Radial Velocity Detection of Planets:II. Results

1. Period Searching: How do you find planets in your data?

2. Exoplanet discoveries with the radial velocity method

Finding a Planet in your Radial Velocity Data

1. Determine if there is a periodic signal in your data.

2. Determine if this is a real signal and not due to noise.

3. Determine the nature of the signal, it might not be a planet!

4. Derive all orbital elements

1. Period Analysis

How do you know if you have a periodic signal in your data? Here are RV data from a pulsating star

What is the period?

Try 16.3 minutes:

Lomb-Scargle Periodogram of the data:

1. Period Analysis: How do you find a signal in your data

1. Least squares sine fitting:

Fit a sine wave of the form:

V(t) = A·sin(t + ) + Constant

Where = 2/P, = phase shift

Best fit minimizes the 2:

2 = di –gi)2/N

di = data, gi = fit

Note: Orbits are not always sine waves, a better approach would be to use Keplerian Orbits, but these have too many parameters

1. Period Analysis

2. Discrete Fourier Transform:

Any function can be fit as a sum of sine and cosines

FT() = Xj (T) e–itN0

j=1

A DFT gives you as a function of frequency the amplitude (power = amplitude2) of each sine wave that is in the data

Power: Px() = | FTX()|2

1N0

Px() =

1N0

N0 = number of points

[( Xj cos tj + Xj sin tj ) ( ) ]2 2

Recall eit = cos t + i sint

X(t) is the time series

A pure sine wave is a delta function in Fourier space

t

PAo

FT

Ao

1/P

1. Period Analysis

3. Lomb-Scargle Periodogram:

Power is a measure of the statistical significance of that frequency (period):

12

Px() =[ Xj sin tj–]

2

j

Xj sin2 tj–

[ Xj cos tj–]2

j

Xj cos2 tj–j

+12

False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal

N = number of indepedent frequencies ≈ number of data points

tan(2) = sin 2tj)/cos 2tj)j j

The first Tautenburg Planet: HD 13189

Least squares sine fitting: The best fit period (frequency) has the lowest 2

Discrete Fourier Transform: Gives the power of each frequency that is present in the data. Power is in (m/s)2 or (m/s) for amplitude

Lomb-Scargle Periodogram: Gives the power of each frequency that is present in the data. Power is a measure of statistical signficance

Am

plitu

de (m

/s)

Noise level

Alias Peak

False alarm probability ≈ 10–14

Alias periods:

Undersampled periods appearing as another period

Raw data

After removal of dominant period

To summarize the period search techniques:

1. Sine fitting gives you the 2 as a function of period. 2 is minimized for the correct period.

2. Fourier transform gives you the amplitude (m/s in our case) for a periodic signal in the data.

3. Lomb-Scargle gives an amplitude related to the statistical signal of the data.

Most algorithms (fortran and c language) can be found in Numerical Recipes

Period04: multi-sine fitting with Fourier analysis. Tutorials available plus versions in Mac OS, Windows, and Linux

http://www.univie.ac.at/tops/Period04/

2. Results from Doppler SurveysButler et al. 2006, Astrophysical Journal, Vol 646, pg 505

Telescope Instrument Wavelength Reference1-m MJUO Hercules Th-Ar1.2-m Euler Telescope CORALIE Th-Ar1.8-m BOAO BOES Iodine Cell1.88-m Okayama Obs, HIDES Iodine Cell1.88-m OHP SOPHIE Th-Ar2-m TLS Coude Echelle Iodine Cell2.2m ESO/MPI La Silla FEROS Th-Ar2.7m McDonald Obs. 2dcoude Iodine cell 3-m Lick Observatory Hamilton Echelle Iodine cell3.8-m TNG SARG Iodine Cell3.9-m AAT UCLES Iodine cell3.6-m ESO La Silla HARPS Th-Ar8.2-m Subaru Telescope HDS Iodine Cell8.2-m VLT UVES Iodine cell9-m Hobby-Eberly HRS Iodine cell10-m Keck HiRes Iodine cell

Campbell & Walker: The Pioneers of RV Planet Searches

1980-1992 searched for planets around 26 solar-type stars. Even though they found evidence for planets, they were not 100% convinced. If they had looked at 100 stars they certainly would have found convincing evidence for exoplanets.

1988:

„Probable third body variation of 25 m s–1, 2.7 year period, superposed on a large velocity gradient“

Campbell, Walker, & Yang 1988

Eri was a „probable variable“

Filled circles are data taken at McDonald Observatory using the telluric lines at 6300 Ang.

The first extrasolar planet around a normal star: HD 114762 with Msini = 11 MJ discovered by Latham et al. (1989)

The Brown Dwarf Desert

Mass Distribution Global Properties of Exoplanets:

Planet: M < 13 MJup → no nuclear burning

Brown Dwarf: 13 MJup < M < ~80 MJup → deuterium burning

Star: M > ~80 MJup → Hydrogen burning

Up-to-date Histograms with all planets:

One argument: Because of unknown vsini these are just low mass stars seen with i near 0

i decreasing

probability decreasing

P(i < ) = 1– cos Probability an orbit has an inclination less than

e.g. for m sin i = 0.5 MJup for this to have a true mass of 0.5 Msun sin i would have to be 0.01. This implies = 0.6 deg or P =0.00005: highly unlikely!

Argument against stars #1

Argument against stars #2

Some planetary systems have multiple planets, for example m1 x sini = 5 MJup, and m2 x sini = 0.03 MJup. To make the first planet a star requires sini =0.01. Other planet would still be mtrue=3 MJup

Brown Dwarf Desert: Although there are ~100-200 Brown dwarfs as isolated objects, and several in long period orbits, there is a paucity of brown dwarfs (M= 13–50 MJup) in short (P < few years) as companion to stars

An Oasis in the Brown Dwarf Desert: HD 137510 = HR 5740

A note on the naming convention:

Name of the star: 16 Cyg

If it is a binary star add capital letter B, C, D

If it is a planet add small letter: b, c, d

55 CnC b : first planet to 55 CnC

55 CnC c: second planet to 55 CnC

16 Cyg B: fainter component to 16 Cyg binary system

16 Cyg Bb: Planet to 16 Cyg B

The IAU has yet to agree on a rule for the naming of extrasolar planets

Semi-Major Axis Distribution

Semi-major Axis (AU) Semi-major Axis (AU)N

umbe

r

Num

ber

The lack of long period planets is a selection effect since these take a long time to detect

The short period planets are also a selection effect: they are the easiest to find and now transiting surveys are geared to finding these.

Updated:

Eccentricity distribution

Fall off at high eccentricity may be partially due to an observing bias…

e=0.4 e=0.6 e=0.8

=0

=90

=180

…high eccentricity orbits are hard to detect!

For very eccentric orbits the value of the eccentricity is is often defined by one data point. If you miss the peak you can get the wrong mass!

2 ´´

Eri

Comparison of some eccentric orbit planets to our solar system

At opposition with Earth would be 1/5 diameter of full moon, 12x brighter than Venus

EccentricitiesMass versus Orbital Distance

There is a relative lack of massive close-in planets

Classes of planets: 51 Peg Planets: Jupiter mass planets in short period orbits

Discovered by Mayor & Queloz 1995

• ~35% of known extrasolar planets are 51 Peg planets (selection effect)

• 0.5–1% of solar type stars have giant planets in short period orbits

• 5–10% of solar type stars have a giant planet (longer periods)

Classes of planets: 51 Peg Planets

Another short period giant planet

Butler et al. 2004

McArthur et al. 2004Santos et al. 2004

Msini = 14-20 MEarth

Classes of planets: Hot Neptunes

If there are „hot Jupiters“ and „hot Neptunes“ it makes sense that there are „hot Superearths“

Mass = 7.4 ME P = 0.85 d

CoRoT-7b

Classes: The Massive Eccentrics

• Masses between 7–20 MJupiter

• Eccentricities, e > 0.3

• Prototype: HD 114762 discovered in 1989!

m sini = 11 MJup

There are no massive planets in circular orbits

Classes: The Massive Eccentrics

Planet-Planet Interactions

Initially you have two giant planets in circular orbits

These interact gravitationally. One is ejected and the remaining planet is in an eccentric orbit

Lin & Ida,  1997, Astrophysical Journal, 477, 781L

Red: Planets with masses < 4 MJup

Blue: Planets with masses > 4 MJup

• Most stars are found in binary systems• Does binary star formation prevent planet formation?

• Do planets in binaries have different characteristics?

• For what range of binary periods are planets found?• What conditions make it conducive to form planets?

(Nurture versus Nature?)• Are there circumbinary planets?

Why should we care about binary stars?

Planets in Binary Systems

Star a (AU)16 Cyg B 80055 CnC 540

HD 46375 300Boo 155 And 1540

HD 222582 4740HD 195019 3300

Some Planets in known Binary Systems:

There are very few planets in close binaries. The exception is Cep.

For more examples see Mugrauer & Neuhäuser 2009, Astronomy & Astrophysics, vol 494, 373 and references therein

The first extra-solar Planet may have been found by

Walker et al. in 1992 in a

binary system:

Ca II is a measure of stellar activity (spots)

2,13 AUa0,2e

26,2 m/sK

1,76 MJupiterMsini2,47 YearsPeriod

Planet

18.5 AUa 0,42 ± 0,04e

1,98 ± 0,08 km/sK

~ 0,4 ± 0,1 MSunMsini56.8 ± 5 YearsPeriod

Binary Cephei

Walker et al. Excluded the planet hypothesis largely because the Ca II line strength showed variations with the same period as the velocity data. However, if you divide the Ca II in half (two time series) a signal is seen in the first half but not the last half. The signal in the last half is not the same period as the planet signal.

CepheiPrimary star (A)

Secondary Star (B) Planet (b)

Neuhäuser et al. Derive an orbital inclination of AB of 119 degrees. If the binary and planet orbit are in the same plane then the true mass of the planet is 1.8 MJup.

The planet around Cep is difficult to form and on the borderline of being impossible.

Standard planet formation theory: Giant planets form beyond the snowline where the solid core can form. Once the core is formed the protoplanet accretes gas. It then migrates inwards.

In binary systems the companion truncates the disk. In the case of Cep this disk is truncated just at the ice line. No ice line, no solid core, no giant planet to migrate inward. Cep can just be formed, a giant planet in a shorter period orbit would be problems for planet formation theory.

The interesting Case of 16 Cyg B

Effective Temperature: A=5760 K, B=5760 KSurface gravity (log g): 4.28, 4.35

Log [Fe/H]: A= 0.06 ± 0.05, B=0.02 ± 0.0416 Cyg B has 6 times less Lithium

These stars are identical and are „solar twins“. 16 Cyg B has a giant planet with 1.7 MJup in a 800 d period

Kozai Mechanism: One Explanation for the high eccentricty of 16 Cyg B

Two stars are in long period orbits around each other.

A planet is in a shorter period orbit around one star.

If the orbit of the planet is inclined, the outer planet can „pump up“ the eccentricity of the planet. Planets can go from circular to eccentric orbits.

This was first investigated by Kozai who showed that satellites in orbit around the Earth can have their orbital eccentricity changed by the gravitational influence of the Moon

Kozai Mechanism: changes the inclination and eccentricity

Planetary Systems: 49 Multiple Systems

49 Extrasolar Planetary Systems (18 shown) Star P (d) MJsini a (AU) eHD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41GL 876 30 0.6 0.1 0.27 61 2.0 0.2 0.1047 UMa 1095 2.4 2.1 0.06 2594 0.8 3.7 0.00

HD 37124 153 0.9 0.5 0.20 550 1.0 2.5 0.4055 CnC 2.8 0.04 0.04 0.17 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34 260 0.14 0.78 0.2 5300 4.3 6.0 0.16Ups And 4.6 0.7 0.06 0.01 241.2 2.1 0.8 0.28 1266 4.6 2.5 0.27HD 108874 395.4 1.36 1.05 0.07

1605.8 1.02 2.68 0.25HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17HD 217107 7.1 1.37 0.07 0.13 3150 2.1 4.3 0.55

Star P (d) MJsini a (AU) eHD 74156 51.6 1.5 0.3 0.65 2300 7.5 3.5 0.40 HD 169830 229 2.9 0.8 0.31 2102 4.0 3.6 0.33HD 160691 9.5 0.04 0.09 0 637 1.7 1.5 0.31

2986 3.1 0.09 0.80

HD 12661 263 2.3 0.8 0.35

1444 1.6 2.6 0.20HD 168443 58 7.6 0.3 0.53 1770 17.0 2.9 0.20HD 38529 14.31 0.8 0.1 0.28 2207 12.8 3.7 0.33HD 190360 17.1 0.06 0.13 0.01 2891 1.5 3.92 0.36HD 202206 255.9 17.4 0.83 0.44 1383.4 2.4 2.55 0.27HD 11964 37.8 0.11 0.23 0.15

1940 0.7 3.17 0.3

The 5-planet System around 55 CnC

5.77 MJ

Red lines: solar system plane orbits

•0.11 MJ ••

0.17MJ

0.03MJ

0.82MJ

The Planetary System around GJ 581

7.2 ME

5.5 ME

16 ME

Inner planet 1.9 ME

Can we find 4 planets in the RV data for GL 581?

1 = 0.317 cycles/d

2 = 0.186

3 = 0.077

4 = 0.015

Note: for Fourier analysis we deal with frequencies (1/P) and not periods

The Period04 solution:P1 = 5.38 d, K = 12.7 m/s

P2 = 12.99 d, K = 3.2 m/s

P3 = 83.3 d, K = 2.7 m/s

P4 = 3.15, K = 1.05 m/s

P1 = 5.37 d, K = 12.5 m/s

P2 = 12.93 d, K = 2.63 m/s

P3 = 66.8 d, K = 2.7 m/s

P4 = 3.15, K = 1.85 m/s

=1.53 m/s=1.17 m/s

Almost:

Conclusions: 5.4 d and 12.9 d probably real, 66.8 d period is suspect, 3.15 d may be due to noise and needs confirmation.

A better solution is obtained with 1.4 d instead of 3.15 d, but this is above the Nyquist sampling frequency

Published solution:

Resonant Systems Systems Star P (d) MJsini a (AU) eHD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41

GL 876 30 0.6 0.1 0.27 61 2.0 0.2 0.10

55 CnC 14.6 0.8 0.1 0.0 44.3 0.2 0.2 0.34

HD 108874 395.4 1.36 1.05 0.07 1605.8 1.02 2.68 0.25

HD 128311 448.6 2.18 1.1 0.25 919 3.21 1.76 0.17

2:1 → Inner planet makes two orbits for every one of the outer planet

→

→

2:1

2:1

→ 3:1

→ 4:1

→ 2:1

•

Eccentricities

Period (days)Red points: SystemsBlue points: single planets

EccentricitiesMass versus Orbital Distance

Red points: SystemsBlue points: single planets

On average, giant planets in planetary sytems tend to be lighter than single planets. Either 1) Forming several planets in a protoplanetary disks „divides“ the mass so you have smaller planets, or 2) if you form several massive planets they are more likely to interact and most get ejected.

The Dependence of Planet Formation on Stellar Mass

Exoplanets around low mass stars

Ongoing programs:

• ESO UVES program (Kürster et al.): 40 stars

• HET Program (Endl & Cochran) : 100 stars

• Keck Program (Marcy et al.): 200 stars

• HARPS Program (Mayor et al.):~200 starsResults:

• Giant planets (2) around GJ 876. Giant planets around low mass M dwarfs seem rare

• Hot neptunes around several.

Currently too few planets around M dwarfs to make any real conclusions

0123456789

101112

0.025 0.225 0.425 0.625 0.825 1.025 1.225 1.425

2 planets with masses 2.1, 2.3 MJup

1 Planet with mass 4.9 MJup

GL 876 System

1.9 MJ

0.6 MJ

Inner planet 0.02 MJ

Exoplanets around massive stars

Difficult with the Doppler method because more massive stars have higher effective temperatures and thus few spectral lines. Plus they have high rotation rates. A way around this is to look for planets around giant stars. This will be covered in „Planets off the Main Sequence“

Result: Only a few planets around early-type, more massive stars, and these are mostly around F-type stars (~ 1.4 solar masses)

Galland et al. 2005

HD 33564

M* = 1.25

msini = 9.1 MJupiter

P = 388 days

e = 0.34

F6 V star

HD 8673

A Planet around an F star from the Tautenburg Program

Frequency (c/d)

Scar

gle

Pow

erP = 328 days

Msini = 8.5 Mjupiter

e = 0.24

An F4 V star from the Tautenburg Program

M* = 1.4 Mּס

Mstar ~ 1.4 Msun Mstar ~ 1 Msun

Mstar ~ 0.2 Msun

Preliminary conclusions: more massive stars have more massive planets with higher frequency. Less massive stars have less massive planets → planet formation is a sensitive function of the planet mass.

Astronomer‘s

Metals

More Metals ! Even more Metals !!

Planets and the Properties of the Host Stars: The Star-Metallicity Connection

The „Bracket“ [Fe/H]

Take the abundance of heavy elements (Fe for instance)

Ratio it to the solar value

Take the logarithm

e.g. [Fe/H] = –1 → 1/10 the iron abundance of the sun

These are stars with metallicity [Fe/H] ~ +0.3 – +0.5

There is believed to be a connection between metallicity and planet formation. Stars with higher metalicity tend to have a higher frequency of planets. This is often used as evidence in favor of the core accretion theory

Valenti & Fischer

The Planet-Metallicity Connection?

There are several problems with this hypothesis

Endl et al. 2007: HD 155358 two planets and..

…[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection

The Hyades

• Hyades stars have [Fe/H] = 0.2

• According to V&F relationship 10% of the stars should have giant planets,

The Hyades

• Paulson, Cochran & Hatzes surveyed 100 stars in the Hyades

• According to V&H relationship we should have found 10 planets

•We found zero planets!Something is funny about the Hyades.

False Planets

or

How can you be sure that you have actually discovered a planet?

HD 166435

In 1996 Michel Mayor announced at a conference in Victoria, Canada, the discovery of a new „51 Peg“ planet in a 3.97 d. One problem…

HD 166435 shows the same period in in photometry, color, and activity indicators.

This is not a planet!

What can mimic a planet in Radial Velocity Variations?

1. Spots or stellar surface structure

2. Stellar Oscillations

3. Convection pattern on the surface of the star

Starspots can produce Radial Velocity Variations

Spectral Line distortions in an active star that is rotating rapidly

Tools for confirming planets: Photometry

Starspots are much cooler than the photosphere

Light Variations

Color Variations

Relatively easy to measure

Ca II H & K core emission is a measure of magnetic activity:

Active star

Inactive star

Tools for confirming planets: Ca II H&K

HD 166435

Ca II emission measurements

Bisectors can measure the line shapes and tell you about the nature of the RV variations:

What can change bisectors:• Spots• Pulsations • Convection pattern on star

Span

Curvature

Tools for confirming planets: Bisectors

Correlation of bisector span with radial velocity for HD 166435

Spots produce an „anti-correlation“ of Bisector Span versus RV variations:

Activity Effects: Convection

Hot rising cell

Cool sinking lane

•The integrated line profile is distorted.

•The ratio of dark lane to hot cell areas changes with the solar cycle

RV changes can be as large as 10 m/s with an 11 year period

This is a Jupiter!One has to worry even about the nature long period RV variations

The Great 51 Peg Controversy, or

My personal piece of professional rubbish

Variations of Bisectors with Pulsations

Gray & Hatzes

Gray reported bisector variations of 51 Peg with the same period as the planet. Gray & Hatzes modeled these with nonradial pulsations

A beautiful paper that was completely wrong.

The 51 Peg Controversy

Hatzes et al.

More and better bisector data for 51 Peg showed that the Gray measurements were probably wrong. 51 Peg has a planet!

How do you know you have a planet?

1. Is the period of the radial velocity reasonable? Is it the expected rotation period? Can it arise from pulsations?

• E.g. 51 Peg had an expected rotation period of ~30 days. Stellar pulsations at 4 d for a solar type star was never found

2. Do you have Ca II data? Look for correlations with RV period.

3. Get photometry of your object

4. Measure line bisectors

5. And to be double sure, measure the RV in the infrared!

Radial Velocity Planets30 90 1000Period in years →

Red line: Current detection limitsGreen line detection limit for a precision of 1 m/s

Summary Radial Velocity Method

Pros:• Most successful detection method• Gives you a dynamical mass• Distance independent

• Will provide the bulk (~1000) discoveries in the next 10+ years

Summary

Radial Velocity Method

Cons:• Only effective for late-type stars• Most effective for short (< 10 – 20 yrs)

periods

• Only high mass planets (no Earths!)

• Projected mass (msin i)

• Other phenomena (pulsations, spots) can mask as an RV signal. Must be careful in the interpretation

Summary of Exoplanet Properties from RV Studies

• ~5% of normal solar-type stars have giant planets

• ~10% or more of stars with masses ~1.5 Mּס have giant planets that tend to be more massive (more on this later in the course)

• < 1% of the M dwarfs stars (low mass) have giant planets, but may have a large population of neptune-mass planets

→ low mass stars have low mass planets, high mass stars have more planets of higher mass → planet formation may be a steep function of stellar mass

• 0.5–1% of solar type stars have short period giant plants

• Exoplanets have a wide range of orbital eccentricities (most are not in circular orbits)

• Massive planets tend to be in eccentric orbits

• Massive planets tend to have large orbital radii

• Stars with higher metallicity tend to have a higher frequency of planets, but this needs confirmation