habitable planet formation in binary star systems

7/31/2019 Habitable Planet Formation in Binary Star Systems

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ICARUS 132, 196203 (1998)ARTICLE NO. IS985900

Habitable Planet Formation in Binary Star Systems

Daniel P. Whitmire, John J. Matese, and Lee Criswell

Department of Physics, University of Southwestern Louisiana, Lafayette, Louisiana 70504

E-mail: [email protected]

and

Seppo Mikkola

Tuorla Observatory, Turku University, 21500 Piikkio, Finland

Received March 26, 1997; revised December 24, 1997

1. INTRODUCTION

Assuming current models of terrestrial planet formation inModeling the accretion of terrestrial planets in thethe Solar System, we numerically investigate the conditions

System (Wetherill and Stewart 1993) and around under which the secondary star in a binary system will inhibitplanet growth in the circumstellar habitable zone. Runaway single stars (Wetherill 1996) suggests that planet formaccretion is assumed to be precluded if the secondary (1) causes within a stars habitable zone may be common. We dthe planetesimal orbits to cross within the runaway accretion a terrestrial planet that forms within the circumstellatime scale and (2) if, during crossing, the relative velocities of itable zone (Kasting et al. 1993; Whitmire and Reythe planetesimals have been accelerated beyond a certain criti- 1996) as a potentially habitable planet, recognizingcal value which results in disruption collisions rather than

many other conditions may be necessary for life to acaccretion. For a two solar mass binary with planetesimals in

evolve on such a planet. Since 2/3 of solar type stacircular orbits about one star at 1 AU, and a typical wide binaryknown members of multiple star systems it is of inteccentricity of 0.5, the minimum binary semimajor axis whichto consider the constraints placed on planet formatio

would not inhibit planet formation,ac , is 32AU. Ifthe planetesi- to the presence of a secondary star. Two configuramals orbit the center of mass of the binary system, ac 0.10AU, which is inside the tidal circularization radius. We obtain will be considered: the internal-planetesimal geomean empirical formula giving the dependencies ofac on the binary which the planetesimals orbit the primary and the exteccentricity, secondary mass, planetesimal location, and critical planetesimal geometry in which the planetesimals orbdisruption velocity. Based on the distributions of orbital ele- center of mass of the binary system. We assume thaments of a bias-corrected sample of nearby G-dwarfs, we find secondary star formed simultaneously with the primathat 60% of solar-type binaries cannot be excluded from this were not the case and the secondary star formhaving a habitable planet solely on the basis of the perturbative

was captured after the initial stages of planet formeffect of the secondary star. This conclusion is independent of

were complete, then planet accretion could havewhen the secondary star formed, nebula dissipative mecha-ceeded as expected for a single star. In this case thenisms, and the time scale for runaway planetesimal accretion,restriction would be the dynamical ejection of the pand is relatively insensitive to the mass of the secondary star,

itself (Graziani and Black1981; Pendletonand Black1the critical disruption velocity, and the location of planetesimalswithin the circumstellar habitable zone. An earlier study of The assumption of simultaneous star formation is coplanet formation in binary star systems came to a different vative in the sense that if it is invalid the probabilconclusion, namely that planet formation, even at Mercurys habitable planet formation is greater than our andistance, is unlikely except in widely separated systems (50 will suggest.AU), or when the secondary has a very low mass and near The accretion of planetesimals from a turbulent gacircular orbit as in the SunJupiter system. The discrepancy dust nebula is not well understood theoretically evwith the present numerical study is due in part to the different

the case of our own Solar System. Nonetheless, dust grunaway accretion time scales assumed and the neglect in the

managed to collect into planetesimals even in the pearlier study of an exact criterion for crossing orbits. 1998asteroid belt where the perturbation due to Jupit

Academic Press

proto-Jupiter would have been stronger than will bKey Words: planet formation; binary stars; life.sumed in our binary star analysis. More direct evid

196


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HABITABLE PLANETS IN BINARY STAR SYSTEMS

that planetesimals can form from dust grains in binary star it is possible for some fragments to achieve escape veeven when U Uc , but most mass will remain bounsystems is given by Kalas and Jewitt (1997), who have

observed a dust disk surrounding the BV5 binary system Depending on the mass of the planetesimals, vepumping by the secondary body will be countered bBD 31643. Based on dust lifetime arguments they con-

clude that the dust must have planetesimal sources located eral dissipative processes, which include inelastic colligas drag, viscous stirring, and dynamical friction. For at 1,000 AU. The observed binary separation is 200 AU.

This system is an (external-planetesimal case) example of ing planetesimals of size10 km the effects of dissipprocesses other than dynamical friction and inelastica binary in which planetesimals have formed at distances

of five times the observed stellar separation. If the binary sions are usually assumed to be negligible. We contively neglect alldamping mechanisms in our analysisorbit were circular, contrary to expectations, the ratio of

planetesimal formation to binary semimajor axis would be the net effect of these processes is to make planet formmore probable. Velocity acceleration due to mutualp5 : 1. This is within a factor of about 2 of the dynamical

limit for planetesimal ejection (of coplanar orbits) from bations between large planetesimals and embryos is imtant in current models for planet formation in the the system and much closer than our analysis will require

(typical ratio 30 : 1). Although the entire disk in this system System and other single stars, causing growing embrycollide and grow. The additional effect of the seconmay have more total mass and therefore potentially more

dissipation than disks typical of solar-type binaries, the star on the interactionsbetween planetesimals will beinto account directly in our numerical calculationdust-to-planetesimal accretion distance is 1,000 AU from

the center of mass of the binary, making it likely that the cussed below.

Internal-planetesimal formation in binary star sysurface density is less than at 1 AU in a solar type disk.The most perturbation sensitive stage in the terrestrial was first considered in some detail by Heppenheimer (

1978, hereafter H78). That investigation was based oplanet formation process is the runaway planetesimal ac-cretion phase (Wetherill and Stewart 1993, hereafter WS; then current GoldreichWard (1973) model of terre

planet formation and on the assumption that planeteLissauer 1993). This phase is rapid because of the smallrelative velocities between the planetesimals and the grow- collisions would lead to disruption rather than accr

if the relative velocities between planetesimals exceing embryo as a result of dynamical friction. The runawayaccretion time scale is 2 104 yr (WS). This phase ends the critical velocity Uc 100 m s

1. The time scaplanetesimalplanetesimal accretion during whichwhen the relative velocities of the growing embryos in-

crease due to their mutual gravitational interactions. Sub- value of Uc would be relevant was assumed to be 1The increase in relative velocity due to planetesimal esequent growth by nondestructive embryoembryo colli-

sions to a final planet occurs on a much longer time scale tricity pumping and differential precession was thenputed from secular perturbation theory. A reductiof107 yr.

If the relative velocities at infinity U of orbit-crossing eccentricity due to two different models of nebuladrag was also considered in the analysis.planetesimals are accelerated beyond a certain critical

value Uc then runaway accretion and thus planet formation The conclusion of Heppenheimers study was that pformation even at Mercurys distance was not likely ewill be precluded since collisions will then cause disruption

rather than accretion. In a binary star system or a system for widely separated binaries (50 AU) or when thondary mass was small and its orbit circular as in thecontaining a massive planet or brown dwarf the secondary

body may accelerate planetesimals beyond this limit. For of the SunJupiter system. Even for this system iassumed necessary to invoke the gravitational dampiplanetesimals bound by nongravitational forces alone (ex-

pected for planetesimal radii up to 100 km) the critical eccentricities by the solar nebula to allow accretion terrestrial planets. If accurate, that study would implvelocity is independent of mass and is100ms1 according

to laboratory measurements (Greenberg et al. 1977) and 2/3 of solar-type stars could be excluded as candidathabitable planets. The present study comes to a diffsimple theoretical arguments (Heppenheimer 1978; Weth-

erill 1991). conclusion and we return to the explanation fordiscrepancy after presentation of our analysisIncluding the gravity of the colliding planetesimals will

increase both the impact velocity U2c V2es and the results.escape velocity from the merged pair. The additional rela-tive kinetic energy due to free fall will result in the (two)

2. ANALYSIScollision fragments having nonzero velocities but, begin-ning with a velocity at infinityUc , these fragments cannot 2.1. Crossing Orbitshave a velocity greater than Ves , thus justifying the neglectof gravity in our conservative analysis. In a more realistic We wish to determine an analytic criterion for the

ing of two coplanar planetesimal orbits given bycollision with a spectrum of fragment masses and velocities


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198 WHITMIRE ET AL.

2.2. Relative Velocity1

r1

1 e1 cos ()p1

(1)Given that two elliptical orbits satisfy the above cro

criterion we determine their relative velocities U atwo crossing points (corresponding to the two general

1

r2

1 e2 cos()

p2, (2)

tions for cos ) from

where r1 (r2) is the radial position of planetesimal 1 (2),

is their common polar angle at the point(s) of intersection, (U)2

e1 sin()

p1 e2 sin

p22

1 2 is the longitude of periastron (i.e., theangle between the two periastron vectors), e1 (e2) is theeccentricity, and p1 (p2) is the semilatus rectum of the

p1r

p2

r

2

,ellipse (1 e21(2))a1(2) .

At orbit intersectionwhere U is divided by the orbital velocity at 1 A30 km s1 and r, p are in AU,

1

r1

1

r2 0

1

p1

1

p2

e1 cos()p1

e2 cos

p2. (3)

rp2

1 e2 cos

p1

1 e1 cos ().

The intersection point angles are

We note that even when orbits cross and the recos

AB C C2 B2A2

B2 C2(4) velocity is greater than 100 m s1 an actual collision

not occur in 2 104 yr since the orbits are not enfilled with planetesimals. The assumption that a destruwherecollision will always occur when orbits cross and thetive velocity is greater than Uc is therefore conservaAp2p1

2.3. Calculation of Orbital EvolutionB e1p2 cos e2p1 (5)

For the internal configuration case where the planC e1p2 sin.mals orbit the primary star, the relevant secular pert

tion theory equations for the time dependence of ePhysical solutions (i.e., orbit intersections) occur when for planetesimals with initial eccentricities 0 are (

C2 B2 A2 0,

e(t)5

2

a

aB

eB

1 e2Bsin

u

2t

yielding the necessary criterion for orbit crossing

tan(t)sin ut

1 cos ut(e1p2)2 (e2p1)

2 2e1p2e2p1 cos (p)2, (6)

where p p2 p1 . u3

2

1

(1 e2B)3/ 2

M

m1/ 2a3/2

a3B,

Two isolated planetesimals will eventually collide if theirorbits come within a critical distance 2.4(1 2)

1/3,

where is the planetesimal mass in solar units (Gladman Where aB and eB are the semimajor axis and eccentof the binary star system and M and m are the mas1993). For planetesimals of density 1 g cm3, located at

1 AU, and having radii in the range 11,000 km the critical the primary and secondary star, respectively.The secular perturbation approximation is valid ocollision radius is 4 1064 103 AU. As discussed

below, if the separation between planetesimals at 1 AU is the limit (a/aB) 1 for the internal-planetesimal conration. This approximation is also inaccurate in theless than 103 AU the perturbation of the secondary star

(not present in Gladmans analysis) will rapidly, within a eB 0 since Eq. (9) predicts that the planetesimal etricity e 0 in this limit. Test calculations using a numfew orbits, increase a to values 103 AU. The time in

which the two nearly circular orbits are within the critical N-body code and an integration time of 2 104 yr resin systematically larger valuesof the critical binary semdistance of each other is negligibly small for the binary

parameters used in this analysis. The orbits can still cross jor axis ac (beyond which planet accretion would ninhibited) compared with the secular approximatiand a collision can be inferred to have occurred.


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was also found that planestesimal semimajor axis variations the binary parameter space of interest, values of 0.001 AU resulted in the osculatinga increasing towere not negligible as assumed in the secular approxima-

tion. The secular approximation formulae are obtained by AU or larger within a few binary orbital periods. Ialso found that values of ao significantly greateraveraging over both the planetesimal and binary orbits

and therefore information about variations in the orbital 0.01 AU never produced crossings within 2 104 yrsimulations were carried out for three values ofao , elements within a single binary orbit are lost. The numeri-

cal calculations showed that typically these variations were 0.003, and 0.01 AU. It was found that the maximum revelocity obtained at orbit intersection was essentiallydominant during the short 2 104 yr integration time of

interest. Applying our conservative theme, andbecause the pendent ofao for ao 0.01 AU. On the other orbit crossing itself was typically dependent on aonumerical results are more accurate, we used the numerical

calculations to obtain the present results and employed a given set of binary parameters, if crossing and a maximum relative velocity were achieved for ao the secular approximation only as a test of the N-body

code in an appropriate limit. AU, the principal change when the simulation wapeated with ao 0.003 and 0.01 AU was that crosThe N-body code used for these calculations is based

on the symplectic mapping methodof WisdomandHolman occurred for a shorter time interval at comparable mum relative velocities.(1991). It was developed by S. Mikkola and K. Innanen

and has proved itself in earlier works (e.g., Mikkola and The recorded planetesimal orbital elements weserted into Eqs. (6) and (7) to determine if the oInnanen 1995). For the present application several addi-

tional tests were performed to ensure that the program crossed and, if they did, what the relative velocities

at the points of intersection. As noted earlier, even was functioning properly, including comparison with theanalytic secular perturbation equations in the limit orbits cross an actual collision need not occur in

104 yr since the orbits are not entirely filled with plan(a/aB) 1, large binary semimajor axis, and moderateeccentricity. In another test we compared the numerical mals. The assumption that a collision will necessarily

is thus conservative.output with an analytically derived Jacobi constant. Forthis test eB 0 and the planetesimal was given an arbitrary

3. RESULTSeccentricity and inclination. The Jacobi constant was foundto be conserved to the expected high accuracy at each

3.1. Internal-Planetesimal Casecomputational step.

The initial conditions of the simulated 4-body systems We focus on planetesimal accretion in the habitableof a 1 M primary. The habitable zone for a 1 Mwere chosen as follows. Two planetesimals of negligible

mass were started in coplanar circular orbits around the depends on the evolutionary state of the star and the hability time scale of interest (Kasting et al. 1993; Whiprimary star in the invariant plane of the binary system

and orbiting in the same sense as the binary. The initial and Reynolds 1996): The narrowest habitable zone coered was the 4.5 Gyr continuously habitable zone. Upositions of the two planetesimals were 90 from the

binary semimajor axis and the secondary star was started at the most restrictive climatic assumptions this zontended from 0.951.15 AU. Less restrictive climatbinary periastron. This configuration was chosen because it

was found empirically that it resulted in the largest pertur- sumptions or shorter time scales result in somewhat habitable zones. The presence of a second star of lumbation (relative velocities) during crossing and is therefore

the most conservative initial configuration. This is likely ity equal to or less than that of the primary will not scantly alter the location of the habitable zone for the due to the fact that this configuration results in the greatest

initial differential torque on the planetesimals. The orbital of semimajor axes of relevance for the internal-planmal case.elements of the planetesimals were recorded only at binary

periastron since it was found empirically, as expected, that Figures 14 show the dependence of the critical bsemimajor axes ac on the binary eccentricity eB , the mthe orbital phase corresponding to the maximum perturba-

tion of the planetesimals (as measured by relative velocity) the secondary star m, the mean radius of the planetesa, and the critical disruption velocity Uc . Habitable pwas near periastron. Comparing the orbital elements at

fixed time intervals (and therefore at random orbit phases) growth will not be inhibited in binaries with semimaxes greater than ac . Except when specified otherwissystematically resulted in smaller relative velocities, and

therefore smaller values of ac , during the fixed integra- secondary star mass m 1 M , the binary star syeccentricity eB 0.5, the average planetesimal semimtion time.

From Eqs. (6) and (7) it is seen that in general crossing axes a 1.0 AU, and the critical planetesimal disruvelocity Uc 100 m s

1 0.003 VKepler.and relative velocity during crossing depend on the osculat-

ing values of a, e, and . For our initial conditions Fitting the numerical data in Figs. 14 gives an empfunction relating a

cto the system parameters:both e

oand

o 0. Experimentation showed that, for


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200 WHITMIRE ET AL.

FIG. 1. Critical binary semimajor axis ac beyond which planet forma- FIG. 3. Critical binary semimajor axis ac beyond which planet tion at 1 AU will not be inhibited by a 1 M secondary star, as a function tion at 1 AU will not be inhibited by a 1 M secondary star, as a fuof binary eccentricity eB . Nonexclusion requires a binary periastron dis- of the mean planetesimal semimajor axis, a.tance q 16 AU.

accretion (over the range of semimajor axes stuLarger values of the mass of the secondary star and lac(eB , m, a, Uc) 16

1

1 eB

m

1 M

0.31

(12)values of the average planetesimal radius a will incthe perturbation and thus increase ac . Larger values critical disruption velocity Uc means that a larger re

a

1 AU

0.80 100 m s1Uc

0.30 AU.velocity at infinity Uis required for disruption, thus ring ac .

Fixing the other three parameters, these dependencies The critical binary semimajor axis is seen to be incan be understood qualitatively as follows. The eB depen- tive to secondary mass and critical disruption velocdency corresponds to a constant periastron distance (for is somewhat sensitive to the mean planetesimal semimtwo 1 M stars this constant is 16 AU), which implies

axis, but since we are interested in habitable planet fothat the dominant effect is, as expected, the maximum tion the actual range of a is restricted to 0.951.15 Aperturbation at periastron. Larger values of a with the somewhat larger depending on climatic assumptionsame periastron distance are equally effective in inhibiting time scales of interest, as noted above. The critical sem

FIG. 4. Critical binary semimajor axis ac beyond which planet FIG. 2. Critical binary semimajor axis ac beyond which planet forma-tion at 1 AU will not be inhibited by a 1 M secondary star, as a function tion at 1 AU will not be inhibited by a 1 M secondary star, as a fu

of disruption velocity, Uc .of secondary star mass m.


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jor axis was found to be essentially independent of theassumed runaway accretion time scale for integration timesbetween 2 104 and 1 105 yr. This can be understood asbeing due to the dominance of the intraorbit perturbationsover this time scale. For longer integration times such asthe 107 yr accretion assumed in H78 the differential preces-sion of the orbits would dominate and the results woulddepend more on time (as well as the initial a).

3.2. External-Planetesimal Case

Because of the broad distribution of solar-type binarystar orbital elements (Duquennoy and Mayor 1991, hereaf-ter DM91), the external-planetesimal case is much lessimportant for habitable planet considerations. Observa-tions show that solar-type binaries with periods less than11 days (semimajor axis 0.12 AU for two 1 M stars)

FIG. 5. Observed bias-corrected distribution of binary semhave circular orbits (DM91), presumably the result of pre-axes, aB , assuming m 0.5 M . The left (right) vertical dashmain-sequence tidal torques. The narrow habitable zonedenotes the critical semimajoraxis for the external-planetesimal (in

depends on luminosity so for two 1 M stars it movesplanetesimal) case.out to 1.4 AU. Setting a 1.4 AU, ac was found to be

0.11 AU. Since this is less than the tidal circularizationradius no additional eccentricities were simulated.

observed bias-corrected value of 0.5 (DM91), theFor the more typical case where the secondary is signifi-nonexcluded fraction would be reduced to 52%. The ucantly less massive than the primary a 1.0 AU due totainty in the median eB is our least conservativthe strong sensitivity of luminosity to stellar mass. Assum-sumption.ing the internal-planetesimal parameter dependencies

apply, ac 0.10 AU for m 0.5.4. COMPARISON WITH EARLIER WORK

3.3. Statistics of Habitable BinariesOur results are significantly different from those f

in the earlier analysis of Heppenheimer (H78). That sDuquennoy and Mayor (DM91) give the distributionsof the orbital elements in an unbiased sample of nearby which considered only the internal-planetesimal co

ration, concluded that planet growth even at MercG star binaries. The median binary eccentricity is 0.5after correction for observational bias. The observed me- distance of 0.39 AU would require binary semimajor

50 AU, or small mass secondaries in circular orbitdian mass ratio is no greater than 0.5 and we take m 0.5 M as a conservative limit for the median secondary that of the SunJupiter system. Even for the SunJu

system it was assumed necessary to invoke nebulamass. Using this mass and the median eccentricity we ob-tain from Figs. 1 and 2 a median value of ac 26 AU. gravitational damping of planetesimal eccentricitie

consistency with the existence of terrestrial planets iThe median orbital period of the sample is 180 yr, whichcorresponds to a semimajor axis of 36 AU. Figure 5 gives Solar System.

For the typical internal-planetesimal binary eccentthe distribution of aB , based on the period distributiongiven by DM91 and the median secondary mass. The right of 0.5 and secondary mass 0.5 M , our analysis a

planet growth at 1 AU to occur for semimajor axesvertical dashed line at aB 26 AU (log(aB) 1.415) de-notes ac for the median system. Statistically, the fraction of AU. The discrepancy between Heppenheimers an

present study can be traced to three factors: (1) The dinternal-planetesimal binaries which could have accreted aplanet at 1 AU is the relative area under the curve to the ent time scales appropriate for the planet accretion m

used, (2) the absence of an exact criterion for croright of this line, which is 57%. The left vertical dashedline is the external-planetesimal ac 0.10 AU. The fraction orbits in Heppenheimers study, and (3) the applicat

the secular-average approximation in that analysisof binaries with semimajor axes less than 0.10 AU is thearea to the left of the dashed line 2%. Thus the total primarily differences (1) and (2) that explain our sm

values for ac .fraction of solar-type binaries for which habitable planetaccretion cannot be excluded is 59%. There is some uncer- In Heppenheimers analysis the planetesimal accr

time scale, during which the critical disruption velocittainty in the median eB for the internal-planetesimal case.If the median e

Bwere random and 0.7, rather than the set equal to 100 m s1, was taken to be 107 yr. Thi


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202 WHITMIRE ET AL.

contrast to our use of current terrestrial planet accretion crossing occurred the relative velocity was comparaits maximum value (Umax emaxVKepler) since the omodels in which this phase is only 2 10

4 yr (WS93).During Heppenheimers much longer time scale the rela- are essentially randomized. This Umax is typically

greater than 100 m s1. However, the requisite disrutive velocities of planetesimals tendedto achieve their max-imum values due to differential precession of their orbits. velocity for embryos is also much greater. Embryo

gravitationally bound and have sizes between those oThe differential precession time scale depends on the plan-etesimal separation a, which was somewhat arbitrarily Moon and Mercury (WS93; Wetherill 1996), whose e

velocities are 2 and 4 km s1 respectively. Assutaken to be 0.01 AU. For this value ofa the precessiontime scale was 105 yr for the typical binary (which was 3 km s1 for the escape velocity of a single embry

increase this by a factor of 2, obtaining 4.2 km snot specified). Thus, in the assumed planetesimal accretiontime scale, there was more than enough time for the take into account the fact that disruption requires e

from the gravitational force of two embryo massesorbits to become randomized, in which case Umax emaxVKepler 100 m s

1 for the typical binary. This is not all eB 0.9 the maximum relative velocity is less4.2 km s1 for aB ac , as determined in the planetethe case for the much shorter runaway accretion time scale

appropriate to current accretion models. disruption analysis. Therefore the results for ac basthe planetesimal disruption analysis will not be sIn Heppenheimers analysis there was no assurance

that when the relative planetesimal velocity exceeded quently invalidated by embryoembryo collisions epossibly in cases with very large binary eccentricitie100 m s1 the orbits actually crossed, allowing for the possi-

bility of a collision. A critical relative velocity is a necessary In our simulations we have assumed (as did H78

the binary and planetesimal orbits were coplanarbut not sufficient condition for disruption. Our analysiscomputed the relative velocity only if the crossing criterion likely that this is approximately true for binary semi

axes less than 30 AU as indirect observations (Hale was met.As noted earlier, the secular approximation used by and our own Solar System suggest. All planets, wit

exception of Mercury (which lies in the Suns equaHeppenheimer averages over the binary orbital period andtherefore cannot predict the intraorbit excursions that are plane) and Pluto, lie close to the invariant plane, wh

essentially Jupiters orbital plane, in spite of the facthe dominant effect causing orbit crossing and maximumrelative velocities during the short integration time of rele- the Suns equatorial plane is tilted 7 relative to this p

The observed large comets/planetesimals in the Kvance in current accretion models. The secular approxima-tion, when applied to the accretion time of 2 104 yr, was belt continue this trend to over 40 AU. For a 1 M se

ary it is likely that the accretion disk would relax tfound to systematically lead to smaller values of ac for agiven set of parameters compared to our numerical calcula- invariant binary orbital plane prior to planetesimal a

tion to distances equal to or even closer than Mercurytions. Thus, although Heppenheimers secular calculationfor his longer time scale was different from our numerical the internal-planetesimal case and out to distances

further than 40 AU for the external-planetesimal cacalculations for the shorter time scale, this is not why ourvalues of ac are significantly less than those of Heppen- In binaries with aB greater than ac it is conceivabl

over 107 yr time scales relative velocities sufficient theimers study.Since our approach and assumptions have been conser- rupt embryos could develop due to differential noda

cession if the relative inclination were sufficiently lvative, the calculated function ac(eB , m, a, Uc) may betoo large (small) for the internal-planetesimal (external- Should this occur, the small debris from such coll

would itself relax through inelastic collisions to the inplanetesimal) case and therefore, in reality, a greater frac-tion of solar-type binaries may have accreted a habitable ant binary plane and the entire solid body accretion pr

would begin again, though without the full gas neplanet. This is in contrast to the negative approach of

Heppenheimer which, for example, required additional as- present.Although not considered binary star systems, the nsumptions about the physics of dissipative mechanisms (an

important mechanism in current planetesimal accretion discovered extrasolar planets and brown dwarfs catreated as the secondaries in our model and we can inmodels is dynamical friction, which was not considered in

that study) and roughly simultaneous formation of both whether a habitable planet could accrete in these syassuming the secondaries formed in situ in their prstars.orbits. These primary stars are solar-type and have mnear 1 M . The secondaries have masses ranging 5. DISCUSSION0.47 MJ to 60 MJ , where MJ is the mass of Jupit0.001 M . Using data for the 18 confirmed plaEmbryoembryo collisions occur over time scales of

107 yr (WS93). Internal-planetesimal numerical simula- brown dwarfs compiled by Schneider (1997), we finthe following six systems, all of which are the extetions of this phase of planet formation showed that when


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planetesimal type, cannot be excluded from having a habit- Gladman, B. 1993. Dynamics of systems of two close planets.106, 247263.able planet at 1 AU: 51 Peg, And 55, Cnc, Boo, HD98230,

Goldreich, P. M., and W. R. Ward 1973. The formation of planeteand HD283750. As an additional illustration we simulatedAstrophys. J. 183, 10511061.the SunJupiter system assuming (contrary to conven-

Graziani, F., and D. C. Black 1981. Orbital stability constraints tional theory) that Jupiter (orproto-Jupiter) formed beforenature of planetary systems. Astrophys. J. 251, 337341.

planetesimal accretion at 1 AU. Our model was consistentGreenberg, R., D. R. Davis, W. K. Hartman, and C. R. Chwith the existence of a planet at 1 AU but not at the inner

1977. Size distribution of particles in planetary rings. Icarus 30edge of the asteroid belt at 2.2 AU.

779.Heppenheimer, T. A. 1974. Outline of a theory of planet forma

6. CONCLUSIONSbinary systems. Icarus 22, 436447.

Heppenheimer, T. A. 1978. On the formation of planets in binaAssuming current terrestrial planet accretion models,

systems. Astron. Astrophys. 65, 421426.the critical binary semimajor axis, beyond which habitable

Kasting, J. F., D. P. Whitmire, and R. T. Reynolds 1993. Habitableplanet formation will not be inhibited by the presence of around main sequence stars. Icarus 101, 108128.the secondary star, has been calculated as a function of Lissauer, J. 1993. Planet formation. Annu. Rev. Astron. Astrophbinary eccentricity, secondary star mass, planetesimal loca- 129174.tion, and critical disruption velocity. Using the distributions Mikkola, S., and Innanen, K. 1995, Mon. Not. R. Astron. Soc. 27

501.of orbital elements of an unbiased sample of nearby solar-Pendleton, Y. J., and D. C. Black 1983. Further studies on the ctype binary stars, we find that 60% of these systems

for the onset of dynamical instability in general three-body sy

cannot be excluded from having a habitable planet solely Astron. J. 88, 14151419.on the basis of the gravitational perturbations of the sec-Schneider, J. 1997. Extrasolar Planets Encyclopedia. Availableondary star. Future astronomical searches for habitable

www.obspm.fr/planets.planets, as well as targeted SETI searches, need not exclude

Wetherill, G. W. 1991. Occurrence of Earth-like bodies in plabinary star systems whose semimajor axes, eccentricities

systems. Science 253, 535538.and masses lie above the curves in Figs. 13.

Wetherill, G. W. 1996. The formation and habitability of extr

planets. Icarus 119, 219238.ACKNOWLEDGMENTS

Wetherill, G. W., and G. R. Stewart 1993. Formation of planeta

bryos: Effects of fragmentation, low relative velocity, and indepWe thank Ray T. Reynolds and Patrick G. Whitman for advice and sug-variation of eccentricity and inclination. Icarus 106, 190209.gestions.

Whitmire, D. P., and R. T. Reynolds 1996. Circumstellar habitable

Astrophysical considerations. Circumstellar Habitable Zones: PrREFERENCES

ings of the First International Conference (L. R. Doyle, Ed.), pp142. Travis House Publications, Menlo Park, CA.Duquennoy, A., and M. Mayor 1991. Multiplicity among solar-type stars

Wisdom, J., and Holman, M. 1991. Symplectic maps for the Nin the solar neighborhood. II. Distribution of the orbital elements inan unbiased sample. Astron. Astrophys. 248, 485524. problem. Astron. J. 102, 15281538.

habitable planet formation in binary star systems

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