An Estimate of the Prevalence of Biocompatible and Iiabitable Planets

Jowl ofTh. Bdkh ltterylanaarysocietr vol. 45,w. 3-12,1992.

AN ESTIMATE OF THE PREVALENCE OF BIOCOMPATIBLE AND IIABITABLE PLANETS

MARTYN J. FOGG. Pfobability ResearchGroup, clo 44 Hoganh Coart, FoLntain Driye, Londotl SE19 I Uy, United Kingdotn-

A Monte Carlo comtuter model of extla-solarplanetary fomration ard evolution, which includesthe planetarygeochemical carboncycle, is prcsented,The lesults of a run of onemillio! galactic disc sta$ arc showDwbere the aim was to assesstie possibleabundarce ofboth biocompatibleand habitable pla[ets. (Biocompatibleplanets are defined as worlds wheie the long- term prcseoceof suface liquid water providesenvircnmental conditions suitable for the origitr andevolution oflife. Habitable planetsare those worldJ witn more specmcallyEadnike conditioDsr.Tbe model gives atr;sdmate of 1 biocompatiblepla{et per 39 stars.with the subsetof habitableplanets being rnrch rarer at I suchplanet per 413 stars.The nearestbiocompatible planetmay thus lie -14LY distant andthe nearesthabitable planet -31 LY away.If planet! folm in multiple star systemsthen the aboveplanerstar ntios may bemore tlan doubled.By applyingthe rcsultsto st rs in the solarneighbourhood, it is possible to identify 28 staN at djJtancesof< 22 LY with a non-zeroprobability ofpossessinga biocompatibleplaoet

1. INTRODUCTION

It is likely &at life was alreadypresent by a billion yearsafter averageglobal surfaceteinperature fes between a ]ittle less the forfiation ofthe Earth.Unless our planetwas'\eeded" with thaDOC up to somevalueatwhich annaway greenhouseeffect life ftom without, a hypothesisooly tal(enseriously by a small occurs.This zooe, the ecospfule, has inner and outer bounda- minority of scientists,ils genesismust have occuned spontane- ries defitring the valuesat which envimDmentalconditions are ously within a few bun&edmillion yearsfollowing the Earth's respectivelyeither too hot or too cold to permit the genesisor accretion.One inte4)retation ofthis factleadsto the speculation sustenanceof life. that life may originate comparativelyftpidly in any planetary Beforethe spaceage, it wasthought quite possiblethat both envlonment similar to that of the early Earth and that the Venusand Mars wereeBviroBmeDtally benign and inhabited by Gala.\ymay b€ strewnwith nurnerouslife-beadng planet!. The life. Somemodels of Venuspainted the picture of vast steamy odgin ofterrestrial life is still anunsolved problembutthe most swampsor a wodd gtdliDg seltzerocean, while obsenationsof populartheory tnkes,as its startiDgpoint,Darwh's "warmlit e the changingcolou$ of Ma$ suggestedthe Fesence of pladt pond", containing an aqueoussolution of o{ganic chemicals Siowth, fluctuating with the seasonsUl. Thus, the Sun's producedftom reactionsbetween atnospheric gases, triggered ecosphercwould have exteDdedat least betweenthe orbits of by eoergysomces such as lightning andultra-violet light. Thus, these platretsgiving the distarces ftom the Sun of the inrcr for a planet to give rfue to and rnahtain ao indigenousbio- boundaryrr = 0.71 AU andtheouter boundary r, = 1.52AU (ng. sphere,one of ib prime featurcsmust be the prcsenceof large and stablebodies of liquid water on its surface.Thjs requirc- Dole has presenteda model of an Eartlilike planet with ao ment setJstrong corsuaints oDsudace tempenrtrc and atmos- optically thio atmosphercwhich was subjectedto vaiiations itr phericpressure, ensudng thal similar environmentalcoEditions illumination and axial itrclinatioa [4. Assuming 6at such a will prevail as do o! lhe Earth. planetwas "habitable" ifatlea$ l07o ofthe sudacehad ayerage How aburdalrtarcsuch biocompafible "water wodds" likely to be in the Milky Way galaxy? Although therc is, as yet, no unequivocalevidence for a plaoetary systemabout ally o$er slar lhan our owo, it is expectedthat extra-solarplaDets rnay be

Knowledgeof modem astophysics and planetologyis now sufficient to permit a reasonableestiDate of the rnassrange of starsabout whicb biocompatibleplanets are likely to exirt this is donebelow by using a siople computermodel of plateta.ry systemfornation and evolution. A! estimateofthe ftequency per fteld star of biocompatibleplanet! tien allows a surdyto be madeof stals within iie near-solarneighbourhood to identify candidatesupon \r/hichthe searchfor extratenestriallife might be concentrated. 9@d o.7 1.0 AU 1.5 1.8 2. THEECOSPIIERE Fig. 1 The Sun's fluctuaring ecosph@. EstiDated widths are due to, The orbital mdius of a biocompatibleplanet aboutits pdmary fton top: pre-spa.eagc ide€s; DoL [2]; Rasoolsnd de Bergh [3]; Hait mustlie within a zooetlemally coDpatiblewith Me, wherethe I4l and Kasting dr a, t121. ye,nly tempelaturcsbetweeo 0 and30.C, with the mostextreme account the weathedng of silicate rccks by CO, to goduce daily temperature betE€en -10 and 4&C, he was able to carboDaleshedid not modellhe geological recycli-Dg ofca oo estinate the widtb of the ecospherc.AccordiDg to his calcuta- belweengaseous and mircral phasesthat is caried out by ter- lions,lheecospbere lvas sUllquirc wide witb r, - 0.725AU and rcstrial tectonic processes. r, = 1.24AU: vrz closelo tbeorbir of VeDusaod hatl wayout 11is thb cycling of carbon which has rccently bee! put to tie o$it of Mars. forward asa major stabilbhg influenceot the Earth's climate. However, the atinosphereof the Earth is not opticafly thin. Ca$on dioxide dissolvedin water reactswith silicate mcks to Its watervapour and carbon dioxide componentsadd up to exert producecarbonate minelals, such as the forEation of calcite agre€Dbouse eflbct thatmaintainsthe suface about33 K above ftom wollastonite: the planet's effective temperatD.e.Rasool and de Bergh [31 pointed out that a terestrial platet might undergoa runaway CaSiO3+ CO, --> CaCOj + SiO, (1) grcenhouseeffect upo! outgassingif situaiedtoo Be€rthe Sutr. As 40 andCO, build up in the atmospherc,the lempemtuleoi Thus Cq io fte atmosphereof even a lifeless wo d wilh ttre suface is nised too high to pemit the condensatiotrof sudaceliquid water,tends to be consumedgradually by chemi- oceans,They calculaled that the Earth would have suffered cal weathering.On Earth,this prcce8sis not all one-way,due to such a fate if situatedcloser than 0.93-0.95AU ftom trc Sun. the fact that carbonatesediments are not pernanendy deleted Sucha value of rr so close to the orbit of the Earth prompteda f|om the geochemicalcarbon cycle. Tectonic movements within reassessmentof previous optimistic estimalesof the width of tXeclust, suchas subduction, may buly calbonatesdeep enough the ecosphere, lo betbermally decomposed, relensing COr whichmigbt rietr ?he Sun's shriDkingecosphere reached its nanowest with beca-rried back up to the surfacedissolved io o?gmas. Walker the model of Hart [4]. Ambitious in scale,Hari constucted a ?r al [6] preseotedevidence that the CO, weatheringmt€ is compulcr simulation of the evolution of the atmosphereof the temperatureselsitive with higherrates at higher tempemtures. Earth,sbning with the origin of the Earth ald running it to the This, and tle fact that CO2on the Earth is cycled back into the Fesent day. The model included a wide rangeofprocesses, "... atmospheeby volcaDism,prcmpted them to sugg$t the g€o- the rate ofdeSassinslron the inteior aM th? nean conposi- chemical carbon qcle as the basis for a powerful negative tion of juyenile wlatiles; condeksationof water tapoar into feedbackwith influence over long texmclimatic fluc[rations. ocea$; solution of atrnospheficgas$ in the oceans;photodis- When tenp€mtures rise, weathering iBqeases and CO2 is yopow sociation ofwater in the upper afiasphere; escapeof dlawn out ofthe ahosphere, Esulting i! a reduced$eedouse hydrogenfton the ernsphere; chenical reactiow between effect atrd lower temleratures. Convenely, weatheringis re- atmospheric gases; the presence of life, and vtriations in ducedwheD teBperatues fal, resulting in CO, builditrg up io biomass;photosJ thzsis and butial oforyanic setliments;lhe the atmosphercftom volcanic degassiog,increasiDg the green- UfeJ reaction; oidation of surfacemineraLt; j,ariatioks in the houseeffect and walming the planet Such a processoffers an solar luminositt; vriarions in the Earth's albed.o;a d the explamtion ofwhy the Earthhas maintai[ed a surfacetempera- SfeenhoweefecL'1 ture aod atnosphericpressure compatible with the presenceof The regulationofsurface temperature was modelled by three liquid water ftom tle eadiert times discerDablein the geologi- fcedbackloops: cal record.Such conditions would havebeen maintained cyber- netically ftom an initial situation wheaeocea$ were present (1) the ice positive feedback that accentuatedany climatic a[d volcadsm and tectonicswere ongoing. The formation of cooling by hcEasing the amountof high albedoice cover, the Earth'sfirst ocearsrnay tbus have setoe scetrefor the entite (2) the water vaporr greenhousepositive climatic evolutioo of our planet up to now. As the Sun's feedback that - accenfuateda.lly warming tend by inq€asing mass lumiDosity increasedftom its initial value of 0.7 L., the the of partial -l qO itr rbeaDnosphere, and carbon dioxide Fessure might have declined irom bar to its current value of 3 x 10+bar I?1. (3) the cloud-albedo negative feedback that would exert a Geochemicalcalbon cycliDg alsohelps explain someofthe stabilisitrg infl[ence on sudacetempemture by ilcreasing oLlestgeological featurcs oDMars. Theplanet's a.ncientcatercd the arcaof rcflective cioud cover at high tempemturesand terrafu, dnled at > 3.5 Gyr old, fu extensivelycut by numerous "runoff channels" [8] that have been interyreted as airiedup dver beds.These structures have been cifed as evidenc€fo. an The pdncipal finding of lfurt's model wasjust how unstable early wa]m phaseof Maftiar bistory when the persjrterce of the Ea{h's climate seemedto be. In fact, all the aboveioDut liquid water at the sudaceof the planet was possible.This, in paramelersbad robe fine-tuDed to wilbio20q,ofa certaiovaiue tum, would requte MaIs to havehad a denseatnosphere with to gel the prognmme to produce an Eaililike planet and to sufficient grcenhouseeffect to keep the MartiaD surfacetem- maintair it4.6 Glr into the simulation.Mosttuns rclulted in the peratureat > 273 K. Pollack et a, [9] have suggestedthat this model plalret eitler undergoinga ronaway grcenhouseeffect, ahosphere coosistedof severalbars of COr, maintabed by a producinga newVenus, or aruDawayglaciation itr which Nortl geochemicalcarbon cycle hvolviDg ioleosevolcan ic re(yclitrg andSouth polar ice capsmerged at the equator.Hart's estirnate of caIbooate sedim€nts.They calculale that such a Focess of the boundariesof the ecospheE,or the continuouslyhabit- could havekeptthe Martian envircloelt i! this biocompatible = able zoneas he called it, were ! 0.95 AU aod r, = 1.01 AU. statefor up to a billion years,possibly loDg enough to allow for Accordiog to him, tle persistetce of a cleDent tereshial lhe brief appear"arceof life [l01. However, this wet and warm envtonment for so long reptesentJa coNidetable fluke as the epoch eventually ca-6eto an end when volcanic and tectonic Earth, when looled at tbrough this sieulation, app€a$ deli acti\,ity on Mars declinedto the poiot at which the equilibdum cately balarced on the cusp of a catastrophe.I{art's model has mass of lXe atmosphercwas not sufficient to stop the planet thus beensubject to cdticism, especiallyin view ofthe fact that ftom fteezing over completely.Over tie aeoDssinc€ tben, the his assumptionofthe presenceof atrearly reducingatuosphere atmosphercwould have dwiDdled further, reacting peihaps is almost certaidy wrcng and rcsponsible for mrch of the with silicate mioerals in moist pocket! withi! the soil [11], to model's iostability [5]. Moreover, although l{af took into Foduce the tbin remnantwe seetoday. An Esbtute oJthe Ptdalde ol Bioctnparible anAHabitabk Pbret!

Such a model hasprofound implications for the positioDof the outer boundaryof the ecosphereF,121. It suggeststhat, ro long as a planet remains sufrcietxly geologicaryyactive to nnihta[n a geochemicalcalron crcle, biocompatibleenviron- mental cooditions arepossible for planetr with irradianciesas Iow as that for Ma$ > 3.5 Gyr ago.Since the Sun's luminosity wasthen - 0.7 Lo, this meansthat the presentouter boutrdary of theSUD'S ecosDhere is r^ > 1.8AU. Kasting aad co-worki:rs have alsoestimated a value for the 1.5 inner edgeofthe ecosphereby studyingthe responseofa model tenestrial amosphere witb ftilly saturated,cloud ftee, conditions to inqeasesin solar flux [7,12,13]. At a solar inadiance value of 1.4 56, (wherc So is the Earth' solar constant),the 1.2 oceans evaporaie entire,ly, Foducing he classical runaway geenhouseeffect. However,at a lesserirradiance of 1.1So they < rr identified another possible planetary envirotrmeot,the "wet grcenhouse".Herc, scaldilrgoceans at - 1OOCare still stableas they arep.evented ftom boiling by the pressue of a massive-2 .E 0.9 bar water-laden atmospherc.Ir both grcerhouse states the .? 0.8 water vapour rises high up io 1ie almospherewherc it calr be photodissociatedby UV lightrcsulting, asin rle caseof Venus, o;1 in the ultirnate desiccation of the planet In fact, the wet greenhousemodel can betteraccount for the presentscarcity of 0.6 water oDvenus, so venus Day have startedits history with an 0.5 a -500 oceanwhich wasgmdually lost to spaceover M):f. Once 0.4 tie water wasgoDe, CO2 would havebuilt up in the atmosphere wilh no way of weatheringback into the sudace,rcsulti[g iDthe 0.3 prcsent day rnassive Venusian atmosphere.In neither case, 0.2 however, carl it be said that Venus was likely to have been biocompatibleand so Kasting et al arrived at r, = 0.95 AU, the 0.1 samevalue as Rasool and de Be.gh alrd I{art's estirnateofthe positioDof the intreredge ofthe ecosphere,albeit for a different reason. Thus, for present pu4,oses,the boutrdariesof the Sun\ = = presentecosphere arc chosento be rr 0.95 AU atrdL 2 AU, given the condition that such boundariesare only Deanirgful Fig- 2 Cli@tic evolutiondytncks tor Venusthe Earthed Mds, for a planet with a closedgeochemical carbon cycle. However, coDldins illumin&ce venusgeological activity ovq time,l@ked when looking at ecospheresabout otler st $ with differcnt inintcnalsof1 [email protected]@ntr ldividinSline luminosities and when taking into account the variation 1! atlogG/TF) - 0flEscnts thepointinaplmet's gcoloSicalcvolution stellar lumiDosities with time, the definition of ecospheric at which it cd no lonSersuslah !l&te tectonicsd a geochemicel boundariesin tems of distanceis clunsy. A universaldefitri- tioDofrr and12 can be obtained if, instead,the valueofplanetary bmdianceat thosedistances is used.The averageirradiance of a planet in terms of So is: evolution of a similar eDviroEneDttotlrat on the Earth sioce the start ofthe Phalerozoic Aeon - 600 Myr ago. s =I-lR" (2\ It will be seenthat Venus was aever within tle ecospherc where L is the stellar lu]ninosity in Lo and R is the planetrry and,if it ever possessedoceans, tiese werc litely to bale been semi-majorards iD AU. Thusthe Edefined valuesofecospheric lost early oD.Mars, becauseof its rapidly declining volcanic boundarieslbalapplyloallstarsarerr=I.l Soatrdrr=0.2556. activity, left the ecosphereafter - I Glr. The Eartb, however, Thediscussionio thissecdoo is sunmarizadin lig.2where tas rcfilailled biocompatibletbroughout the history of lhe Solar the evolutionsof Veous,the Earth and Mars aredisplayed on a Systero,fiough the diagram wams of posrible houble ir the ofirradiance,5/56, vs a scateofgeological activit, T/TFr $aph next biilion years. (explainedlater). InGrvals of 1 Gyr aremarkedo! eachplanet's Such a biocompatible zoDe will exist about ottrer sta$, evolutiooarytrack. The c€ntral dividing line at log (T/T-) = 0 scaled up or down in size, so when estimating he galactic represen6lhe poiot io a plaoel'sevolu[ioo wberc it idn no abutrdanceof biocompatible plarets tie concept of tie eco- longer sustai! a geochemicalcarbon cycle. spheremustbeembealded withir a broaderastonomical ftafe- The ecosphercis divided into tlrce climatic zones: 11)Jwenili Mofiian, (025 So< S < 0.7 SJ wh€{ebiocompatible planetswould be similar to early Mars; 3. A BRIET'MODEL OT'EXTRA-SOLAR PLANET \2t JuvcnileTeftan,t}.TSo < S < 0.94So)where such worlds FORMATION AND EVOLUTION would be smilar lo tle Earlb in tbe Precambriao;and The model to be describedfom$ the ba$isfor a Monte Carlo (3\ Habitabk, (0.94So < S < l.l SJ wherea biocompatible computer simulatiotr, the results of which are gesented io planet would be rcceiving suffrcient sutrlight to permit the Section5. Earlier rcsultsofthis simdation can befound in 1141. 3.1 Stellar Parameters The amount of hydrogen bumed by a star oo the nrain sequenceis mughly prcporhonal to its mass atrd the maia Starsoccu over a wide range of mass,ftom about^O.1 Mo to sequencelifetime, Tw of a I Mo star ii - 10 G)r. Thus: -100 Mo. Lighter sta$ are the more abundafl and here the distribution is modelledby = r- (6) the Scaloinitial massspectrum [l5]: . TMs 10(I\ol4) cyr dN/dM (t Ma (3) The luminosity of a main sequencestnr gmdually inseases with time. The foilowing irrctiotr was adaptedfiom Gough's whee M is the stellar massir solm units and T = 1.94 + 0.94 lumioosity/time rclatioDfor the Suo [19], assumiDgin additioD Loc(M. that for all stellar massesAL/A(T/T6) is a constant For a starto possessterrestrial planeb it would haveto have formed ftom a nebula contaioing suf6cient heavy olemeDts. L(T) = Lantsexp 10.045(10T/T6)131, A, The starwould haveto bePopulation I andyounger theo the age wherc T < T16. offomation ofthe galacticdisc (-10 G}{). Overthis period,the metallicity of the inte$tellar medium has risen due to the 3.2 PlanetaryParam€terr Foducts of nuclesynthesisft om successivegenemtions of stars. The canonicalmodel of galactic chemicalevolution is 116,17l Model planet ry systerN are constructedby the ' ACRBTE' assumedto hold in the solar neighbou*ood which describesa Monte Cado computer algorithm qaitten by Dote This roughly lioear increasein metnllicity, z, with age,T/G),i. An [20]. gives the number of pla{ets vdthin fie equationwhich fits the model isi simulated system, calcubting a semi-major axis, R, orbital eccentricity, e, ,nd rnass, nL, for each oDe. Although many of the details of z = 0.13(10- T) + zo, (4) 0_3 cosmogo'nyare yetto be understood,the use ofAcRETE here is ajustifiable simplificatioD as pla[etary systernsdiffercnl in where zo - 0.02 is the heavy elementfraction of the Sun. Tbe detail but similar iB overall form to the Solar Systern are propotio! of balo Population II starsin the solar Deighbour- produced(ftg. 3). This is wbatmight beexpected for extra-solar hood is a miniscule - 1/800 and so, assuding a constantstar plaietary systernsif the Principle of Mediocrity appliesto our formationmte the agesof the geatFeponderurc€ of stars [17], own system,making it ar1average and uorernarkableexafiple nearthe Sun can be assumedto be distributed evenly between of a commonphenomenon. 0 - 10Cyr. However, Dole's simulations were aI performed on the A [u0ctioofor calculating 6e slell ar zero age main seque0ce assumptio!that the massofthe centsalstar vr'as 1 Mn. Isaacman lumhosity wilhiD the massrange 0.1 - 2.0 l"{o wasderived fiom atrdSagan exploredACRETE furlheraod s[owed lbal the theoreticalmodels of lben Pll [18]: wiftin limits, it waspossible to alter the prcgamme's pafime- ters without atr ou$ut that appearedphysically LzAr{s= 0.71(IVI/MJ' L6, (5) Foducing unlealistic. Here, the algorithm must be specfically modified to accommodatea wider rangeof stellarmasses. Logically, one wherefor Mo < M < 2.0 Me): n = 4.75and for I Mo < {0.7 {0. might expectthe rnaximum rnasscondensation mdius within M < 0.7Me): o = l.750WMo)+ 2.125. the pre-planetarynebula to vary with stelar luminosity:

Fig. 3 Pla&ty systeN ?rcdu@d by the Dol€ "ACRETR'alsqithn. The priDary st8 is 1 1.4, thc odses of plmcts @ given in E3nh units and thc horizontsl ujs is a loSditbmic scrle ofAU. Iie Sold SysteD is includ€d third ftom to! for

- xa" At Estbtuk oJthe Ptfuk^ce oJBia@hpottbtE dal HdbitabL Plnets

R_= 5.8(LM/0.71)'" AU. (8) wherek is tle momentof inetia factor, taking a value of - 0.33 for a tenestrial planet andj = 1.46 x lo'zom'?s' kgr. Moreover,the cenfal densit ofnebular alust,A, the parame- The final mtation rate is calculateda.fter taking into accoutrt ter fmm which the rnassof the oebulais scale4 might vary in decelemtiondue to tidal breakingftomthe pdmary overthe age direct propotion to the massaDd metallicity of the cellfal star. of the systen Tidal forces are propoitional to the massof the Thus when revised, Dole's releyantequation becomesl tide rabing obj€ct and inversely proponioml to the cube of distanc€.The tidal decelerationtorque is proportional to the A * (a'/ 1.3x l0)(M/ Ma\@/Z)WAIJ3, (9) squareofthe tldal force and so: whereo = 9R* nB.However, it would seemlikely that the mass (do/do : (doJdDGJk)(r/ro)(mJm"XM/M6)'z8srR)6, ofgas within 6e nebutawould only be proportionalto the lnass (13) of the starand not 1othe metallicity. Thus,when calculatingthe total massof the nebulathe gas/dustrado is assumedto vary as wherc doJdt = -1.3 x 106 rad si / 1f )r. (zJa. The geochemicalcarbon cycle modet of Walker €t al [6] is RunningACRETE with thesemodiEcations produces plau- usedto define the boundariesofthe ecospheEand to sdggesta sible planetary system$.For instance,systems about old,low roughatnospheric compositlon and sufacetemperature. Thus, fiurss,stars arc scaleddown in both massand mdial size. The any terrestrial plaftt witl ar fumdianceat age T in the fange coove$e is tme for massive,yomg stzrs (flg. 4). 0.25So < S < 1.1 So,which is still volcanically andtectonically Investigating any tenestrial planetsgenerated by ACRETE actlve,has the potentialofpossessiDg a biocompatibleenvircn- further, the planetary ladius, r, and, thus, its bulk density, is menl anNz/COTAITO atmosphec, a sudaceternpem!]rc alittle fouod by solving Dole's empirical equalion Bl: above273 K and stablesudace water. The pre$enceoflife asan additional stabilizing influence on climate and a8nosphedc a/ r^ lJFo-m =n (10) oxygetr is trot taten into account as tie geochemicalca.bon cycle can opemteabiotically. wherea = 1.08x lO7and po=n70kgrtra, An estimate of the duratioD of viable volcanic/tectotrrc The valueof planetaryaxial hclioatio!, i, is detemined rccycling of volatiles oo a giveEplaoet is cdcial as it can also randonlyftom Dotre'semphical Fobab iry distribution[2]: be regardedas all estirnateofthe timescalefor biocompatabil- ity. However, the deiailed modelling of planetarycooling and P=1-(1-V180o)4r, (r1) oustal oveftirm is complex, plagrcd \r,ith unknowns, a]]d inapproprialein the cootext of lhe simple model described.A where P is the probability that the inclination is less than io. solutioo war found [14] in a function rclatilg tectonic activity Taking note of a rclation betu/eenthe rctatiotral energyper to planetary mass derived by fifting to Condie's model of uitmass ofplanet with tte planetarymass, Dole [2] derivedan comparativeplanetnryhistodes [22]. Platetectonics terminates empirical equatioo for the iDitial angular velocity of a planet at &e tiDe T;

o)= t(2jme)/ (tl)l ',, (r2') rn = 5.1(np /mc) o' Glr (14)

Fi& 4 PlaneialysysieEs Foduced by trc @odjned Dole algoriilm about ,rars of varying ageand

X/1 a€ This givesTh- 1.1 clr forMars, itr goodagreemeat with the representsa sphericalvolume of str|ace- 830LY acrosscotrtain- scenarioFesented in [9]. For the Barth T_ - 5.1 cyr, which ing 449,440 siDgle Population I stars. All such stars of age accods with Condie'sprediction that plarctAbnics wif largely betv,/eenI Gyr aodTre andEngitrg in massbetweeo 0.45 - 1.8 -500Myrin cease rbefuhfe. Any planetwithT- > I Gyr will M; werc passedto the plarctary generation algodthms for bemassive eoougb to beable lo holdoo to volatijemolecules i]rther prccessing. aslight aswater for many billions of yearswithout appreciable The numericalresults are set out in Tablg 2. Listed are data loss, unlesssubject€d to a wet or ruaway greeohouseeff@t for N(M), the oumber of single M/S starsin tie stellar mass Thus,fo. biocompatibleplanetu ttrerc is no need10 calculate for il(rement M, and D(IIP) and n(BP), the Duinberof habitable the loss of atnosphercs, Tbe requircment fot a funclional plaft1s a[d biocomparib]eplaftts h eacb lEllar mass incre- geochemicalcarbon cycle alsoplaces a lower limito! planetary mentiespectively.Also includedarc lhe rafiosf(IIP/N(M and tr(BP),4.I(M)the ftequenciesof habitable and biocompatible planetsabout sta$ of massM. The total number of qenerated 4. REQUREMENTSFORBIOCOMPATABILITY habitableptam$ was2419 giving rheoverall Hp freq-ueDcyfor the solarneighbouhood to ben(HPIN = 0.0024;about I in 413 The principal criteria assumedfor planetarybiocompatability starsarc accompaniedby a habitableplanet the spacialsepara- are listed in Table 1. All are dictated by the need for the tion of suchworlds being - 3l LY. BiocoDpatible planetsas a maintenalce of planetary suface tempemtDrewithin a range whole werc much more common,25875 being Foduced, compatiblewith the existenceof tiquid water. The role of tie giving a BP frequencyofn(BP),/N = 0.0259;about 1 in 39 srals value of stellar irradianceand the presenceof clxstal tectonics possesssuch a platretthe spacialseparatiotr of them being -14 have b€e! outlined. However, even if sifuatedwithitr an eco- LY. spherc,d$stic variatio[s iD iradiarce would be expectedto The number of planets of each type in each stellar mnss compromisethe capacityof a planetto sustainlife. when a $tar incrcmentare plotted oDfig. 5aand their ftequeociesare plotted becomesa red giatrt, itJ atteda[t iDoerterrestria.l planets are on fig. 5b. It is nolic€ablethat habitableplanet! occur over the incberaledaod so lbe rnax imum age ofa biocompaibteplanel stellar rDassrange 0.8 - 1.8 I\4, over 5070 of tiem being would be the rnaiD sequencelifetirne of tbe pdlury star. Seasonalor da.ily extremes of Lmdiance, causedby a high TABLE 2t AruIysis of N = 1,000,0{nStar SJste/N,449,440 orbital ecceotdcity, axial tilt, or rotation period could cause Singk, Pop lation I Stofs,Datafor MtS SingleStats Mass Range such a violeody flucfuating climate as to reDderthe eqvton- 0.45- 1.8Mo. ment uofit for life. The biocompatiblethreshold values of these parametersare uDlnowo and thosein Table I are choseDfrom Stell.a! n(lF) Dole [2]. A lower biocompatibteage threshotdof I Gyr was !er) Mass, M. N(14) !(IIP) N(M) n(BP) N(M) chosento allow for the higb impact rate of planetesimatsleft over form tbe planetary accretionprocess to die down to safe 0.45 19549 0 0 0 0 When examining starswithin the solar neighboufiood for 0.50 t7t4r 0 0 52 0.003 their poteDtial to host life-bearing plaoets, the most usefirl t5 0 0 308 0.020 parameter is the biocompatible range of stellar mi$s, An 0.60 13609 0 0 'tm 0.058 estimateofthis, andthat for the subsetofhabitable Dlanets.can 0.65 1198 0 0 1389 0.116 beobtaroed by !tatisricalanalysis oflbe ouput ofdiecomputer 0.70 10517 0 0 1792 0.170 0.75 915r 0 0 2304 0.252 0.80 8514 0.006 29c0 0.341 T ABLE l| Prine Requnenentsfor PlanetaryBiocompatibitity. '7556 0.85 D5 0,039 ?376 0.381 Agql G)'r < T < TMs, 0.90 6819 3A 0.044 7l 0.383 0.95 598 316 0.053 19 0397 Orbital Eccelaicity < 0.2, 1.00 5487 240 0.051 2065 0.3'16 Axial loclination < 55", 1.05 4746 255 0.061 r'1'18 0.429 Rotatioo Period < 96 hr, 1.10 3177 0.078 l4t6 o.446 1,15 u47 191 0.078 7072 0.418 Illumioarcq '705 0.25So < S < 1.1So, r.20 1901 132 0.069 0.37r Acdve Volcanism Tectonics t.E r416 116 0.079 452 0.306 and '74 1.30 t250 0.059 321 0.257 1.35 9t2 54 0.059 24 0.?j8 5. RUNNING THE COMPUTER MODEL 1.40 112 34 o.044 147 0.r90 1.45 649 30 0.046 105 0.ra A large numberof lu]ls wererequtued to obtain good statistics r.50 500 13 0.w 77 0,154 ftom lhe ouout of tbe model. In Ref. tl4l the computer r.55 456 t3 0.028 6l 0.134 processed105 star systems but the numberofst rs ofM > 13 Iq r.60 3n8 0.025 33 0.r02 was still not great etrough to prevent unacc€ptablenndoni n66 0.022 22 0.080 fluctuations in tle output alata.The computer was the@fore 1;70 257 3 0.011 0.058 given tbe taskofinvestigating amiltioo field stalsdistributed itr L;75 222 0 0 5 0.(23 incEments of 0.05Mo over the initial massspectrum described 1.80 t1'l 1 0.005 3 0.017 by Equation(3 ) atrdranging in ageevenly betwe€n0 - l0 Gx. Sincethe stellar numberdensi9 in the solar neighbourhoodis Sntln,ry: n(BPyN= 0.026 d(BD = 14LY 0.116 pc'r ad the relative bioary ftequency is 0.55 I23], this n(rrPyN=0.002 d(HP)= 31LY a Ar EstME oJh. Prdala.. oJ atMnp.lbl. dna Habxabt. Plaub

Fig. 5 Plot of data ftom Table 2. a) The nubd ofBPs od HPslroduc€d about st€rsof b) The ftequeneyofBPs and HPs.

\ \-\ tt ne Fig. 6 Bio@mpatible !]metary abund6ncedetd ior sta$ of 0.6 - L I \4. JM= Juvenile MetjM. lT = JDvenileTelmn. H -Habirable. I

conceotraledabout stals of 0.85 - 1.05 LL. The peak HP Iaage0.75-1.0I\4.Thep€akBPfiequeacyis-45Traboutshrs ftequencyb however- 8%about sta$ of 1.2t\q. Bi&ompat- of 1.1Me. ible planetsmay be foundover the stellarrnasi range0.5 - Thesedata can be srplained by consideriryhow HP aodBP 1.8L4,with about60% of tlen occurringabout sfiIs ill the abundancesvary with the massand age of the primarystar. Figure6, ftom Ref. [ 14], showsthe resultsof suchan investiga- to the semi-majoraxis ofthe closecompoDentbe somewhere in lion.For slars bcr\reeo 0.6 - I . I M", |000 ruDs for eacbinteger the rulge 3-4, regardlessof which is the pla{et It so happetrs Cr belweeoI G).r and TK wde per{omed and fte tolal that nearly all the multiple star systeos in the solar neighbour- number of BPs of eachtpe plotted. hood wiII thus have highly stable planetary o$its within the The resultsfor 0.9 and 1,0 Mo aresimple to accoutrtfor. The ecosphercof each componentan4 so long as bottr stars are relative abundancesof Juvenile Martian, Juveoile Terran a_nd withiD 0.5 - 1.8 Mo and still on ttre main sequeoce,therc is a lfubilable BPs reflect the differilrg widtls of their rcspective chanceof the edstence of biocompatible platrets,It was as- zorcs withiD the ecosphere(fig. 2). The declinein n(P) with age sumedfu Dole's study [2] that habitible planet orbitl would be is causedby the declinein planetarytectonic activity with time, stablein 959, ofmuttiple sur systems. asmodelled by Equation (14). The fall offis particularly ste€p To convert tie data produced by the simulation to the after T = 6 Gyr as few terrestrial planets fomed about such scenadowhere planetsalso form in multiple star systemsone reladvelymetal poor star:sare massive enough to sustaincnrstal multiplies the frequenciesn(HP)/N aad lr(BP)N by 0.95 x the rccyclitrg to the plesent clay. rcciprocal of one minus the relative biDary frequency,i.e. by The grapbfor 1.1 Mc showsOal, for starsof > Mo, tbe 2.11. This givesthe result that about 1 in 197stars may possess decliDeinto plaoerar)senesceDce will. io maoy cases,be a habitableplanet and I itr 18stss abiocompatibleplaneE these hrelevant as such a situation would be preempted by the wo ds havitrg a! avemgespacial sepaiationof24 ad 1l LY primary star evolviDg off the main sequeoce.In this case, respectively. severalhundred BPs still survive at 7 cyr which is Tm for a l 1 A sunmary of the conclusions rcgarding ablndances of M; star. This has the effect of increashg the ftequency of biocompatibleplanets is shown in Table 3. biocomDatibieplanefs about M/S strrs of 1.05 , 1.35 M. becausesucb a slaris morelikely to beyounger ban a r)?icat starof < 1\4o.However, the peals offigs. 5a and5b aredisplaced T ABLE 3. S nnary of Sinulatiotl Results. from eachother by 0.3 14 becausestars of> Mo aremuch more scarce.Not only is this becauseof the influerce of the initial IIPSmay exist about stfis bef,yeen0.8 - 1.8I\4, mass spectsum,fewer of thesesta$ will havebeen bom in the BPsmay exist about st rs between0.5 - 1.8Mo, first place, but also becausernany of thenr" beiDgolder than T6, wili havevanished. The presentday mass spect um ofstars HPsmay occur about ) 37"of starsbeween 0.85 - 1.45Iq. > Mo thus falls off with an exponentthat is the sumof thosein BPsmay occur about > 30qoof starsbetween 0.8 - 1 25 Mo. Equations(3) and (6), -(1 + 3.75). With jncrEasilg srellarmrss Ts isreduced unril al l.8MeitisoolyjuslabovelC),r.This e{plain\ wh} oo BPs a-refound aboutmore masstveslars Casel: OnIy Single Stars PossessPlanets. becauseof rhe assumptior of a 1 Gyr minimum age for a planet biocompatible Frequeoc)ofHabilable PLanets I HP/ 41J srui_:. Tbe graphfor 0.8 M6 starsillustrates the influe&€ ofanother coDstanrton biommpatibleplanet abundrnces. Habiiable planets Meatrdistalc€ betweenItubitable Planets- 31 LY. arenow raje ard only occur in young systemsofT < 3 Gyr. This Frequencyof Biocompatible PlanetsI BP / 39 stars. is becausethe luminosity of a 0.8 M" star is tow enoughsuch lhat the wamer rcgions ofthe ecosphereaf,e situated so closeto Mean distancebetweeD Biocompatible Planets - 14 LY. the prinury that any plalet there is subjectedto excessive stellar tidal forces which mpidly despin its rctation to a syn- Cose2: PLapts Can Form in MuhiDle Star Svstens. ctuonousstate. Since stellarlumioosity is sucha strongfirnction of stellar mass(Lo Mlrr) alrd tidal forces so crucially depend- ent on distance(Udes Cl' R.M), the tidal force o! a planetvdthin Frequencyof HabitablePlanetr 1 HP / 196 stats. the ecosphereof a given staris roughly proportionalio M{. The Mean distancebetween Ilabitable Plarcts - 24 LY. datafor strrs of0.7 Mo revealsthat a drop ofa mere0.1 Mo nrles out the existeoce of habitable plalets aod all but the very Fr€quencyof BiocompatiblePlanets 1 BP/ 18 stars. youngestjuvedle teran planet. However,planets of the juve- Mean distatrcebetween Biocompatible Planets - I I LY. nile Marlian type rcrnain sufficientty distant ftom ttrepdmary lo be unaffected by tides ovet the timescale considered.A fiuther reduction to 0.6 Mo showsthat eventhe abundancesof JM biocompatibleplanets are being reducedby the effec$ of 7. THE SOLAR NEIGEBOI,'RHOOD stellar tides. At 0.45 M6 it was found that no biocompatibte planets possible were at all. CombiDiogdata on nearby starswith tte rcsilts of tie model pemits the identification of starswhich may possessbiocom- 6.'I'HEQUESTIONOFMULTIPLESTARSYSTEMS patible planet! and which arecalrdidates in the se?rchfor extra- ten€strial 1iG.Qualifying sta$ wilhio 22 LY ftom the Sun are Thb analysiswas dore on the assumptionthatonly single st rs tisted in Table 4 along with their spectraltlpes aod esfimated haveplanets. This is valid if planets caDnotform in binary or masses.Paramelers a€ taken from [r] or, when not hcludei multipl€ starsystems However, [24]. the validi9 ofthis conjec- in tXis refeEnceftom [21.The probability of &e existenceof a ture is difficult to assessi! view ofthe conthuing uocertainty babitableplanetPp = o(HP)/N(M)aDd a biocompatibleplanet planetary associatedwi$ the planet ry fomation proc€ss[25]. PtrF- n(BP)fN(M) arr also tabulatedwith an asteriskdeDoLing orbits can be dFamica.Uy stable about biDary shrs, either that the value listed only applieson the assumptionthat planets circling eachcompooeDt, or both compooentsof a very close exist withitr E ltiple star systems. pair. Harington 126l has estimatedftom three-bodyproblem Table 4 showsthat there arenumqous potentially biocom- numerical integrationsthat tle limitation for stability is that the patible locatioos wittrin fie solar neighbourhood.The stars€ ratio of the periastrondistance of tie outer tertiary component Eridani, € Indi, r Ceti, o Draconis, 6 Pavonis, 82 Eridad, B A, En ME oft z Prdaleae ofAb@tup4tltte ani Eabitable PlaE t

T ABLE 4, Staf Systehi.swith bioconpatible potential within 22 IW, years,

Sr Distarc€ Specfal MasVSoIar PP Type Units (E")

& CentauriA 4.38 GzV 1.1 7.8* e CentauriB 4.38 K6V 0.89 38* € Eridad 10.69 K2V 0.8 0.6 61 Cygli A lr.1'1 K5V 0.59 0 5.8+ 61 Cygri B 11.17 K7V 0.50 0 0.3* € Indi tt.2r K5V 0.7r 0 r8 \,a.9352 t1.69 M2 0.47 0 <0.3 1 CeIi 11.95 G8V 0.82 1.5 35 Lac 8760 MlV 0.54 0 Grm1618 15.03 K7 0.56 0 2.5 70 Ophiuchi A 16.73 K1 0.89 38+ 70 Ophiuchi B t6.73 0.68 0 16* 36 OphiuchiA 17.13 KOV 0.77 0 8* 36 OphiuchiB r7.73 Klv o.76 0 z7* 36 OphiucbiC r7.73 K5V 0.63 0 9.0+ trR 7703A 18.43 K3V 0.76 0 n1 o Dracods 18.53 KOV 0.82 b Pavonit 18.64 G5 0.98 5.1 39 I CassiopeiaeA 19.19 GOV 0.85 3.9 38+ I Cas$iopeiaeB 19.r9 MO 0.52 0 0;7* HD 36395 19.19 MIV 0.51 0 0.5 Wolf 294 19.41 M4 0.49 0 <0.3 + 53'1320A 19.65 MO o.52 0 0.6* + 53"1320B r9.65 MO 0.5r 0 0.5+ - 45 1367'7 2n.6 MO 0.48 0 <0.3 82 Eri&ni 2i.9 G5 0.91 38 F Hydri 21.3 r.23 7.5 IIR 8832 21.4 K3 014 0 probability pBp= Notes:PE= -7o of theoccuratrce of a trabitableplanet, 9oprobability of the occura[ceof a biocompatibleplanet Probabilitiesmarked * oDIyapply if platretsfolm andbave stable orbit$ in binarystar systems.

Hydri and HR 8832, being single and > 0.7 Me, are the best HR 7703andl Cassiopeiaealso merit seriousconsideration. As candidates,all having a >> 1070chance ofpossessing a biocom- for the subsetofhabitable planets, the st,I themodel predict as patrble planet. All except e Indi and HR 8832 oay also be having the highestprobability of possessilgsuch a wo d is o accompaniedby a habilable planet, although € Eridad is Crntauri A - a sun tlat is right on our cosmic doolstep. borderline, beiog of - 0.8 N4.. (A re.ent report [281claiming that e Eridad is a close binary syst€mof seili-major axis 0,35 8. CONCLUSIONS AU, which would lule out the existenceof any biocompatible planets,is basedon discrediteddata and is thusin enor [29,30]). ]f Kalting et al [12] aie conect in speculatingthat the outer All the multiple star componentslbted i! Table 4 ca! have ecosphericboudnry lies much finther ftom the Sm than stable plarclary orbils within their resp€ctive ecosphercs.If previously supposed,theD the biocompatible range of stetlar planetr have fonned in tiese rcgions &en the biocompatible firassmay extend to quitelow masses,^0.5 M". Altiougb most poential within the solar neighbourhoodis substattially in- biocompatibleplatrers would ocqlr aboutstars of specEatt)?e crea$ed.s Ceotauri,70 Ophiuchi aDd36 Ophiucli bavesignifi- early K, ltrJoughG, lo lale F, lhe eolire raDgeof main sequeDce cant prcbabilities of possessingbiocompatible planets about starsftomeadiest M to late A shouldbe considered io the search eachcomponent 36 Ophiuchi, befug hiple, actualy hal a - for altratenestrial life. Biocompatible planets may thus be 0.6% cbanceof possessing3 BPs. The pdmariel of 61 C)gni, cornmoDtbroughout the UDiverse,the model presentedhere

II estimatingone such planet per 18-39stds ofmefalicity > 0.3 TABLE 5:

Table5 reveat how tus conclusionru$ counterto previous Ref n(HP) d(LY) trends. It lists estimatesof the abundanceof tbEe previous N studies of the preva.lenceof "habitable" planets. These esti- matesvary enormously,due partialy to diffedtrg definitions of the parameterspace defiDing a habitableplaDet Dotre[2], for Dole[4] 1n,o instance,iDcluded multiple sta$ in his analysis,whercas BoDd andMarliB [3 1] and Pollard[32] adoptedthe ecosphereof Hart Bond& Mantu [5] 1/6000- l/r2000 80- 100 [4] and sel out, deliberately,to cometo a conservativeconclu- sion. Tbe prcsentstudy coDculswith the datai! Table5 in that Potard [6] 105- 10r 200- 1000 it suggestslhat specifically Earthliko, habitnblq planetl are likely to be quite rarc (1 in 188 - 413 stars)but cont€ndstiat suchplanets ale only a subsetof a geafly more abundantset of potentially lifebearing biocompatibleplanets. We may ttrusrequirc aootler explanationfor creat "The Si- (1989\, lerce" other thanthe lack of suitablesites for the orisin tife. Di Schwartzt:m dd T. Volk, Notue, 340, 457-460 h^ye of shownthat chemicalweathering of basaltis gready feilitaten by fic lresence of pldts and oiqooiganisos. A ge@hemicslcdbor cycle ACKNOWLEDCEMENTS drkled by biology would theEforc act d m evetr morc rcbust plmetary th.mostot. This eff@t hd &t b@n included in thir paper The author would like to tiant Salvatore Santoli and Jim beause theprcbability ofthe oriain oflift tu comlletely un&lowDand Kastins for their intercsl b@ausethe Seochemicalcdbon cycle can olerate abiotically.

REFERENCF^S

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