optimistic" case of baseline error 20 pm, however, the maximum detection distance increases to over 17 pc for

solar-mass stars (Fig. 1b), for a total of over 300 candidate stars (Fig. 2b).

4.3. CASE 3: TRUE EARTH-LIKE PLANETS

The considerations made for big-Earth planets apply a fortiori to true Earth­like planets. Even with abase = 20 pm, such planets, which have an astromet­ric signature 10 times smaller than big-Earths, cannot be detected beyond 1-2 pc. Therefore, no suitable candidates exist. A further improvement of a factor of 5-10 in the baseline accuracy would push the detection distance to about 6-10 pc for solar-mass or slightly more massive stars, and yield 10-20 candidates. This level of accuracy implies also the ability to push the fringe measurement to its photon limit for very bright stars (V rv 5 mag) for a single-measurement accuracy of 1 }.Las or better. This will require very good control of all systematic effects, as the fringe position must be measured to 10-5 of its width. Therefore, detection of a small number of candidate Earth­like planets with GAIA appears very difficult, but perhaps not impossible with sufficient interest and expenditure of technical effort.

5. Discussion

It is clear that the current GAIA mission concept (Lindegren and Perry­man 1995, 1996) will be capable of detecting Jupiter-like planets around rv 106 candidate stars. This exceeds the likely output of any existing or proposed program, regardless of the technique employed, space- or ground­based. Unlike other techniques, such as microlensing, astrometric detection of a planet provides full knowledge of the mass and orbital parameters of the planet. If Jupiter-like planets are common, GAIA will produce a large dataset of planetary systems, which will be invaluable for any statistical

102 S. CASERTANO ET AL.

discussion of the frequency, formation, and properties of planetary systems around normal stars. Questions such as the possible correlation between mass of the star and of the planet, the distribution of major axis, orbit ori­entation with respect to the rotation of the star, and the isotropy and eccen­tricity distribution of the orbits, all need large samples with good quality information. A significant number of cases will have sufficient signal that a second giant planet may be detectable as well.

On the other hand, should Jupiter-like planets prove to be uncommon, the GAIA results, covering a large number of stars of diverse spectral types and properties, will be even more important in characterizing where and how often such planets form. The presence of gas giants in a planetary system may be relevant not only to its formation process, but also to the likelihood of the development of life on any terrestrial planets in the same system, as they can act as a shield against an excessive rate of destructive comet hits.

Astrometric detection of less massive planets with GAIA will require special attention to the accuracy with which the position of the baseline of each interferometer can be monitored over time scales shorter than the spin period. This information is essential to remove any time-dependence in the basic angles between the interferometers, which are used in the global sky reconstruction. An equivalent baseline accuracy of about 20 pm, corre­sponding to an uncertainty in the basic angle of 1. 7 /Las, is required in order to observe effectively a few hundred big-Earths (planets in Earth-like orbits but 10 times as massive). Observations of true Earth-like planets will only be possible with very accurate baseline monitoring (at the few pm level), and even then only for 10-20 stars. These results assume that a signal-to­noise of order 3 in one year is sufficient for detection; preliminary numerical simulations indicate that this may be a conservative assumption.

A caveat is in order regarding the possibility of detecting low-mass planets via their astrometric signature, namely the possible presence of astrophysical "noise" in the photocenter position of the target star. For example, starspots that shift the photocenter by 10-4 stellar radii would produce a signal com­parable in amplitude to that of an Earth-like planet, although with a very different period. This is not unlikely for the Sun, and starspots may be even more prevalent for cooler stars. The main periodicity in the signal pro­duced by such distortions would be the same as the stellar rotation period, but other, much longer periods may appear with lower amplitude. Intrinsic irregularities in the photo center position due to photospheric asymmetries may well set the ultimate limit to astrometric planet detection. Similar con­straints apply to other indirect methods (spots and low-level variability to transits, stellar oscillations and pulsations to radial velocity measurements).

While our results are still preliminary and await a full study of the plan­et detection process, they clearly indicate the double strength of a high­accuracy survey mission like GAIA: the ability to find many objects of the

ASTROMETRY FROM SPACE: GAIA 103

Jupiter class, and a few objects requiring extremely high accuracy. They also indicate the need to place the appropriate emphasis on the development of the technical aspects of baseline monitoring, which are crucial in order to realize the full photon-limited measurement accuracy for bright targets.

References

Bahcall, J. N., Casertano, S., and Ratnatunga, K U.: 1987, ApJ 320,515 Bernstein, H., and Bastian, U.: 1995, 'Finding planets and brown dwarfs with GAIA', in

Future possibilities for astrometry in space, ed. M. A. C. Perryman and F. van Leeuwen, ESA SP-379, p. 55

Burke, B. F., et al.: 1993, TOPS: Toward Other Planetary Systems, NASA publication Burrows, A., Saumon, D., Guillot, T., Hubbard, W. B., and Lunine, J. I.: 1995, Nature

375,299 Butler, R. P. and Marcy, G. W.: 1996, 'A Planet Orbiting 47 Ursae Majoris', Astrophysical

Journal, Letters to the Editor 464, L153 Casertano, S., Lattanzi, M. G., and Perryman, M. A. c.: 1995, 'Astrometric detection

of extra-solar planets with GAIA', , in Future possibilities for astrometry in space, ed. M. A. C. Perryman and F. van Leeuwen, ESA SP-379, p. 47

Galligani, I., Lattanzi, M., Bucciarelli, B., Tommasini, T., and Bernacca, P. 1.: 1989, 'General and Numerical Approach to the Sphere Reconstitution in FAST', ESA SP-1111, Vol. III, p. 141

Gatewood, G.: 1987, Astronomical Journal 94, 213 Gai, M., Lattanzi, M. G., Casertano, S., and Guarnieri, M. D.: 1995, 'Non-conventional

detector applications for direct focal plane coverage', in Future possibilities for astrom­etry in space, ed. M. A. C. Perryman and F. van Leeuwen, ESA SP-379, p. 231

Gliese, W.: 1969, Ver. Heidelberg Astron. Recheninstitut Nr. 22 (Karlsruhe) Gliese, W., and Jahreiss, K: 1979, Astron. & Astrophys. Suppl. 38, 243 Gursel, Y.: 1993, in Proc. SPIE 1947, Spaceborne Interferometry, ed. R. D. Reasenberg,

p.188 Lindegren, 1.: 1978, in IA U Coil. 48, Modern Astrometry, ed. F. V. Prochazka and

R. H. Tucker, p. 197 Lindegren, L., and Perryman, M. A. c.: 1995, 'The GAIA concept', in Future possibilities

for astrometry in space, ed. M. A. C. Perryman and F. van Leeuwen, ESA SP-379, p.23

Lindegren, 1., and Perryman, M. A. C:: 1996, 'GAIA: Global Astrometric Interferometer for Astrophysics', Astron. & Astrophys. Suppl. 116, 579

Major, M. and Queloz, D.: 1995, 'A Jupiter-mass companion to a solar-type star', Nature 378,355

Marcy, G. W. and Butler, R. P.: 1996, 'A Planetary Companion to 70 Virginis', Astro­physical Journal, Letters to the Editor 464, L147

McCuskey, S. W.: 1966, in Vistas in Astronomy, Vol. 7, ed. A. Beer, p. 141 McMillan, R. S., Moore, T. L., Perry, M. 1., and Smith, P. H.: 1994, Astrophys. & Space

Sci. 212, 271 Mihalas, D. and Binney, J.: 1981, Galactic Astronomy (San Francisco: Freeman), p. 113 Noecker, M. c.: 1995, in Proc. SPIE 2477, Spaceborne Interferometry II, in press Noecker, M. C., Phillips, J. D., Babcock, R. W., and Reasenberg, R. D.: 1993, in

Proc. SPIE 1947, Spaceborne Interferometry, ed. R. D. Reasenberg, p. 174 Perryman, M. A. C., et al.: 1995, Parallaxes and the Hertzsprung-Russell Diagram from

the Preliminary Hipparcos Solution H30, A, in press Perryman, M. A. C., and van Leeuwen, F.: 1995, Future possibilities for astrometry in

space, proceedings of an ESA/RGO workshop, ESA SP-379 Pravdo, S. H., and Shaklan, S. B.: 1996, Astrophysical Journal 465, 264

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Reasenberg, R D., Babcock, R W., Murison, M. A., Noecker, M. C. Phillips, J. D., and Schumaker, B. 1.: 1995a, in Proc. SPfE 2477, Spaceborne fnterjerornetr·y II, in press

R.easenberg, R. D., et al.: 1995b, paper presented at this meeting Wielen, R, Jahreiss, H., and Kruger, R: 1983, in fA U Call. 76, The Nearby Stars and

the Stellar Luminosity Function, ed. A. G. D. Philip and A. R Upgren (Schenectady: 1. Davis Press), p. 163

Wolszczan, A., and Frail, D. A.: 1992, Natu.re 355, 145

Hal Levison

Christ Ftaclas (L) and Robert Reasenberg (R)

GROUND-BASED INTERFEROMETRY

MICHAEL SHAO Jet Propulsion Laboratory, California Institute of Technology

Abstract. This paper summarizes the limits of ground-based interferometry for differen­tial astrometry as well as ground-based interferometry for direct detection of exo-planets and exo-zodi dust levels. For direct detection, ground-based interferometry at near IR wavelengths using large telescopes with adaptive optics offers a significant advantage over single telescopes with adaptive optics. Ground-based differential astrometry for exo-planet detection is extremely accurate with sufficient accuracy to detect Neptune mass planets around 400 - 600 nearby stars. Ground-based interferometry using large (>6m) telescopes is also capable of detecting the 10 pm emission of the zodiacal light around nearby stars with zodi levels similar to our solar system

1. Introduction

The original title of the talk was "Ground-Based Interferometric Imaging". Because the topic of interferometric astrometry was not covered by H. McAl­ister in his ground-based astrometry talk, a brief summary of what ground­based astrometry is capable of is included here. The topic of this paper is ground-based interferometry with three subtopics: (1) differential astrome­try; (2) interferometric imaging of planets in the near-IR; and (3) interfero­metric detection of exo-zodi levels at 10 p,m.

Differential astrometry is a technique for detecting the wobble of a star due to the presence of an orbiting planet. This topic has been described in several papers (Shao & Colavita 1992; Colavita 1994). The basic principle will be reviewed in the next section, and extrapolation of previous work to an ultimate ground-based instrument is discussed.

In ground-based imaging, the history is more convoluted. The idea for direct detection of warm (250 K) Jupiter-sized planets was discussed by Shao in the TOPS report. A number of people discussed the use of adaptive optics on large telescopes to detect Jupiter sized planets around nearby stars (Nakajima 1994; Angel 1994). What is described here is a variation ofthe use of adaptive optics (AO) with large telescopes. For direct detection of planets, the technique is to use an AO / coronagraph on each of two large telescopes and then combine the light to form an interferometer. The advantages of this technique over the use of a single telescope are discussed.

The long range goal of detecting Earth-like planets around other stars is most easily met by a space-based IR interferometer in the 10 p,m band. One of the most serious problems for this type of IR interferometer is the dust in the target solar system which if it is like ours, would be hundreds of times brighter than an Earth-like planet. The exo-zodi problem, as it has corne to

Astrophysics and Space Science 241: 105-11 0, 1996. © 1996 Kluwer Academic Publishers.

106 MICHAEL SHAO

Table I Astrometric Search for Planets: 100m 2 p,m Mauna Kea Interferometer

Planet mass p,as at 10 pc

1 Jupiter 1000 1/30 Jupiter 30

Distance at 10 p,as

1 kpc 30 pc

Stars/Volume

be called, could increase the required interferometer baseline and collecting aperture by as much as a factor of two. Fortunately, the detection of this exo-zodi is possible on the ground using large telescopes with AO operated as a nulling interferometer. This is described in the fourth section of the paper. While not theoretically impossible, the direct detection of Earth-like planets from ground-based interferometers is exceedingly unlikely. This is discussed in the last section.

2. Differential Astrometry

The basic premise of differential astrometry is that, when two stars are very close together on the sky ( < 20 arcsec), the differential image motion from a long baseline interferometer is extremely small. As little as five years ago it was thought the atmospheric limit for astrometry was on the order of 1 mas (10-3 arcsec). Shao & Colavita (1992) explain the theoretical calculations that led us to predict the possi bili ty of doing 10 - 20 p,as (10-6 arcsec) differential astrometry from the ground.

Since then, several developments have led us to revise that estimate towards higher accuracy. The events are the measurement of a very short outer scale at the Keck Observatory using a seeing camera that measured tip/tilt over the 10m aperture. The second event was a similar measurement of a small outer scale using the recently constructed 110m IR interferometer at Palomar Mountain. In 1-arcsec seeing, typical good seeing at Palomar, the expected image motion for a 100m baseline interferometer is f"V 175 mas. The measured image motion due to the atmosphere was'" 35 mas, about a factor of 5 smaller.

From this, we conclude that the predictions in the 1992 paper were pes­simistic, perhaps by a factor of 3 - 4. For a f"V 100 m baseline interferometer on Mauna Kea, we would expect that the atmospheric limited accuracy for differential astrometry might be as low as 5 - 7 /-las in a 1 hr integration time. To put this in the context of exo-planet detection, Table 1 lists the distance at which a Sun-Jupiter and Sun-Uranus with 12-yr orbits could be detected.

The accessible volume, even for Uranus-mass planets, contains so many stars that the actual number observed will be limited by the available observ-

GROUND-BASED INTERFEROMETRY 107

ing time. If we observe each star four times per year and assume that 2000 hrs of observing time are allocated for exo-planetary searches, the search list is '" 500 stars.

3. Ground-Based Direct Detection with Interferometry

There are two scientific goals that can be successfully attacked with ground­based interferometry: (1) direct detection of Jupiter and Saturn-sized planets (at Jupiter's distance) around nearby stars; and (2) detection and charac­terization of exo-zodical dust around nearby stars.

Direct detection of a planet is technically challenging because the parent star is so much brighter than the planet. At a contrast ratio of a billion to 1, some technique is needed to suppress the light of the star so that the planet can be detected. In an 8m-class imaging system, the star's image will have diffraction rings, and close to the star ('" 0.5 arcsec) the diffraction rings may be several hundred thousand times brighter than the planet. A coronagraphic instrument behind the telescope can eliminate most of the diffracted light, sufficient to detect a planet the size of Jupiter.

For a ground-based telescope however in addition to diffracted light, there is light scattered by the phase fluctuations in the atmosphere. Adaptive optics can be used to compensate much of the error due to atmospheric turbulence. This technique is described in greater detail by another paper at this conference. The resulting image will consist of a diffraction limited spike plus a "halo". At the location of the star, the halo background is easily calculated. The extent of the halo is proportional to liN where there are N actuators across the diameter of the telescope in the adaptive optics system. The integrated light of the halo is I-Strehl. We take an '" 8 m telescope with a 25,000-actuator "hyper" adaptive optics system as an example.

The actuator (as projected on the primary) is 5 cm; the halo will have a diameter of '" 4 arcsec (at 1.1 f.lm). If the Strehl ratio of the AO system is 98%, the integrated light in the halo is 2% of the light of the star. If the telescope's diameter is 8m, the surface brightness of the halo is about 1 million times lower than the stellar peak, and about 1000 times brighter than the planet. The halo is not static but varies as the atmospheric turbulence changes. Typically the fluctuations have a 100% peak-to-peak amplitude; every millisec or so, any given pixel will vary by an RMS value", 300 times larger than the planetary signal. If we wish to detect the planet with a SNR = 5, this fluctuation must be averaged down by a factor of 1500. This would require about 1 hr of integration time.

Speckle noise as described is just one source of noise. Photon fluctuations of the halo background is another. For an ideal AO system the level of photon noise is roughly equal to the level of speckle noise. However there

108 MICHAEL SHAO

will likely be fixed pattern errors or slowly varying patterns in the speckle pattern that will mimic the presence of planets.

The application of interferometry essentially eliminates speckle noise as a significant noise source. With speckle elimination, it becomes possible to detect planets with a less-perfect AO system or to detect a larger number of planets. The reasoning goes as follows. With a less-perfect AO system the "halo" gets brighter. An increase in the halo brightness by a factor of N results in an increase in the "speckle" noise by N and an increase in the photon noise by a factor of VIV. A less-perfect AO system (lower than 0.98 Strehl) would push speckle noise up faster than photon noise, making speckle noise dominate over photon noise.

3.1. ELIMINATION OF SPECKLE NOISE WITH INTERFEROMETRY

The type of interferometer being envisioned combines the light from two large 8-10 m telescopes, after the light has been corrected by a Hyper AO system and the starlight has been severely attenuated with a coronagraph. The images from the two telescopes are then combined coher~ntly in a focal plane. Because of the high resolution of the interferometer, an 85m inter­ferometer would have a fringe spacing of 2.7 mas. A typical planet would be ",0.5 arcsec from the star, 187 fringes away from the central fringe of the star. The fringe pattern in the speckle pattern would lack temporal coherence and would have much lower visibility. Depending on the spectral bandpass of the interferometer, the reduction in visibility would change, but for a 0.2 fraction bandpass the fringe visibility would be attenuated by at least 1/1872 ~ 0.00003. With speckle noise reduced by this factor, photon noise would dominate at all times.

4. Exo-Zodi Survey with Large Ground-Based Interferometers

The zodicial dust around another star will emit 10 J-lm radiation that is much brighter than the 10 J-lm emission of the planet. This dust emission is spread over an angular extent of '" 1 arcsec. With high angular resolution imaging, the 10 J-lm flux per pixel from the dust can be made smaller than the flux from the planet. The amount of dust in other stellar systems sets the size of the interferometer needed to detect an Earth-like planet.

The basic technique is to measure an IR excess in the starlight. However, for a zodi disk similar to our solar system, the IR excess is very small. Interferometry is used for 2 reasons: one is to null out the starlight, and the second is to provide sufficient angular resolution so that one can exclude light directly from the star.

At 10 J-lm, an 8m telescope has a diffraction-limited resolution of 0.25 arcsec. We are interested in the 10 J-lm emission ~ approximately 0.5 arcsec

GROUND-BASED INTERFEROMETRY 109

Table II Direct Search for Earth-like Planets

Location Diameter Time SNR

Ground 1 10m 10 hr 0.1 Ground 2 10m 75,OOOhr 10 Ground 3 150m 2hr 10

Space: 1 AU 6.0m 2.5hr 10 Space: 5 AU 1.5m 2.3hr 10

or one Airy ring from the star. If we can null the light by 99% at 10 /Lm, and the surface brightness of the first airy Airy ring is "'-'2% the brightness of the star, the diffracted starlight would be attenuated by 2 X 10-4 and at 10 /Lm the dust emission would only be a factor of rvlliower. With a high degree of starlight nulling, detection of a solar system-level of zodi dust would only require our ability to model the blackbody radiation of the parent star to 10%. At 5 /Lm the dust would have an IR excess less than 3 X 10-4. Imaging the system at several thermal IR wavelengths, along with interferometric nulling of the star, will enable us to measure the dust to "" 1 solar zodi level.

5. Direct Detection of Earths from the Ground

This is really not yet possible, but it is included to illustrate the difficulty of the problem. In space a nulling interferometer is needed to null the starlight to "'-' 10-6 . On the ground, the time-varying atmosphere will limit nulling performance to 10-2 at 10 /Lm. The other disadvantage of a ground-based observatory at 10 /Lm is the thermal emission of the optics and atmosphere. Table 2 compares a space-based system with a ground-based system. The baseline of the interferometer is assumed to be large enough in both cases to resolve the planet from the zodi. The assumed planetary system is an Earth-Sun system at 15 pc. The ground-based systems are assumed to have an emissivity of 5% at 275 K.

With the largest telescopes currently in existence, integration times of ",,20 yr are needed on 1 planet to get a SNR = 10. To get the integration time down to "'-'2 hr, typical of a space based system, the collecting area must increase to 40,000 m 2 .

Acknowledgements

The work described in this paper was performed at the Jet Propulsion Lab­oratory, California Institute of Technology under contract with the National Aeronautics and Space Administration.

110 MICHAEL SHAO

References

Angel, J. R. P.: 1994, "Ground-based imaging of extrasolar planets using adaptive optics", Nature 368, pp. 203-207

Colavita, M. M.: 1994, "Measurement of the Atmospheric Limit to Narrow-Angle Interfer­ometric Astrometry using the Mark III Stellar Interferometer", Astron. & Astrophys. 283, pp. 1027-1036

Nakajima, T.: 1994, "Planet detectability by an adaptive optics stellar coronagraph", ApJ 425, pp. 348-357

Shao, M. & Colavita, M. M.: 1992, "Potential of Long-Baseline Infrared Interferometry for Narrow-Angle Astrometry", Astron. & Astrophys. 262, pp. 353-358

Shao, M., & Colavita, M. M.: 1992, "Long-Baseline Optical and Infrared Stellar Interfer­ometry", Ann. Rev. Astron. Astrophys. 30, p. 457-498

Wesley Huntress (L) end Bernie Burke (R)

FRESIP: A MISSION TO DETERMINE THE

CHARACTER AND FREQUENCY OF EXTRA-SOLAR

PLANETS AROUND SOLAR-LIKE STARS

W. J. BORUCKI, E. W. DUNHAM and D. G. KOCH NASA Ames Research Center, Moffett Field, CA 94035

W. D. COCHRAN Univ. of Texas, Austin, TX 78712

J. D. ROSE Univ. of North Carolina, Chapel Hill, NC 27599

D. K. CULLERS, A. GRANADOS and J. M. JENKINS SETI Institute, Mountain View, CA 94043

Abstract. FRESIP (FRequency of Earth-Sized Inner Planets) is a mission designed to detect and characterize Earth-sizes planets around solar-like stars. The sizes of the planets are determined from the decrease in light from a star that occurs during planetary transits, while the orbital period is determined from the repeatability ofthe transits. Measurements of these parameters can be compared to theories that predict the spacing of planets, their distribution of size with orbital distance, and the variation of these quantities with stellar type and multiplicity. Because thousands of stars must be continually monitored to detect the transits, much information on the stars can be obtained on their rotation rates and activity cycles. ObservationS of p-mode oscillations also provide information on their age and composition. These goals are accomplished by continuously and simultaneously monitoring 5000 solar-like stars for evidence of brightness changes caused by Earth-sized or larger planetary transits. To obtain the high precision needed to find planets as small as the Earth and Venus around solar-like stars, a wide field of view Schmidt telescope with an array of CCD detectors at its focal plane must be located outside of the Earth's atmosphere. SMM (Solar Maximum Mission) observations of the low-level variability of the Sun (",1:100,000) on the time scales of a transit (4 to 16 hours), and our laboratory measurements of the photometric precision of charge-coupled devices (1:100,000) show that the detection of planets as small as the Earth is practical. The probability for detecting transits is quite favorable for planets in inner orbits. If other planetary systems are similar to our own, then approximately 1% of those systems will show transits resulting in the discovery of 50 planetary systems in or near the habitable zone of solar-like stars.

1. Brief History

Over the centuries, much philosophical, religious, and scientific thought has been given to the possibility that other habitable or inhabited worlds exist. The intense popular interest surrounding Percival Lowell's work a century ago and the publicity surrounding the recent discoveries of planets orbiting solar-like stars as well as pulsars all testify to the continuing depth and breadth of this interest. We live at a singular moment in history in which it is has become possible for the first time to detect planets orbiting other

Astrophysics and Space Science 241: 111-134, 1996. © 1996 Kluwer Academic Publishers.

112 W. J. BORUCKI ET AL.

star. A key step toward settling the question of the existence of other life in the U ni verse.

Recent discoveries have brought several surprises. Roughly Earth-mass planets have been found in orbit about two pulsars: PSR B1257+12 (Wol­szczan 1994) and PSR B0329+54 (Shabanova 1995). The violent explosions that produced the pulsars were not expected to be conducive to the forma­tion or survival of planetary systems. Hence, the discovery of planets around pulsars implies the existence of robust physical processes that readily lead to the formation of planets. However, because the supernova events that gave rise to these planets are so different from the processes that gave rise to our solar system, it is difficult to generalize from the pulsar observations to the formation of planetary systems like our own.

A second surprise is the discovery of approximately Jovian-mass plan­ets in inner orbits about several G dwarf stars (Mayor and Queloz, 1995; Marcy and Butler, 1996). Not only do the discoveries show that our solar system is not unique in having massive planets, but they suggest that oth­er planetary systems are likely to be significantly different than our own. Previously, only models of planetary system evolution that reproduced the characteristics of the solar system were considered useful. Now that several stars have been found with a massive planet well inside both the "ice zone" and the zone expected to account for the accretion of the rocky planets, it is clear that a substantial range of "initial conditions" and/or evolutionary histories must exist to explain the observations. It is no longer necessary to constrain all model parameters to insure that the model produces only planetary systems similar to the solar system. Preliminary results based on the presence of massive accretion disks and the coupling of planets to such disks (Lin, Bodenheimer, and Richardson 1996) suggest the possibility that planet formation and evolution in some accretion disks lead to a series of planets forming and moving inward toward the central star. Only those plan­ets survive that have not fallen into the stellar envelope at the time the disk is cleared. These results suggest the possibility that Earth-like planets might be absent in those disks with massive inner planets.

The current theory for the formation of our solar system, the Sun, and its planets, postulates that they developed from an accretion disk formed from the collapse of a portion of a giant molecular cloud (Cameron, 1988; Shu et al., 1993). This theory also implies that planets form concurrently with most stars. Studies of stability in many-body systems indicate that most single stars, and many binary stars are expected to have planets (Lissauer, 1995). The numerical modeling of Wetherill (1991) shows that the accumulation of planetesimals after molecular cloud collapse can be expected to produce several inner planets similar to those found in the solar system. Although his results predict substantial variability in both the number and size of the planets, they often predict that two of the planets are approximately Earth-

THE FRESIP MISSION 113

sized and that two are smaller. His results indicate that the positions of the Earth-sized planets can be anywhere from the position of Mercury's orbit to that of Mars. Therefore, a search for Earth-sized planets should cover this orbital range.

The calculations of Boss (1995) indicate that temperatures in the inner portion of the accretion disk are nearly independent of the stellar mass, but are instead controlled by the disk properties. Further, even variation of the assumed disk mass from 0.01 to 0.1 of the star's mass makes little difference in the location of the ice condensation radius and thereby the orbital distance for the formation of the giant planets. If the model is correct, then the inner planets as well as the giant outer planets should form at distances independent of the stellar and accretion disk masses. During or after their formation, angular momentum is lost to the disk and the orbital radii decrease. With the recent observations of giant inner planets around G dwarfs, this result demonstrates the need to search the region of short-period orbits.

For stars like our Sun, inner-orbit planets are likely to be the only ones to have conditions conducive to the development of life in what is referred to as the habitable zone. Figure 1 shows the habitable zone as calculated by Kasting, Whitmire, and Reynolds (1993) for main-sequence stars as a function of spectral type. The habitable zone shown here is bounded by the range of distances from a star for which liquid water would exist and by the range of stellar spectral types for which complex life had enough time to evolve (no earlier than F) and for which stellar flares and atmospheric condensation due to tidal locking do not occur (no later than K). A chapter in this volume by Kasting provides further detail. Thus, FRESIP will explore the zone with orbital periods between 0.2 to 2 years (Mercury to Mars) for stars of spectral type FO to K5.

However, if our ideas regarding the formation of the solar system are wrong, then the measurements would show few to no inner planets around solar-like stars or show different distributions of size and position than pre­dicted. Even a null result would be significant, as it would indicate that our understanding of planetary formation must be revised and that Earth-sized planets must be rare in our Galaxy.

2. Goals Of The FRESIP Program

While most proposed planet detection methods are sensitive to giant plan­ets, FRESIP presents a practical way to detect small inner planets the size of the Earth or Venus, to determine the sizes of the planets and the charac­teristics of their orbits, and to identify those stars that should be monitored by Doppler velocity and astrometric systems to make further measurements.

114

B

10

W. J. BORUCKI ET AL.

.. a a

Planetary Orb' ": Ital Period (Y a a r)

Pulsar System x xx

."t:: I -e 01, Habitable Zone

(Kasting, Whitmire and Reynolds. 1993)

Terrestrial Accretion Zone (Weth<eri!l.1991)

0.1 I I I 11111 I I II! III I I "'111 I I 111111 I I "'111

0.001 0.01 0.1 10 100

Stellar Radii and Planetary Orbital Semi-Major Axis (A.U.)

Figure 1. Relationship of stellar proerties to the habitable zone and planetary systems. Each main-sequence spectral type B, A, F, G, K, M is plotted to indicate its mass and radius on the left side of the diagram. The Terrestrial Accretion Zone and Habitable Zone are indicated. The planets in our solar system and in the B1257+12 pulsar system are shown. The scale for planetary orbital periods, based on stellar mass and orbital radius, is also indicated.

Specifically, the scientific goals and objectives of this mission are to:

Determine the frequency of Earth-sized and larger planets in inner orbits around solar-like stars Determine the distributions of size and radial position of these planets Determine the properties of those stars found to have planetary systems Estimate the frequency of planets orbiting multiple-star systems Provide critical information on the distributions of planetary size and orbital periods for development and testing of models of planetary sys­tem formation

Rosenblatt (1971), Borucki and Summers (1984), Borucki et al. (1985), and Schneider and Chevreton (1990) have discussed several approaches for using high-precision photometric methods for detecting planets by measuring the

THE FRESIP MISSION 115

variation of the stellar brightness and/or color that occurs when a planet transits its star. They find the photometric transit method to be particular­ly effective and robust. Larger planets produce a larger signal and a higher recognition rate, while smaller planets, although still detectable, have a low­er recognition rate. The innermost planets have short orbital periods, and therefore show many transits for a given mission duration. Planets in larger orbits show longer transit durations but fewer transits. The geometric prob­ability for detecting transits is quite favorable for planets in inner orbit,s. Once the orbital period has been determined and verified, the prediction and detection of all subsequent transits can be made. This periodic repeatability leads to a high level of confidence of discovery and should allow confirmation and follow-on studies by ground-based observatories.

Today, the FRESIP mission is practical given the acquisition of new data and the progress of technology. Variability data of adequate precision now exists for one star, our Sun, based on results from the Solar Maximum Mis­sion (Willson and Hudson, 1991). Analysis of these data indicate that, even during maximum activity, the variability of main-sequence dwarf stars on the time scales of a planetary transit is a factor of eight below the ampli­tude change caused by the transit of an Earth-sized planet. Further, recent developments in the photometric capability oflarge-format Charge-Coupled Devices (CCD) have demonstrated that the precision required for the FRE­SIP mission is achievable (Robinson et al., 1995). By combining the new CCD technology with ultra-lightweight mirror technology, it is possible to launch an instrument above the distorting effects of Earth's atmosphere and provide continuous and simultaneous monitoring of thousands of stars with the precision necessary to detect planetary transits. A comprehensive description of the mission is given by Koch et al. (1995).

3. The Need for a Space-Based Platform

To accomplish FRESIP's goals, 5000 solar-like stars must be continuously and simultaneously monitored for evidence of the brightness changes caused by Earth-sized or larger planetary transits. The magnitude of the brightness reduction due to a transit is proportional to the ratio of the planet's area to that of the star. When observing stars the size of the Sun, the decrease in light amounts to approximately 1 % for giant planets such as Jupiter and Saturn, 0.1% for planets like Uranus and Neptune, and 0.01% for planets like Earth and Venus (see Table 1). The design requirement for a system noise (instrument plus star) is to have a 1a noise level of 1:50,000 so that a transit of an Earth-sized body (!:!..L/ L = 1/12,000) will result in a 4 a detection per five-hour integration interval for the faintest star (about 12th magni tude for a 1 m aperture telescope). This level of precision includes

116 W. J. BORUCKI ET AL.

system noise and stellar variability in the pass band between 17 mHz and 69 mHz. To obtain the precision required to detect Earth-sized planets, the photometric system must also avoid the scintillation limit incurred by ground-based observations (Young 1974). Even !!lore limiting for ground­based observations are atmospheric transparency variations due to large air mass changes over the periods relevant to planetary transit detection. The ground-based photometric precision for events with durations of order 12 hours is less than one part in 1000 for ground-based observations even when extreme measures are taken to minimize photometric drifts (Frandsen et al., 1989; Lockwood et al., 1992). The day-night cycle and seasonal effects also make it essentially impossible to continuously monitor a single group of stars for the several years needed for reliable planet detection. Thus, a space-based mission is required.

4. Planetary Transits

4.1. ORBITAL CHARACTERISTICS

For a single star, three parameters describe the character of a planetary transit: the change in the stellar flux or brightness; the duration of the transit; and the periodic reoccurrence of the transit. The relative brightness change is used to calculate the size of the planet, while the orbital period of the planet is simply the recurrence period of the transits. The fractional brightness change, b.L / L, or transit depth is equal to the ratio of the area of the planet to that of the star. Table 1 lists these values for the solar system.

Planet

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Table 1 Transit Properties for Solar System Objects

Transit Transit Orbital Orbital Geometric

Depth Duration Period Radius Probability

b.L/ L (%) Tc (hrs) (yrs) R (AU) d*! D (%)

0.0012 8.1 0.241 0.39 1.19

0.0080 11.0 0.615 0.72 0.64

0.0084 13.0 1.00 1.00 0.47

0.0023 16.0 1.88 1.52 0.31

1.01 30. 11.86 5.2 0.089

0.68 40. 29.5 9.5 0.049

0.116 57. 84.0 19.2 0.024

0.096 71. 164.8 30.1 0.015

Inclination

to Ecliptic

(degrees)

7.0

3.4

0.0

1.9

1.3

2.5

0.8

1.8

THE FRESIP MISSION

Stellar Diamet~

d*

T

r-- 0/2 --~~I Orbital radius I , I ,

d* I

1) Range of Pole Positions = - -----t~~: ~ 0/2 , ,

__ i i __ 2d* 10 I" 2n

2) Solidangleo.f4nd*/0 .. ----~-~--e', N-nn0-for all possible pole posllIons _ ~ for any given LOS _____ ..,..~

3) Geometric Transit Probability = d*/D

117

Figure 2. Geometric probability for proper orbital alignment to see a transit. The orbital plane must be within an angle d./(D/2) of the LOS, or likewise the orbital pole must be within the same angle, for all pole positions around the LOS. The total solid angle of pole positions is 47rd. / D sterradians, and the fraction of sky covered by this angle is d. / D (Koch and Borucki 1994).

For transits across the center of a star, the transit duration is given by:

( R )1/2 Tc = (13.0 hrs) d* M* ' (1)

where d* and M* are the stellar diameter and stellar mass in solar units, and R is the orbital radius in AU. Since d* depends on M* by about the 3/5 power (see Fig. 1), the transit duration is only weakly dependent on the spectral type.

4.2. GEOMETRIC PROBABILITY FOR ALIGNMENT

Transits can only be detected if the planetary orbit is near the line of sight (LOS) between the observer and the star (Figure 2). This requires that the planet's orbital pole be within an angle d*/ R, measured from the center of the star and perpendicular to the LOS, where d* is the stellar diameter (0.0093 AU for the Sun) and R = D /2 is the planet's orbital radius. This is possible for all angles about the LOS, i.e., for a total of 47rd*/ R sterradians

118 W. J. BORUCKI ET AL.

of pole positions on the celestial sphere. Thus, the geometric probability for seeing a transit for any random planetary orbit is simply d*/ D (Borucki & Summers 1984). For the Earth and Venus, this is 0.47% and 0.64% respec­tively (see Table 1). Because grazing transits are not easily detectable, we will ignore those with a duration less than half of a central transit. Since a chord equal to D /2 lies at a distance of 0.866 times the radius from the center oif the circle, the usable transits account for 86.6% of the total.

If other planetary systems are similar to our own solar system, in that they also contain two Earth-sized or larger planets in inner orbits (Wetherill 1991; Wolszczan 1994) and if the orbits are not coplanar to within 2d*/ D, then the probabilities must be summed. Thus, approximately 0.011 X 0.866 :::::: 1 % of the solar-like stars with planets are expected to show transits from inner planets. Therefore, a photometric system that continuously and simul­taneously monitors 5000 such stars should easily detect 50 planets if the cur­rent theory of planetary formation is correct in hypothesizing that planet formation accompanies star formation.

After a set of several transits with a sufficiently high signal-to-noise ratio (SNR) is recorded, the planet size and orbital period can be found. Then, the prediction and detection of subsequent transits for that system can be made for confirmation by independent systems. From the orbital period and the brightness change (along with stellar mass and size) one can calculate the distance from the star to the planet and the size of the planet.

Earth-sized planets in Mercury-like orbits producing four transits a year should be detected in the first year of observing. Those with Earth-like orbits will require 3-4 years of observing, and those with Mars-like orbits will require 6-8 years. For planets with orbital periods as short as those of 51 Peg b (Mayor & Queloz 1995), the detection of four transits would occur within 18 days. If, on the other hand, no small planets are discovered, the this null result would have fundamental scientific and cultural implications.

4.3. PROBABILITY OF MULTIPLE TRANSITS

Current models for planetary formation assume that the planets are formed out of a common nebula with the star, and that the orbital planes should have small relative inclinations (Hale 1994). For the solar system, these inclinations are on the order of a few degrees, except for Pluto (see Table 1). They are also small for the inner moons of Jupiter, Saturn, Uranus, and Neptune. If one were to view the solar system near either node of the intersection of the orbital planes of two planets, then clearly both planets would be observed. For very small relative inclinations of the planes, ¢ ~ 2d*/ D, both planets would almost always be observed. For ¢ > 2d*/ D, the

THE FRESIP MISSION 119

probability of seeing a second planet in the system is given by (Koch & Borucki 1994),

_ 1 . (Sin[2d*/ D]) P2 - - arCSIn . A. '

K Sln~ (2)

For the Venus-Earth combination, there is a 12% chance of seeing both planets. Thus, there appears to be a significant chance that multiple-planet systems will be seen. This argument tempers the previous one that the probability of detection is the sum of the individual components of each system. If the inclinations of planetary orbits in other systems were all very close to zero, the the total number of planets detected would be closer to 25. This result should lead to a further refinement of the models that describe both the frequency of planetary formation as well as the coplanarity of their orbits.

4.4. EFFECT OF MASSIVE OUTER PLANET ON TRANSIT DURATION

Calculations of of the precession of the line of nodes caused by massive outer planets show that is possible to detect their presence by monitoring the change in the duration ofthe transits, as the inner-planet orbital plane moves across the disk of the star. For example, assuming a solar-like star, a low­mass planet at 1 AU, a Jupiter-mass planet at 5 AU, and a 10° inclination between the two orbital planes, then for the calculated precession rate of 0.0022 degrees per year, the transit duration would change by an amount in excess of 6 minutes over an 8-year period. However, this change would occur only for the situations where the transit line was displaced from a central transit by 75% or more of the stellar radius. A more comprehensive discussion of this effect for a variety of assumptions about relative masses and orbital radii will be presented elsewhere.

5. Signal Detection in the Presence of Noise

To minimize the mission cost, it is necessary to operate at the minimum SNR and the shortest mission duration that accomplishes the goals dis­cussed earlier. To ensure that a null result for the ensemble of observed stars is statistically meaningful, the total number of false alarms for the entire experiment must be less than one. Assuming that a uniform detec­tion threshold is applied to each star, the required false rate can be chosen by setting the SNR threshold high enough so that the false alarm rate for each test, times the number of statistical tests performed per star, times the number of stars is less than one. Therefore, the minimum planet size that can be detected at a specific recognition rate is determined by the noise

120 W. J. BORUCKI ET AL.

measured for each star, the number of observed transits, and the chosen val­ue of the SNR threshold. Due to the large number of stars to be observed, the number of tests performed per star is determined in large part by the range of orbital periods and transit durations of interest, and it depends only secondarily on the power spectrum of the measurement noise. Because we want to detect planets as small as the Earth or Venus, it is important to demonstrate that the system noise can be made low enough that the SNR from four transits of an Earth-sized planet will be at least as great as the threshold value required to keep the total number of false alarms below one. In the following sections, we will show that a threshold SNR of 70' for a set of transits is required when 5000 stars are searched for planets with orbital periods between 90 and 730 days. First, we derive the expected noise level, and then we present the results of a simulation that uses a matched filter algorithm to detect sets of transits.

The recent discovery of giant planets with orbital periods shorter than Mercury provides a motivation for searching for terrestrial planets with sim­ilar orbital periods. Although our previous discussion considered a range of planetary orbital periods, corresponding to those of the terrestrial planets in our own solar system, there is no practical barrier to expanding the search space to include planets with other periods. This expansion will not cause a dramatic increase in the required number of statistical tests, as long as the following strategy is employed: (1) Set a lower limit on the size of poten­tial planets, so that the number of transits needed to reach the detection threshold can be calculated; (2) Conduct the search only until this time­limit is reached. By restricting attention to planets of radius comparable to or larger than the Earth, it is possible to detect such planets against an increased photon noise background coupled with shorter transits, given that four or more transits occur during the observation period. Thus, for a plan­et with a IS-day orbit in a grazing occultation geometry (2.2 hr duration), approximately 1.25 years of observation would be required to reach the same detection probability as for the same planet with an orbital period of one year observed for four years. This estimate includes the increased shot noise appropriate to the shorter transit duration.

The major sources of noise that are expected to compete with the tran­sit signal are stellar variability, photon shot noise, and "instrument noise" (including detector noise and other effects such as pointing jitter). Since they are not correlated, these sources of noise can be combined as:

(SysNoise)2 = (StellarVar)2 + (ShotNoise)2 + (InstrNoise)2 . (3)

Table 1 showed that the expected signal level from Earth-sized planets will be approximately 8 X 10-5. The present mission is designed to hold the total system noise to a value of 2 X 10-5, including the effects of stellar variability. This will produce a SNR of 80' for a a set of four transits. Note that the

THE FRESIP MISSION 121

SNR of a set of transits grows as the square root of the number of transits times the SNR of a signal transit, and that a four-year mission will give four transits for planets with orbital periods near one year. Thus, an eight-year mission will produce a SNR greater than lla. Clearly, the system noise can be kept below 2 X 10-5 only if the noise introduced by each source is below this value.

5.1. STELLAR VARIABILITY

Although many stars are variable, stellar variability will not interfere with the detection of the transits, unless the variability is at the time scale of the transits. Said another way, the noise is introduced within the band pass of the matched-filter detection algorithm. The Hertzsprung-Russell diagram has been fairly well surveyed for variability, and at this time the solar-like stars, especially older ones with low activity, are among the quietest stars known.

Much of the measured variability is found in the ultraviolet portion of the spectrum, especially in the Ca II Hand K lines. Therefore, the FRE­SIP measurements will be confined to wavelengths longer than 400 nm. If solar-like stars have a variability similar to that of the Sun, then intrinsic brightness fluctuations will range from 10-3 at the rotation period of the star (due to the presence of large sunspot groups) to values of less than 10-5 with durations of several hours (due to turbulent motions and gravity waves in the stellar atmosphere [Frohlich 1987]). Note that the duration of a transit ranges from 4 hrs for a Mercury grazing transit to 16 hrs for a Mars central transit (see Table 1). Brightness variations with duration greater than approximately 16 hrs will not significantly affect the detect ability of transits. It should also be noted that there is no reason to believe that the noise characteristic of other solar-like stars differ substantially from the Sun in the band pass of interest. Specifically, there are no other experimental data and no theories that discuss any variation of this noise with spectral type.

Figure 3 shows the measured power spectrum of the Sun, obtained with the ACRIM-1 radiometer (Woodard et al. 1982). It demonstrates that in the frequency band pertinent to planetary transits, the stellar variability noise is much less than that which occurs at frequencies characteristic of stellar rotation and the evolution of star spots. Although the effects of star spots will be observed and could show periodic brightness variations larger than those from transits from small planets, their presence will cause difficulty only for stars with both short rotation periods and extensive spotting. Stud­ies show that rotation periods increase with stellar age (Soderblom 1983) and become quite long for stars later than spectral class FO (Stauffer and Hartmann 1986). Spectral classes F5 through K5 have periods of weeks, sim-

122

-1 10

-2 '7 10

N I

ill -3 S 10 o (L

g; 10-4 § OJ a: 10-5

10 -il

10 -7

W. J. BORUCKI ET AL.

-3 -2 10 10 10 -8

-7 10

Frequency, Hz

Figure 3. Power spectrum of the Sun from the ACRIM-1 (SMM) data. The intrinsic peak variability of the Sun is on the order of one part in a thousand, and the relative intensity (square root of the power) on time scales for a transit (12 hrs) is a factor of a hundred less. Thus, the variability is ~ one part in 105 (Woodard et al. 1982).

ilar to that of the Sun. Consequently, the presence of spots on these stars should not prevent the detection of planetary transits. Many stars earlier than F5 have rotation periods shorter than weeks. However, these stars also show much less star-spot activity, as evidenced by their lower Ca II Hand K line activity (Noyes et al. 1984). Much of the variability in solar-like stars has been found to occur in the UV from ionized calcium and magnesium lines. Therefore, the short wavelength cutoff for the instrument will be at 400 nm to reduce flux variations due to Ca II lines and other UV-variable sources.

In a study being conducted at NASA-Ames, the SMM data are being examined to reduce the telemetry and instrument noise, to better estimate the noise due to the Sun's variability. Further, the contribution of the UV portion ofthe spectrum to the total flux measured by the ACRIM-1 radiome­ter is being assessed by comparison with the UV radiometric measurements made aboard the SOLSTICE spacecraft. Preliminary results from this study indicate that the solar variability in the visibel portion of the spectrum and in the band pass of interest is approximately 0.7 X 10-5 . This value implies that planets substantially smaller than the Earth should be detectable with

THE FRESIP MISSION 123

some combination of larger apertures, longer mission durations, or shorter orbital periods.

5.2. CONTROL OF OTHER NOISE SOURCES

For the present mission design, the major source of noise is the statistical noise introduced by the finite number of photons counted. For a given inte­gration interval, this noise an be reduced to any desired level by increasing the size of the telescope aperture and/or observing brighter stars. The first option carries a financial penalty, while the second option reduces the sci­ence yield. Tradeoff studies suggest a shot-noise error budget of 1.4 parts in 105, and thereby a requirement for a minimum of 5 x 109 counts per integration. The integration time available varies from 4 hrs for a grazing transit at 4 AU, to 16 hrs for a central transit at 1.5 AU. The combination of telescope aperture and efficiency, and detector bandpass and quantum efficiency, have been chosen to achieve the required sensitivity for stars with visual magnitudes of 12 and brighter (see Koch et al., 1995).

Laboratory tests of available research-grade CCDs were conducted at the expected flux levels and time durations to demonstrate the photometric pre­cision required for FRESIP. Independent groups working at Ball Aerospace and at Lick Observatory performed tests, using relative photometry of arti­ficial standards (ratioing the flux of an individual star to that of all other stars on the CCD). It was found that the dominant error source in the exper­iments was image motion, such as that caused by flexure of the mechanical system as the cryogenic coolant boiled off. By accurately centroiding star images and fitting a linear function of the relative photometry to the image position, combined with a term which fitted an observed non-linearity in CCD response as a function of brightness, Robinson et al. (1995) demon­strated that front-illuminated CCDs can routinely provide near shot-noise limited performance. A full discussion of the system noise is presented in Koch et al. (1995).

6. Simulated Transit Events

Figure 4 illustrates the difference in detect ability of single and multiple transit events. Each simulation includes the three primary noise sources expected in the data: instrument noise, photon (shot) noise, and stellar variability. The simulations are generated by algebraically adding two data sets: CCD laboratory data of artificial stars with a CCD fractional error of 1.4 X 10-5 , and solar variability data from SMM with a fractional error of 1.0 X 10-5. Pointing noise is included with the CCD data by assuming spacecraft pointing jitter (0.55 pixels or 0.16 arcsec). Because the SMM

124 W. J. BORUCKI ET AL.

o 50 100 150 200 Elapsed Time (Hours)

250

Simulated Transit

2

3

4

Figure 4. Detectability of transit events. Four independent simulations of an Earth-sized transit are shown. The data contain actual CCD noise and solar variability from SMM data. Gaussian shot noise and pointing equivalent noise were added. The bottom trace is a sum of four separate data sets.

data had no appreciable photon noise, Gaussian-distributed random noise was added to simulate the expected photon noise (1.4 X 10-5). The root sum square of the errors is 2.26 X 10-5, which is a reasonable approximation to the budgeted error of 2.0 X 10-5 and to the error measured in the simulations, which has a mean of 2.15 X 10-5 • All quantities were binned into four-hour intervals, and a 12-hour (3 data point) Venus-size transit (8.0 X 10-5) was added to the data. A polynomial fit to the data was used with a high-pass filter. Multiple simulations show that, on average, a single transit event is a 3.50' detection. Note that, while the data were binned into four-hour intervals, the time resolution for locating events is much higher, since the integrated brightness for target stars is taken with 15-minute centers.

The bottom plot in Figure 4 shows the result of combining or "folding" four transit data strings together. The result is a 7.50' detection, such that 83% of planetary transits will be detected with four data strings. Note that this simulation utilizes real solar variability and real CD noise. Thus, this demonstrates that CCDs can consistently operate at the level of precision necessary for the mission, and that solar-type stars are sufficiently quiet to allow detection of transits of Earth-sized planets.

Although Figure 4 makes it easy to visualize the result offolding the entire data string for an individual star, once the phase and period of the orbit have been found, the procedure required to find the phase and period is not shown. The precedure we have chosen is to use a matched-filter algorithm, such that the time series observations for each star are first whitened and then cross-correlated with a mask whose length has a Keplerian relationship

THE FRESIP MISSION 125

to the orbital period sought. Because the detection efficiency falls when the mismatch in the time lag is equal to the decorrelation length, a very large number of phases and periods and periods must be searched. In particular, we estimate that approximately 1011 statistical tests must be made when 5000 stars are searched for orbital periods between 90 and 700 days. Thus, an "event" (a set of transits) must have a SNR of at least 7 a to exceed the SNR threshold that will produce no more than 0.1 false alarms for the entire mission (or a SNR of 6.7 a if a false alarm rate of 1 event can be accepted).

Because the SNR of a set of transits increases with the square root of the number of transits, the above requirement implies that the average SNR of an individual transit must be 3.5a for a set of four transits (Le., a one­year orbital period for a four-year mission, or a two-year orbital period for an eight-year mission) and 1.75a for a set of 16 transits (Le., a 90-day orbital period for a four-year mission). The observations provide the actual noise level for each star. This noise level will be different for each star because the brightness of the target star will range from approximately 9th to 12th magnitude, and because the variability of individual stars of differing spectral class might also vary. In every case, a threshold of 7 (j is applied, and only those events above the threshold will be examined further as a possible transit signal. For stars no dimmer than 12th magnitude and no noisier than the Sun, planets as small as the Earth and Venus should be detectable. For the brightest and quietest target stars and for mission durations exceeding four years, even smaller planets should be detectable. Also note that whenever the observed orbital period is short enough that more than four transits occur, it is possible to restrict further statistical tests to just the star showing the transits and to its measured orbital period. Such tests dramatically reduce the possibility of false detections.

6.1. CHOICE OF STELLAR TYPE

The decrease in brightness due to a transit is proportional to the ratio of the planet's area to that of the stellar disk. For a given planet size, smaller stars will provide a higher SNR than larger stars. Therefore, FRESIP will monitor main-sequence dwarf stars similar in size to the Sun, not giants or early spectral class dwarfs. We will perform spectral and luminosity classification of all stars in the field of view (FOV) to about 12th magnitude to select the target stars. Although Galactic M stars are the most abundant by total number, in a magnitude-limited sample F, G, and K stars are the most abundant, accounting for aprroximately 70% of the stars, based on SAO, HD, and AGK3 catalogs which have limiting magnitudes of mv ~ 9.5.

126 W. J. BORUCKI ET AL.

1.0

• •• 0.8

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~ .D E '" z 0.4 F a; c 0 :g 1= ~ 0.2 u..

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•

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• • } Fraction of .... unstable orbits

• • ..... , ..... llH

0.001 0.01 0.1 1.0 10 100 1000 10000 Binary Separation in AU

Figure 5. Distribution of binary separations (Heacox and Gathright 1994). Nwnerical computations have shown that planets in binary systems may have stable orbits when the planetary orbit about a close binary is at least 3.5 times greater than the binary separation, and in an open system when the planetary orbit is at least 3.5 times smaller than the binary separation. These cases account for about 77% of all solar-like binary systems.

6.2. TREATMENT OF BINARY STARS

If half the stars monitored are binaries, and if binaries do not have plane­tary systems, then only 25 planetary systems should be detected. Howev­er, numerical orbit integrations (Szebehely 1980; Graziani and Black 1981; Black and Pendleton 1983; Dvorak, Froeschle, and Froeschle 1989; Donni­son and Mikulskis 1992) indicate the possibility of stable planetary orbits around binaries in which the planetary orbital radii are classified as either more than 3.5 times the stellar separation (close system) or less than 3.5 times the separation (open system). Based on an analysis of observed binary systems from Heacox and Gathright (1994), we can estimate the maximum number of planetary systems with orbital distances between 0.4 and 2.0 AU in binary systems (see Fig. 5).

Of the systems analyzed, close systems, in which the binary has a sepa­ration much less than Mercury's orbit, account for 17% of the cases. Open systems, where the binary has a separation at least as large as Jupiter's orbit, account for 60% of the cases. Therefore, only the remaining 23% of the systems are expected to be unsuitable for planets in the habitable zone. For open systems, planets could potentially form about both members of

THE FRESIP MISSION 127

the binary. If a planetary transit of one of the two stars in an open binary were observed, and if both stars were of comparable brightness, then the SNR would be approximately one-half that for a similar transit occuring in a single-star system, because the stars would not be resolved by the pho­tometer. The reduced SNR would make the transit more difficult to detect. Because the observations of the brightness distributions of companions to G dwarfs in binary stars has been tabulated by Duquennoy and Mayor (1991), it is possible to determine the fraction of G-dwarf binaries that have a sec­ondary too dim to cause a significant reduction in the SNR of a transit. From an integration of the curves they present, we find that 85% of the binaries have secondaries that will cause less than a 20% reduction in SNR. Consequently, the fraction of solar-like binaries that could have detectable planetary systems is 17% + 0.85 x 60% = 68%. A sufficiently large num­

ber of suitable binary systems should be available: (1) to establish whether planets can be found in binary systems; and (2) to ascertain their frequency of occurrence and distribution in close and wide binaries

6.3. VIEWING CONSTRAINTS AND ORBIT SELECTION

The first viewing constraint is that the FOV must be out of the ecliptic, so that it is not blocked by the Sun on an annual basis. Low-Earth orbit is also inappropriate, since there is no part of the sky that is not blocked by the Earth as a result of orbital motion and precession of the orbital pole. From a high-Earth (several Earth radii), low-inclination orbit, portions of the sky near the equatorial poles are continuously accessible. However, these are regions well off the Galactic plane, where the star densities are relatively low. Trapped radiation also remains a problem at these altitudes. Thus, one can use a halo orbit about the Earth-Sun L2 Lagrangian point, about 0.01 AU from Earth. This orbit will permit continuous viewing of much ofthe sky, particularly near low Galactic latitudes where the star density is sufficiently high. Alternately, one can use a heliocentric orbit, like that proposed for the revised SIRTF (Space Infrared Telescope Facility) mission.

6.4. CHOICE OF STAR FIELD

U sing the HST Guide Star Catalog as a basis for obtaining star densities, a region centered on Galactic longitude" = 70° and latitude b = 5° has been found satisfactory, in that 18,000 stars brighter than mv = 12 are present in the instrument FOV. This field is at least 55° off the ecliptic, and it is not directly in the Galactic plane where giants would dominate the star counts. The fraction ofthese stars ofthe desired spectral type is estimated to be 70%, using the spectral distribution in the SAO, HD, and AGK3 catalogs. The fraction of each spectral class composed of main sequence dwarfs (luminosity

128 W. J. BORUCKI ET AL.

class V) was estimated to be 50%, based on the Galactic model of Bahcall and Soneira (Bahcall 1986). Thus, this region should contain a sufficient number of F, G, and K stars with the required brightness.

6.5. METHOD FOR SELECTING TARGET STARS

There is no existing catalog of spectral type and luminosity class containing our proposed field, down to the required magnitude limit. The HST Guide Star Catalog has a limiting magnitude of 16, but it has neither spectral or luminosity information. The AGK3 catalog, with limiting magnitide 9.5, lists only spectral type but no luminosity classification. Thus, a ground-based observing program is needed to determine the spectral type and luminosity class of each star in the FOV to about mv = 12. An efficient method for performing these observations on large numbers of stars has been developed by Rose (1991). This method combines the speed and FOV of objective prism spectroscopy with the sky suppression of narrow-band photometry. A system of spectral indices is used to measure the ratio of the residual central intensity of two neighboring spectral lines. The Hb (A4102)/Fe I (A4063) ratio provides the spectral-type classification for F, G, and K stars in the MK system (Morgan et al., 1943), and the Sr II (A4077)/Fe I (A4063) ratio provides the luminosity classification (see Fig. 6). These observations can be made using the Burrell-Schmidt telescope at Kitt Peak National Observatory and will require on the order of two weeks of telescope time.

6.6. SUPPORTING DOPPLER VELOCITY OBSERVATIONS

It will be important to maintain a ground-based observing program to deter­mine the parameters of the eclipsing binary stars that are discovered by FRESIP. The transit signature is more complex than for the transit of a single star (Bell and Borucki 1995). However, matched-filter detection algo­rithms can still be used if the properties of the stars are d~termined from a combination of photometry and radial velocity measurements (Jenkins et al., 1995).

In addition, once a companion is found for either a singular or binary sys­tem, ground-based observations, using the Doppler method, will be needed to rule out the possibility that the transits are caused by stellar objects such as white dwarfs or substellar objects such as brown dwarfs. The preci­sion of the Doppler velocity method often reaches 20 m s-l (McMillan and Smith 1987; Latham 1992; Hatzes and Cochran 1993). Recently, Butler et al. (1996) found that they can reach a precision of 3 m s-l when they use iodine absorption cells with the echelle spectrographs at either the Keck or

-Q)

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THE FRESIP MISSION

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Figure 6. Luminosity classification based on the measurements of three spectral lines (Rose 1991).

the Shane telescopes. For a precision of 3 m s-l, the minimum detectable companion is given by:

(4)

where the companion mass is given in Earth masses, the stellar mass in solar masses, and the orbital radius in AU. Thus, an Earth-mass object can readily be discriminated from a sub-stellar object and even from a Saturn­or Jupiter-mass planet.

7. Expected Results

Measurements of each star will provide the amplitude, duration, period, and epoch of each transit. The amplitude is a direct measure of the ratio of the projected area of the planet to the projected area of the star. Because both the spectral type and luminosity class of each target star will be known beforehand, from a ground-based observation program, the size of the planet can be calculated from the known size of the central star. From the epochs of a pair of transits, an estimate will be obtained of the orbital period, accurate to within one hour. Given the predicted time of transit and the

130 W. J. BORUCKI ET AL.

identity of the star, it should be possible to use a large-aperture, ground­based telescope to verify the transits. A large aperture is required to keep the scintillation noise low enough to get a significant SNR (Young 1974). Although such telescopes do not have FOVs large enough to continuously monitor thousands of relatively bright stars (mv < 12), they can measure the brightness changes at the beginning and end of a transit, when they monitor only a single target star. Because the time of transit will be known, the large telescope time is needed only when a transit is imminent.

From the mass of the star and the orbital period of the planet, the radius of the orbit can be calculated. From the orbital radius, one can determine if the planet lies within the habitable zone of the particular star and begin to make estimates of the planetary conditions (see Kasting, Whitmire, and Roberts 1993). Most significantly, FRESIP will determine whether Earth­sized planets exist in inner orbits around solar-like stars, and will measure their frequency of occurrence. Because of the statistically large sample of stellar data obtained, finding few or no planets would lead to the conclusion that Earth-sized planets are rare. Models of planetary system formation would then need to be revised, and the origin of the Earth reconsidered. On the other hand, detection of the expected number of Earth-sized inner planets would confirm currently-held theories, and would have an impact on both the scientific and public communities. The effect will be significantly enhanced if some of the detected planets are found to exist in the habitable zones for their parent star. A positive result should motivate the resources needed for more expensive programs to measure the spectra of planetary atmospheres. Furthermore, the results are necessary to provide an estimate of the range to the nearest stars with Earth-sized planets and thereby deter­mine the size-scale of the instruments needed for such programs.

These results will also provide an estimate of the size and radial distribu­tion of inner planets. The question as to whether only small rocky planets like the Earth are present, or whether much larger planets are also found in inner orbits, will be answered. Further observations with Doppler velocity or astrometric systems could then be used to detect any outer planets in these systems.

If our solar system is typical, with two Earth-sized planets in mildly inclined orbits, then we expect to find multiple planets in about 12% of the cases, based simply on the chance of viewing the system not too far from the line of nodes. On the other hand, if the typical relative inclinations are closer to zero and multiple planets exist, the we should almost always see multiple planets.

Depending on the nature of the result, one may be able to draw further conclusions based on the dependence of these properties on stellar type. Since about half of all stars are binary systems, we will also expect to determine the frequency of planets in binary systems. This group will subdivide into close

THE FRESIP MISSION 131

binaries, where planets could exist in close orbit about the pair, and open binaries, where the stars are so widely separated that planets could exist around the individual members of the system. Finally, we expect to see a few transits of Jupiter-sized outer planets if most solar-like stars have such planets. Calculating the probability from d*/ D (see Table 1) and applying it to Jupiter for eight years of observing (2/3 of Jupiter's 11.86 yr orbital period) yields a probability of 6 X 10-4 of observing a transit. For 5000 stars, we would expect to see about three Jovian-type transits. Since the transit depth would be on the order of 1%, a single transit would be of very high confidence level; the signal-to-noise ratio would be 50 and the probability of a random occurrence from a Gaussian distribution would be less than 10-17• Hence, only a single transit would be required for a detection. Since the inclination of the orbit would be known, Doppler velocity observations could then be used to determine the precise mass. From the photometric and Doppler velocity observations, the time of subsequent transits could be predicted. Ground-based observatories could readily observe the predicted transits of these planets, because the signal amplitude would be well above the scintillation noise. These ancillary observations would serve to confirm the detection and would determine a precise orbital period. With the mass and size information, the mean density of the planet can be calculated.

Because a very large number of stars will be observed continuously for several years, a great deal of information will be available on star spots, activity cycles, oscillations, and rotation rates. From p-mode observations, the age, mass, and composition of the stars can be obtained (Brown and Gilliland 1994). It might be possible to associate activity levels with other stellar properties and to identify the factors that control when a star is in a low activity level, such as occurred for the Sun during the Maunder Min­imum. If non-solar-like stars are also included in the monitoring program, the the dependence of these properties can be studied as functions of stellar type. A more comprehensive discussion of the astrophysical application of FRESIP observations can be found in the monograph Astrophysical Science with a Spaceborne Photometric Telescope (Granados and Borucki 1993).

8. Summary

Results from FRESIP will provide information on the existence, sizes, and distribution of inner planets around solar-like stars. One can imagine the ramifications of the explicit knowledge of the frequency of small, possibly habitable planets in extra-solar planetary systems. For a long-duration mis­sion and for the brightest low-noise stars, planets smaller than Earth and Venus could be detected. Thus, much of the size range of habitable planets and their distribution in and near the habitable zone will be covered. On

132 W. J. BORUCKI ET AL.

the other hand, it would be sobering if FRESIP finds that the probability of habitable planets is so low that a null result is obtained.

In summary, FRESIP is a mission that can:

Determine the frequency of Earth-sized and larger planets in inner orbits around solar-like stars Determine the distributions of size and radial position of these planets Determine the properties of those stars found to have planetary systems Estimate the frequency of planets orbiting mutiple-star systems

- Provide critical information on the distributions of planetary size and orbital periods for development and testing of models of planetary sys­tem formation

Acknowledgements

The authors would like to acknowledge fruitful discussions with Anthony Dobrovolskis, positive suggestions by the reviewers, and the support by Codes S and X of NASA Headquarters.

References

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THE FRESIP MISSION 133

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Hatzes, A. P. and Cochran, W. D.: 1993, 'Long-Period Radial Velocity Variations in Three K-Giants', Astrophysical loumal413, 339-348

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134 W. J. BORUCKI ET AL.

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Panel discussion: left-to-right are Alain Leger, Anneila Sargent, Alan Stem, David Black, and Roger Angel

THE DARWIN PROJECT

An Infrared Nulling Interferometer in Space

A. LEGER, J. M. MARIOTTI, B. MENNESSON, M. OLLIVIER, J. L. PUGET, D. ROUAN and J. SCHNEIDER

I.A.S., C.N.R.S., Bdt 121, Universite Paris XI, 91405 Orsay, Cedex, France

Abstract. Angel and co-workers have proposed to detect exoplanets around nearby stars in the infrared (6-17 Jim) and to analyze their spectra, searching for H20, CO2 , CH4, NH3 , and 0 3 spectral features. The presence or absence of CO2 would indicate either a strong similarity or difference with Solar telluric planet atmospheres. Water would indicate a habitable planet, and 0 3 would reveal significant photosynthesis activity, due to the presence of carbon chemistry based life. Like these authors, we suggest an infrared nulling interferometer pointing to the star and working as a coronograph. Our main contribution is to propose an observatory made of four to five I-meter class telescopes observing from about 4 to 5 AU to avoid the Solar Zodiacal Light (ZL) background at 10 flm instead of four 8-meter ones observing from the Earth vicinity. This allows the mission to be feasible in the near future. The concept, named DARWIN, is under consideration by the European Space Agency for its Horizon 2000 Plus program.

1. Introduction

The search for life in the Universe will be a central item in the scientific activ­ity of the 21st century. For many millennia, humans have tried to understand how we and our world came to be. A related question is "the prevalence of planetary systems throughout the Universe ... and the likelihood that other planets have given birth to life, even advanced and intelligent forms of life. We live in a remarkable time, when human beings ... have attained the pos­sibility of finding the first real answers to some of these most meaningful questions" (TOPS report, 1992).

As financial resources are scarce, it is important to distinguish which are the key steps. Current opinion holds that we are to find many more exoplanets in the next 10 years (e.g., by microlensing, star radial velocimetry, and astrometry). The next breakthrough would be the knowledge of the frequency of appearance of life on habitable planets, if they exist, because the mere detection of Jupiter-like planets would not really answer our basic quest. The following concept is one of the few possibilities we have to address this question in the near future.

Astrophysics and Space Science 241: 135-146, 1996. © 1996 Kluwer Academic Publishers.

136 A. LEGER ET AL.

2. How to Find Life by Remote Sensing

2.1. THE 02 CRITERION

Demonstrating the presence of life on an exoplanet by remote sensing is a formidable challenge. In an interesting paper, Owen (1980) showed that, if based on chemistry, life is likely to rely on organic chemistry and require the presence of liquid water. As the raw material in the primitive atmosphere of a terrestrial planet is expected to be fully oxidized carbon (C02), a massive development of life would imply some reduction of C02 by photosynthesis and release of free 02. As this gas is highly reactive with reducing planetary rocks, Owen concluded that the massive presence (1-1000 mbar) of 02 would be a strong indication of the presence of (primitive) life. An alternative source of free 02 is the UV photolysis of H20. However, this process is likely to occur only in planets with temperatures higher than that of Earth (e.g., Venus). We should have a good idea of this temperature from the planet-to-star distance and information about its atmospheric greenhouse effect.

2.2. THE 03 CRITERION

02 has spectral signatures in the visible, e.g., at 760 nm, but such a search would face the huge ratio of the star-to-planet fluxes (5 X 109). Bracewell (1978) and Angel et al. (1986) pointed out the advantage of searching in the mid-IR, where this ratio is improved by almost three orders of magnitude. The latter authors showed that the 6 - 17 11m region is very informative, as it contains spectral features of H20 « 8 11m), 03 (9.6 11m), and C02 (15 11m). Several authors (Kasting et al. 1985, Leger et al. 1993; and refer­ences therein) have shown that 0 3 is an attractive tracer of 02 because it has a logarithmic dependence on the 02 concentration; even a small amount of the latter (e.g., 1 mbar) would give rise to a significant 03 band at 9.6 11m, much easier to detect than the corresponding visual 02 features. In a further paper, Angel (1989) proposed a nulling interferometer made of four eight­meter class telescopes, pointing to the target star and blocking its light in order to observe possible planet( s). The reason for such big telescopes was to overcome the strong zodiacal light (ZL) background at 1 AU. Unfortu­nately, large optics may postpone the project to a far future when such large telescope assemblies could be launched.

3. The DARWIN Proposal

The aim of this communication is to show that a similar goal can be achieved with smaller telescopes, provided that the interferometer is carefully designed

THE DARWIN PROJECT 137

<P = 1.S m

Figure 1. Scheme of DARWIN in a five-telescope design.

and sent to 4-5 AU, where the 10 /lm ZL emission is much weaker (Bracewell and McPhie, 1979). Our concept, called DARWIN, is similar to that of Angel (1989), but for its dimensions. It has four to five IR telescopes of the 1 m class, regularly located on a 2r ~ 30 - 50 m diameter circle (Fig. 1). Trans­mission maps for interferometers are shown in Figure 2 (4- telescopes) and Figure 3 (5- telescopes).

3.1. CONDITION FOR PLANET-STAR SEPARATION

For a planet, at a sufficient distance from its star to be at about 300 K, the condition to have a good angular separation from its star, at A ~ 10 /lm and in the five-telescope configuration (Fig. 3), is that the planetary system lie nearer than

-1/2 --1 Dsep < (18.3 pc)L (2r) A , (1)

where Land L0 are the luminosities of the star and the Sun [L = L/ L0 ], 2r is the interferometer diameter [2r = (2r/30 m)], and :\ = (A/I0 /lm). Assuming a total efficiency of 15% for the optics and detector, when the

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THE DARWIN PROJECT

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Figure 3. Same as Fig. 2 for a 5-telescope interferometer with 0.07 contour steps. The mean value of the transmission over the whole map is 20%. The Fourier spectra are quite different for a planet (b) and a exo-zodiacal disk (c), because the transmission map has no central symmetry. On the other hand, the maximum transmission at the first hilltops goes up to 0.70 only. This configuration would be preferred to the 4-telescope array if most exo-ZL appear to be brighter than the Solar one.

140 A. LEGER ET AL.

transmission of the interferometer is maximum (70%, see Fig. 3a), provided that an efficient recombination mechanism of the beams is available, the number of photoelectrons generated by the planet in one spectral element is

--2 -2 - -1 -2 -Npe = (280)D <1>5 (Res) Rpe t . (2)

Here, D is the distance of the system [D = (D/10 pc)], <1>5 is the telescope diameter in units of 5 m, Res is the spectrometer resolution in units of 20, Rpe and RE are the radii of the planet and of Earth [Rpe = Rpe/ RE], and t = (t/1 hr).

Now Npe is a small number indeed and it must be extracted from noise and spurious signals, such as the starlight leaks, Nleaks. If P is the interfer­ometer rejection factor and {I is the flux ratio of the star and Sun at 10 /Lm, one finds

4 --1 - --2 - -1 -2 -Nleaks = (2.5 X 10)p f L D (Res) <l>s t , (3)

where 75 = (p/10 S). Clearly, a high and stable p is needed. Its limiting factors are: (i) optics defects, (ii) imperfect optical path difference (OPD) cancella­tion, (iii) imperfect guiding of the individual telescopes and (iv) finite star diameter. We believe that the three first factors can individually be kept less than 0.5 X lOs if optical filtering is used for factor (i). For (ii) and (iii), one can take advantage of monitoring the quantities in the visible (A ~ 0.5 /Lm) and getting 20 times better accuracy at A ~ 10 /Lm; keeping Av /200 control of the OPD is adequate. Factor (iv) is solved by using a 4- or 5-telescope interferometer, where transmission varies as ()-4, with () the angular separa­tion between the source and the system axis (Angel, 1989).

3.2. THE SOLAR ZODIACAL LIGHT PROBLEM

In the Earth's vicinity, the Solar ZL over 75% of the sky has a surface brightness Ah..(10 /Lm) ::; 7.5 X 10-6 W m-2 sr- 1 (Boulanger and Perault, 1988). With sn = 3.7.\2 for each telescope and a mean transmission of the interferometer of 20% (Fig. 3a), the generation rate of photoelectrons by the ZL is NZL = 4 X 106 (Res )-1 hr- 1, a prohibitively large photon noise. This is why Angel (1989) proposed larger telescope diameters, because Npe increases as <l>g, whereas NZL is independent of the telescope size. An alternative solution is to go farther away from the Sun, so that the zodiacal dust is cooler and its mid-IR emission weaker. Bringing NZL lower than Nleaks/2.5 requires lowering the ZL at 10 /Lm by a factor 400 for nominal values of D, <1>5, and Rpe. This is achievable, according to recent ZL models (Reach et al. 1995). if we go to 4-5 AU, Then, at 10 /Lm,

(4)

THE DARWIN PROJECT 141

3.3. THERMAL, DETECTOR, AND CIRRUS SOURCES OF NOISE

Lowering the thermal emission of the optics and detector noise to similar levels is achievable if the telescope temperature is S; 30 K, the detector dark current 2 e- s-1, and the readout noise 13 e- . In this case, the number of thermal and detector photoelectrons are:

4 - 1-Ndet < (2.4 X 10 ) (Res)- t,

(5)

(6)

assuming two detectors per spectral element. The valuable studies by the EDISON team (Thronson et al., 1993) have shown that the former objective is attainable by passive cooling at 4 AU. Good BIB detectors characteristics should meet the detector specifications in the near future provided that they are actively cooled to S; 4 K. The mean infrared cirrus surface brightness (Boulanger and Perault, 1988) leads to

4 - -1-Narrus = (1.2 X 10 ) (Res) t, (7)

To separate the planet signal from the stable, but stronger, spurious signals, we propose to use the Bracewell (1978) concept of slowly rotating the inter­ferometer (fo ~ 1 turn hr-1 ) while continuously pointing to the star. The planet signal is then periodic, whereas spurious signals are not modulated (Fig. 2b and 3b).

3.4. EXO-ZODIACAL LIGHT

There is a serious exception to the above statement: the exo-ZL signal. For a system similar to the Solar one, when the Earth-like planet is at X = 1.1 (Fig. 3a) and the exo-ZL correspondingly spread in the transmission map, it gives a photon flux 43 times stronger than Npe:

4 --2 - -1-Nexo-ZL = (1.5 X 10 ) D (Res) t, (8)

When the exo-system is observed face on, it does not give a modulated signal, but this is no more true when the angle between the normal to the exo-ecliptic plane and the line of sight increases (Fig. 2c and 3c). Regarding the capability to distinguish between the exo-ZL and planet signals, a five­telescope configuration has a major advantage: the main planet signal is at 5io, whereas the former is at 10io and higher harmonics (Fig. 3b and 3c). For instance, even with an exo-ZL 100 times stronger than the Solar one, we find that one-third of the stellar systems of Table 1 could still be studied. However, the transmission map of the five-telescope interferometer is not dense (Fig. 3a). For a given planet, to efficiently cover the whole 6 -17 p,m,

142 A. LEGER ET AL.

range, the interferometer dimensions need to be uniformly increased by a factor r..J 1.5. This would have advantages, especially if the interferometer has a imaging mode, but it makes the structural concept more difficult. On the other hand, a 4- or 3-telescope interferometer, in a diamond shape or a linear array (Angel, 1989 and Angel et al., in preparation) has a dense map transmission and can accommodate fixed dimensions, but it is less efficient for separating planet from exo-ZL signals (Fig. 2b and 2c). The observations by ISO and SIRTF of ZL around nearby stars should influence the choice between the different configurations.

4. Maximum Distance to Obtain Sufficient SNR

4.1. MISSION STRATEGY

Considering a 10-year mission with four years of integration time, we can use the first integration year to detect telluric exoplanets and the next three to spectroscopically analyze the interesting candidates, if any, in the 6 - 17 pm range. By numerical simulation, we have shown that a signal-to-noise ratio (SNR) of 20, when the planet is at an interferometer transmission maximum, leads to an actual SNR of 10 for the planet Fourier main peaks when the interferometer is rotated. This is acceptable to detect rv 50% deep spectral bands. When including the different sources of statistical noise, this leads to a maximum distance DSNR, the solution of:

400 (SNR/20)2 [2.5 X 104 75-1 /L D-2ip52

+ 1.5 X 104 z D-2ip52

+ 4.8 x 104] Res -1 t , (9)

when the exo-ZL is z times the Solar system one.

THE DARWIN PROJECT 143

4.2. NUMBER OF STELLAR SYSTEMS THAT CAN BE STUDIED

Table 1 Limiting Distances: Programs 1 and 2

Planet Detection and CO 2 Spectroscopy

Planets Planets Planets CO2 CO2 CO2 SpT LjL0 Dsep DSNR Nb DSNR t Nb

(pc) (pc) (stars) (pc) (hr) (stars)

FO-4 4.4 51.0 18.6 6 12.9 200 2

F5-9 1.9 33.5 19.7 18 14.1 200 6 GO-4 1.0 24.3 20.3 31 14.7 200 12

G5-9 0.60 18.8 20.6 36 15.1 200 18

KO-4 0.28 12.9 20.8 16 15.3 117 15

K5-9 0.11 8.1 21.0 5 15.6 28 5

MO-4 0.032 4.4 21.3 5 15.9 5 5

Accessible 117 64

Observed 117 44

Table 2 Limiting Distances: Program 3

03 Spectroscopy

03 03 0 3 SpT LjLG DSNR t Nb

(pc) (hr) (stars)

FO-4 4.4 9.5 800 1

F5-9 1.9 10.7 800 3 GO-4 1.0 11.4 800 5 G5-9 0.60 11.7 800 9

KO-4 0.28 12.0 800 12

K5-9 0.11 12.3 240 5

MO-4 0.032 12.7 42 5

Accessible 40

Observed 22

144 A. LEGER ET AL.

By considering the most restrictive condition between relations (1) and (9) for the maximum distance and the star density in the solar neighbor­hood (Scalo, 1986), one can compute the number of stellar systems where terrestrial planets can be studied. Multiple stars are not included, and the calculations assume a 5 X 1.5 m telescope array located on a 2r = 50 m circle. Tables 1 and 2 give the solutions for three scientific programs. Program 1 is planet detection. In about 100 stellar systems, planets can be searched for, during one integration year. Most of them are late F, G and early K stars, which is quite convenient, since they are considered as the best candidates to have habitable planets (Kasting et al., 1993). Table 1 assumes Res = 2, t :S 30 hr, and total integration time of 1 yr, allowing 3 observations of the same system at different dates. The maximum distances are D sep , allowing for the angular separation of a 300 K planet from its star, and DSNR for its detection with SNR = 5. For each spectral class, the limiting distance is underlined. Program 2 is spectroscopy of C02 with Res = 6, SNR = 12.5, t :S 200 h, and total integration time limited to 1 year. Program 3 is spec­troscopy of 02 with Res = 20, SNR = 20, t ~ 800 h, and total integration time limited to 2 yr.

During the next three integration years, longer observations (t ~ 800 hr) at higher spectral resolution (Res = 20) could be performed on typical­ly 45 stellar systems selected among the previous ones. The first objective would be to search for C02 at 15 pm. The presence or absence of this gas would indicate a deep similarity or difference with the atmospheres of Solar telluric planets, because all of the latter contain this gas. That of H20 at A < 8 pm would indicate a habitable planet, and 0 3 (9.6pm) would reveal an important photosynthesis activity, indicating the presence of carbon chem­istry based life, which would be a major discovery. The presence of CH4 and NH3 could also be searched for in this extremely informative part of the electromagnetic spectrum through their 7.65 pm and 10.5 pm bands.

5. Conclusion

The proposed DARWIN mission addresses one of the most fundamental problems that science can deal with. In addition, the mission would have important purely astronomical by-products for studying the central parts of young stellar disks, circumstellar envelopes, and narrow-line regions of AGN and QSO's.

Challenging technological problems have still to be solved, such as our capability to build a very high rejection, achromatic, nulling interferometer. and large deployable or variable size structures in Space. However, none seems out of range of our next decade technology. The European Space

THE DARWIN PROJEer 145

Agency is presently considering such a compelling mission in its Horizon 2000 Plus program.

Acknow ledgements

We are grateful to V. Demuy for her kindness and efficiency during the preparation of this manuscript.

References

Angel, R.: 1989, in The Next Generation Space Telescope, eels. P. Bely, C. Burrows, and G. Illingworth, Space Telescope Science Institute, Baltimore, p 81

Angel, J. R., Cheng A. Y., and Woolf N. J.: 1986, Nature 322,341-343 Boulanger, F., and Perault, M.: 1988, Astrophysical Journal 330, 964-985 Bracewell, R. N.: 1978, Nature 274,780-781 Bracewell, R. N., and McPhie, R. H.: 1979, Icarus 38, 136-147 Kasting, J. F., Holland, H. D., Pinto, J. P.: 1985, J. of Geophys. Res. 90 10,497 Kasting, J. F., Whitmire, D. P., and Reynolds, R. T.: 1993. Icarus 101, 108-128 Leger, A., Pirre, M., and Marceau, F. J.: 1993, Astronomy and Astrophysics 277, 309-313 Owen, T.: 1980, in Strategies for the Search of Life in the Universe, eel. M. D. Papagiannis,

Reidel, Dordrecht Reach W. T., et al.: 1995 Nature 374, 521-523 Scalo J. M.: 1986, Fund. of Cosmic Phys. 11, 1-278 Thronson, H .A., Harwarden, T. G., Penny A. I., and Davies, J. K: 1993, EDISON proposal

to ESA M3 mission, Rutherford Appleton Laboratory, Chilton, UK TOPS Report: 1992, 'Towards Other Planetary Systems', ed. B. F. Burke, NASA Solar

System Exploration Division, Washington D.C.

146

John Bally Chas Beichman

Anneila Sargent

PUBLIC INVOLVEMENT IN EXTRA-SOLAR PLANET DETECTION

PAT DASCH Editor-in-Chief, Ad Astra Magazine

The National Space Society

Abstract. A survey of recent popular literature on planet detection was undertaken to develop a broad view of public reactions to a program to search for planets around other stars. In this article, I discuss the interest in extra-solar planet searches, compared to other space ventures in the current political and economic climate. I also describe the role of the press and the need for public support to develop a nationally-funded space science program.

1. Introduction

A survey of recent popular literature on planet detection was undertaken to develop a broad view of public reactions to a program to search for planets around other stars. Interest in space has waned in the post-Challenger era. The public has become tired of references to "space, the final frontier." The media has become cynical about NASA references to "firsts" and "records." While rocketing humans into space and working in orbit remain costly and dangerous pursuits, they are too routine to be newsworthy. Some leaders in space science and space program management have identified a need for a new focus for future space operations - something exciting that will tease the imagination today without costing a fortune tomorrow.

2. Floating the Trial Balloon

In 1994, NASA Administrator Daniel Goldin floated a trial balloon. To the American Geophysical Union he said: "In the not too distant future, we will have the technology needed to image planets that might orbit nearby stars ... What a revelation that would be. That would change everything - no human endeavor or human thought would be untouched by that discovery." Goldin's choice of words suggests that such a program might contain the necessary magic to again excite the public about space. We could do something, pas­sively, using wonderful technology (rather than risking humans on hazardous voyages) and it would change the way we see life in the universe. As pre­sented here, this concept doesn't commit us to attaining anything beyond our grasp, because the NASA Administrator states that we will have the technology "in the not too distant future" .

Astrophysics and Space Science 241: 147-153, 1996. © 1996 Kluwer Academic Publishers.

148 PAT DASCH

During Spaceweek 1994, the story was elaborated upon, introducing prob­lems with the public perception of a search for extra-solar planets. On the Fox Morning News on July 19, Daniel Goldin said: "We could go to Mars, or we could go back to the Moon and build an observatory that might find planets around nearby stars, blue planets. Think how that would change how we view ourselves".

Later the same day, Goldin developed his theme a little further on AP Radio: "We could even go to the back side of the Moon and build the most incredible astronomical observatory so we could determine whether there are planets around nearby stars and perhaps have a chance to find a blue planet. NASA is getting ready for the next bold step. We are not going to do anything that the American people don't want to do. We reflect the spirit of America. If America wants to go on, NASA will go on."

These statements introduce major problems. First, they draw the search for extra-solar planets into direct comparison with the human exploration of space. Human missions to Mars and the Moon would be in comeptition with the search for planets around other stars as the potential "next bold step" for NASA. Second, in suggesting that we could find "blue planets", i.e. Earth-like planets, a new debate is opened on technological capabilities and the timeline within which NASA might deliver results. We know we can find planets around other stars, because this has already been accomplished. All indications suggest that a program to find Earth-like planets could not be initiated for 20 years. This is too far into the future to muster public support.

Furthermore, looking for an Earth-like planet opens up implications about another place to go - a target for human exploration and expansion, along with the issue of looking for other forms of life in the universe. Journalists in Washington Post, Science, Final Frontier, to quote just three examples, raised these questions, but the scientific community did not respond. One is left asking: what is it that the scientific community suggests we search for? Are the scientists and Administrator Goldin singing the same song? Just what are we about here? How much of this is possible, and how much is not? And is the public interested anyway?

3. Public Interest in Finding Planets around Other Stars

Before developing the discussion further, it is important to ask: How con­cerned is the public about finding planets around other stars? Space explo­ration is not a priority for the vast majority of the American public. An opinion survey conducted in 1994 revealed that only 12% of the population is interested in the space program. Another survey of members of the public interested in space found that their priorities for spending taxpayer dollars

PUBLIC INVOLVEMENT IN EXTRA-SOLAR PLANET DETECTION 149

were:

1. New low-cost launch system to replace the shuttle 2. Space Station 3. Return to the Moon and establish a permanent settlement 4. Mars exploration

Distant planetary science missions figured eighth in a list of twelve items. Search for Extra-Terrestrial Intelligence (SETI) was placed eleventh.

3.1. THE PLUTO FACTOR

One potential barrier to "selling" the search for extra-solar planets to the public is the simple fact that we have yet to complete the reconnaissance of our own solar system. So far, we have not taken a close-up look at Pluto. The space-interested public knows that NASA has been studying a Pluto mission for several years. Why should we b-pass that mission, which could most beneficially be flown in the next few years (to reach Pluto while there is still an atmosphere to investigate and while the planet is not too far away) to commence a major long-term campaign to look for planets elsewhere?

3.2. EMBARKING ON A FALSE PREMISE?

On September 12, 1994, in an address at the Johnson Space Center, Goldin remarked: "I've asked for a national debate on what the next major mis­sion for NASA ought to be ... One human mission is we go to the Moon, we build an astronomical observatory, and we could image planets around nearby stars ... with large baseline interferometers ... Could you imagine if we found a new planet with 25-meter resolution? It would knock your socks off. It would change the way every person on this planet thinks about them­selves ... ".

It is unclear how one would initiate a serious national debate on another major space enterprise in the current political climate. Such an attempt could damage efforts to maintain realistic levels of funding for ongoing and committed programs and would be unlikely to receive a sympathetic hearing in the Congress. Furthermore, there is considerable opposition to the concept of "One Big Goal" in the pro-space constituency outside of Congress. As a strategy, it worked in achieving the Apollo Moon landings, but it was instrumental in ending the Apollo program since the big goal - landing humans on the Moon before the Russians - had been achieved. Other big projects have not had the same "pizzazz" as Apollo and have kept NASA from the cutting edge in technology (where the politics ofthe moment dictate NASA should be) by tying the agency up for years in long-term, big-budget projects.

150 PAT DASCH

However, space activists who advocate expansion of a human presence in space would endorse a search for extra-solar planets that involves the estab­lishment of lunar observatories. Such supporters will recognize the planet search as good science that should be undertaken as a methodical, multi­year project which will simultaneously fulfill their goals of renewed lunar exploration and establishment of a lunar outpost.

3.3. EXTRA-SOLAR PLANETS AND THE PRESS

In April 1994, Science carried an article discussing the search for extra-solar planets which stated that NASA was "still looking for a planet that an alien might call home." The piece continued: "NASA believes nearby Sun-like stars are more interesting candidates to study, since their planets have at least a fighting chance of harboring E.T. or a relation".

This account moves the apparent goal of a planet search another giant step. No longer are we confined to looking for a planet or an Earth-like planet, but for a planet that harbors life. This may enlist some support from SETI and from other groups interested in proving that there is life elsewhere in the universe. But, more importantly, it shows that it simply too tempting to think of the possible implications beyond finding a planet around another star. Kathy Sawyer commented in October 1992 in the Washington Post when covering the start-up of the SETI program at Arecibo (restyled as HRMS, the High-Resolution Microwave Survey by NASA). "Are we alone?" is one of humanity's most profound and ancient questions. However, it is not clear that scientists who advocate a search for extra-solar planets embrace a search for extra- terrestrial life.

4. Rationale for the Search for Extra-solar Planets

In Pale Blue Dot, published in 1994, Carl Sagan put the reasons to search for planets around other stars in this way: "We will begin to know which aspects of our system are the rule and which the exception. What is more common -planets like Jupiter, planets like Neptune, or planets like Earth? What other categories of worlds are there? What do elderly planetary systems, billions of years more evolved than ours, look like?" This is reasoning born of scientific inquiry, and it is probably more in line with the astronomical community's rationale.

In Pale Blue Dot, Sagan makes a case for becoming a truly spacefaring civilization, arguing that humanity needs to move out into the universe to have more than one home base, in order to avoid the fate of the dinosaurs ( " ... in the long run, every planetary society will be endangered by impacts from space, every surviving civilization is obliged to become spacefaring -

PUBLIC INVOLVEMENT IN EXTRA-SOLAR PLANET DETECTION 151

not because of exporatory or romantic zeal, but for the most practical reason imaginable: staying alive.") The discovery of Earth-like planets around other stars would be sure to influence attitudes about moving off-planet.

5. Developing a Base of Public Support for a Space Program

5.1. WHO SUPPORTS SPACE EXPLORATION?

Space enthusiasts fall into two distinct categories. There are those who view space exploration as something to experience vicariously. Among this group we might count those who believe that a virtual reality tour of Mars would be satisfying or those who would be happy to sit back in the comfort of their own living room and watch an international crew land on Mars on TV. The other group of space enthusiasts are those who want direct experience of space. These people want to go into space themselves or see that we are established on a path that will open opportunities for their desendants to go into space. The membership of the National Space Society falls in this category.

It is relatively easy to satisfy the first group. Planetary exploration and astronomy lend themselves to the production of highly impressive visual imagery, and there are many scientists capable of conveying the excitement of their work and describing the advances contained in the newly acquired data. A fair proportion of this group will be prepared to see Congress con­tinue to vote considerable sums for scientific research, will think the results "neat", and may share what they learned with friends and family if they attend an interesting lecture.

While this tacit support is extremely gratifying, these passive supporters are not going to write their Congressman or contribute to a national debate on the future of U.S. space policy. Research shows that supporters who want to experience space for themselves or their children and grandchildren are much more likely to write or visit Congress, to participate in demonstrations, or to attend conferences. In short, theirs are the voices that are heard by those who control the nation's budget for space exploration.

How does one attract this activist branch of the space community to a program that is long-term and doesn't send humans anywhere beyond a few chilly mountaintop observatories? You involve them. You invite them into the observatory, show them how you process data, let them help to produce your newsletter or update your World-Wide-Web home page. You encourage them to help you produce and distribute educational kits. You may even be able to enlist the help of a few in co-authoring technical papers.

What will be the payback? You will have established an interactive rela­tionship with the taxpayers who fund your research, and you will have con-

152 PAT DASCH

nected with a group of people who are vocal, who communicate their enthu­siasm, and who have influence with both the general public and those who represent the public in the U.S. Congress.

5.2. WHY IS IT NECESSARY TO BUILD A PUBLIC CONSTITUENCY?

No one has a "right" to do publicly funded research. That right has to be won by convincing the public and the politicians that what you want to do is worthy and reasonable. Given the policy priorities outlined since the Republicans took control of Congress in 1994, it will be increasingly difficult to convince those in authority that your project is entitled to a slice of a diminishing pie. To stand any reasonable chance of obtaining funding to develop a new project, or to expand an existing program, it will be essential to build a public constituency.

The Republican leadership in Congress has made it abundantly clear that it will listen to all shades of public opinion before determining the future of space policy by committing funds. No longer can NASA deliver a programmatic outline and a budget to match and expect that Congress will sign up. Indeed, the Congressional committees that control NASA and NSF funding are increasingly instructing NASA in the direction that the space agency should follow. And, they are penalizing the agency when it proceeds with a program according to internally pre-determined guidelines, rather than those prescribed by Congress.

This is a very different Congressional environment. No longer are there two or three key people who have to be convinced, in order to get a measure endorsed. The new members listen closely to their constituents. Representa­tives from professional societies, who have a vested interest in the success of a program, carry less weight than individuals from a member's constituency who can show a benefit to the local community, as well as to the scientific community at large, from funding a particular program.

6. Conclusion

In the political climate at the end of the millenium, it is essential to have a clearly defined vision, a small set of easily understood objectives, and a supporting set of goals, some of which (preferably, up to 50%) can be attained within the next ten years. A program that has multiple possibilities and an apparently ever-broadening agenda sends a confusing message and will not take root with the public.

To garner support for space-science programs, it is essential to build a public constituency for the program from the outset and to nourish support throughout the life of the program. Well-coordinated media and education­al outreach programs can help to keep the program in the public eye. If,

PUBLIC INVOLVEMENT IN EXTRA-SOLAR PLANET DETECTION 153

as suggested at the Boulder meeting, it is likely to take 20 years to attain the necessary technological development to identify, for example, a "blue planet" circling another star, then the program should be developed incre­mentally, with meaningful goals along the way. Such landmarks could be technology developments, especially ones with other scientific or industrial applications, or they could be scientific achievements that result from the new technologies.

In the current polical and economic climate, it is important to sign the entire space-science community up to the program and the plan of action. One must resist the temptation, endemic in scientific communities, to "grow the program" to encompass additional goals, additional technologies, and added expense. (This may already have happened, to its detriment, in the search for extra-solar planets.) A program must achieve what it set out to achieve ~ on time and within budget.

Harley Thronson (L) and Michael Shull (R)

ACRIM-l radiometer: 121 Adaptive optics: 105 AFOE spectrograph: 62, 73 Ammonia (NH3): 4, 144 Angular momentum: 29 Apollo program: 149 Asteroid belt: 28ff Astrometry: 43, 77ff, 85ff, 89ff, 106 Atmospheric refraction: 82

Binary stars: 81, 112, 126 "Blue planet": 148 Brown dwarfs: 56

Carbonates: 3 Carbon dioxide (C02): 3, 4,18, l35ff Carbonate-silicate cycle: 4ff Charge-coupled devices (CCDs): 115, 123 Climate: 3ff Comet bombardment: 8 Coronagraph: 105ff CORAVEL program: 52, 64

DARWIN project: 41, l35ff Doppler velocities: 128 Dwarfs stars: 37

Earth-like planets: 101, 109 Eclipsing binaries: 37 EDISON program: 141 ELODIE spectrograph: 62,65, 71

"Faint young Sun": 6 Fabry-Perot spectrograph: 61 Frenchman:

angry 61ff FRESIP mission: 41, I11ff

GAIA mission: 89ff

Galileo mission: 17 Geologic reord: 7 Goldin, Daniel: 147ff Giant planets: 35, 56 Giant impacts: 28 Gliese catalog: 85 Greenhouse effect: 8ff, 136

Habitable zones: 3ff, 25ff, 112, 135, 144 Hipparcos mission: 86, 97ff

INDEX

HST guide-star catalog: 127ff

Ice condensation zone: 87 Interferometry:

imaging interferometry 87, 105ff, 137 Bracewell interferometer 141

Infrared cirrus: 141 Inner planets: 27, 32, 35, 112ff ISO mission: 142

Jupiters: 31, 77ff, l00ff, 112, l31 failed Jupiters 57

Laser metrology: 86 LONEOS project: 39

Mars: 10, 16 Media: 147ff Methane (CH4): 4, 16, 144 Microlensing: 35

NASA: 147ff Neptune: 58 Nitrous oxide (N20): 17

Occultations: 35ff, I11ff Orbital resonances: 27, 32 Organic chemistry: l36 OSI mission: 85, 93 Oxygen (02): l36 Ozone (03): l3ff, l35ff

Parallax: 79 Passive cooling: 141 Periodogram: 48 Photometry: 35ff Photon noise: 62 Photosynthesis: 14, 136 Planetary disks: 26, 29, 37 Planetary embryos: 27 Planetsimals: 27 Planets:

atmospheres 3ff formation 8, 25ff habitable 3ff, 25ff, 112, l35, 144 masses 44ff spacing 12

Pluto: 149 POINTS mission: 93, 98 Proper motion: 47, 77ff

Astrophysics and Space Science 241: 155-156, 1996.

156

Public support: 151ff Pulsar monitoring: 35, 90,112

Radial velocities: 43ff, 61ff Reflex velocity: 45

Scrambler noise: 69, 71ff Secular acceleration: 80 SIRTF mission: 127, 142 Solar Maximum Mission: 115, 122 SOLSTICE spacecraft: 122 Space policy: 151 Speckle interferometry: 78, 107 STARS project: 39 Stars:

Barnard's star 77ff candidates 98ff duplicity 91 variability 58, 121ff

INDEX

Psi Ursae Majoris 67ff Tau Ceti 81 47 Ursae Majoris 55 51 Pegasi 55,118 70 Virginis 55

Starspots: 86ff "Super-planets": 57

Tidal lock: 13 TOPS report: 35,61,75,90,135 Transits: 39, l11ff

Uranus: 58, 77ff Venus: 8

Water (H20): 3, 8 Window function: 52

Zodiacal light: 105ff, 140ff