Mon. Not. R. Astron. Soc. 000, 1 11 (2008) Printd 9 March 2008 (MN LATEX styl fil v2.2) Compound modl using D/H ratio to xplain watr s origins of Earth-lik plants K. d Souza Torrs 1 and O. C. Wintr 1,2 1 Instituto Nacional d Psquisas Espaciais - INPE, São José dos Campos, 12211090. Brazil 2 São Paulo Stat Univrsity, UNESP, Grupo d Dinâmica Orbital & Plantologia, CP 205, Guaratingutá, CEP 12516-410. Brazil Accptd yar month day. Rcivd yar month day; in original form yar month day ABSTRACT Th origin of watr on Earth and othr trrstrial plants rmains on of th most important subjcts of dbat and controvrsy in Solar Systm formation scinc. Comts wr long considrd th most likly sourc of watr, but chmical masurmnts in thr comts indicatd a maximum of 50 pr cnt on th comtary contribution to Earth s watr. Othr sourcs hav bn proposd and som of thm bcam mor prominnt, such as local absorption onto grains and astroids. Howvr, no sol sourc of watr provids a satisfactory xplanation for Earth s watr as a whol. In viw of that, w cratd a compound modl incorporating both th principal ndognous and xognous thoris, and invstigat th implications with dynamical simulations of plantary formation and watr dlivry. Comts ar also considrd in th final analysis, as it is likly at last som of Earth s watr has comtary origin. W analys our rsults using D/H ratio as a discriminator, giving possibl rlativ contributions from ach sourc, focusing on mbryos formd in th habitabl zon of th main star. Th goal is to idntify th sourcs of trrstrial plants watr in th Solar Systm and xpand it to xtrasolar systms. W conclud that th compound modl bttr xplains th D/H ratio of Earth s watr, as wll as xpctd valus of mass and watr contnt for Earth-lik plants. Ky words: Solar systm: formation, Earth, plants and satllits: formation, astrobiology, mthods: N-body simulations 1 INTRODUCTION In its gasous and solid forms, watr is prsnt in distant galaxis, among stars, in th Sun, in its plants and thir satllits and ring systms, and in fcomts. In its liquid form, it has playd an ssntial part in th apparanc, dvlopmnt and maintnanc of trrstrial lif. Th qustion of how trrstrial plants form and how thy gt watr has bn havily discussd in th last fw yars. According to th most accptd thory of plantary formation, th protosolar nbula was hottr and dnsr toward its cntr and coolr and lss dns farthr out (Encrnaz 2006). Ths gradints influncd th chmical composition of diffrnt rgions of th arly solar systm, including th distribution of watr. Clos to th nbula s cntr, high tmpraturs and prssurs vaporisd ic crystals and th light lmnts. Th solar wind blw ths matrials toward th outskirts of th nbula, laving mainly grains of rock bhind to form th innr plants. Farthr out, dbris formd th carbona- E-mails: karlchn79@gmail.com (KST); ocwintr@fg.unsp.br (OCW) cous chondrits that carry up to 10 pr cnt of thir mass in watr ic (Morbidlli t al. 2000). Byond th giant plants, watr condnsd in larg quantitis and formd comts, which ar up to 80 pr cnt of watr (Jssbrgr, Kissl & Rah 1989). Compard with ths icy objcts, Earth contains littl watr: only about 2 prcnt of its mass in its ocans, and somwhat mor watr sits bnath th surfac. Nvrthlss, Earth has substantially mor watr than could b xpctd at 1 AU from th Sun: th minimum valu is 1 O, th maximum valu of 50 O, and an xpctd valu would b 10 O (Drak & Campins 2006). Many modls trying to xplain Earth s watr hav bn proposd ovr th yars (.g. Morbidlli t al. (2000), Raymond, Quinn & Lunin (2004), Stimpfl, Laurtta & Drak (2004), O Brin, Morbidlli & Lvison (2006)) basing on availabl vidnc. Suggstd sourcs can b dividd into ndognous and xognous, and includ mainly watr absorbd by dry silicat grains in th nbula, astroids and comts. Ths diffrnt sourcs may b distinguishd by thir dutriumto-hydrogn (D/H) ratio and othrs isotopic diffrncs, and by prdictions of thir rlativs amounts of watr and mass (Lunin 2006). Th following sub-sctions dscrib th most c 2008 RAS
2 K. d Souza Torrs and O. C. Wintr Tabl 1. D/H ratio valus for comts, nbula gas and Earth. Body D/H Ratio Rfrnc Hally 3.2 ± 0.1 x 10 4 Ebrhardt t al. (1995) Hyakutak 2.9 ± x 10 4 Bockl-Morvan t al. (1998) Hal-Bopp 3.3 ± 0.8 x 10 4 Mir t al. (1998) Nbula 2.1 ± 0.4 x 10 5 Lllouch t al. (2001) Earth 1.49 ± 3 x 10 4 Lcuyr, Gillt & Robrt (1998) Comts wr long considrd th most likly sourc of watr for trrstrial plants in th Solar Systm. A comtary sourc was attractiv bcaus it is widly blivd that th innr Solar Systm was too hot for hydrous phass to b thrmodynamically stabl (Boss 1998) and thus an xognous sourc of watr was ndd (Drak & Campins 2006). Drak & Rightr (2002) affirm that rcnt data, for lmntal and isotopic rasons, limit th comtary contribution for Earth s watr to 50 pr cnt, and th tru valu is probably narr to 10 15 pr cnt. Masurmnts of th D/H ratio of watr in thr Oort Cloud comts ar about twic th valu of Earth s watr and about fiftn tims th valu of th solar nbula gas (Tabl 1). Goms t al. (2005) calculatd th comtary matrial dlivrd to Earth to b 1.8 x 10 23 g, which is about 6 pr cnt of th currnt trrstrial ocan mass (O = 1.4 x 10 24 g). Basd on nobl gas ratios, Swindl & Kring (2001) argu that comts could not hav supplid any significant fraction of Earth s watr, unlss it occurrd in th first 100 Myrs of Earth s history, or cam from comts unlik thos coming from th Oort cloud today. Howvr, Ipatov & Mathr (2006) analysd th orbital volution of Jupitr-family comts (JFCs), Hally-typ comts (HTCs), and long-priod comts, and th probabilitis of thir collisions with plants. Thy found th probability of collisions of formr JFCs with th Earth was nough to dlivr all th watr to Earth s ocans during formation of giant plants. Thr ar som discussions as to which masurd D/H ratio valus in comts ar rprsntativ of thir ral bulk composition. Sinc th primary sourc of information about comts continus to b studis of th coma, Schmidt, Brown & Laurtta (2005) argu that it is ncssary to undrstand th rlationship of th coma with th bulk ic. Wirich, Brown & Laurtta (2004) affirm that th D/H ratio would b xpctd to ris in diffusion and sublimation, and Schmidt t al. (2005) did an xprimntal study of comt sublimation in which was obsrvd an upward trnd in th D/H ratio in th vaporatd matrial indpndnt of th bulk composition. Drouart t al. (1999) suggstd that comts ar likly to rtain th isotopic composition thy acquird whn thy formd and for that it is possibl to us thm to diffrntiat among diffrnt modls of plant formation. Hornr, Mousis & Hrsant (2007) usd obsrvd comts proprtis to dtrmin thir formation rgions. Using a dutrium-nrichmnt profil, which offrs a rlationship btwn D/H ratio incorporatd in th watr within plantsimals and thir formation location in th solar nbula (Drouart t al. (1999), Mousis t al. (2000), Hrsant, Gautir & Huré (2001)), thy xamind th possibl ffct that formation in diffrnt rgions could hav on th valus of D/H ratio in comts today. 1.2 Astroids accptd sourcs for Earth s watr, from which it is possibl to gt an indication of how any trrstrial plant can bcom aquous. 1.1 Comts Whn a comtary contribution for Earth s watr was contstd by masurmnts of D/H ratio valus, hydratd carbonacous astroids coming from th Primordial Astroid Blt bcam a mor likly sourc for trrstrial plants watr. Th D/H ratios of th individual carbonacous chondrits rang ovr th intrval 1.2 3.2 x 10 4 (Lcuyr t al. 1998), so that th D/H ratio of th trrstrial watr is wll within th chondritic valus. Watr-containing rocky plantsimals (.g. Morbidlli t al. (2000), Raymond t al. (2004), Raymond, Quinn & Lunin (2005)) and/or icy plantsimals (.g. Goms t al. (2005)) can b dlivrd from outr rgions (typically > 2 3 AU) bcaus of gravitational prturbation of th giant plants. Morbidlli t al. (2000) hav shown that up to 15 pr cnt of th mass of th Earth could b accrtd lat in Earth s growth by collision of on or a fw astroids originating in th Main Blt. Raymond t al. (2004) usd simulations of lat stag of plantary accrtion, focusing on th dlivry of volatils to th trrstrial plants, to analys th influnc of a giant plant and thy find an ccntric Jupitr producs drir trrstrial plants with highr ccntricitis than a circular on. Som gochmical argumnts ar against a larg contribution of watr from astroids considring, for xampl, nobl gass ratios and osmium isotopic composition in th Earth s Primitiv Uppr Mantl (Drak & Campins 2006). Rightr, Drak & Scott (2006) studid th ida that Earth and prhaps othr trrstrial plants ar not mad from familiar mtorit typs, but instad from a matrial that is not currntly rprsntd in our collctions. 1.3 Adsorption of Watr on Grains As an altrnativ to xognous sourcs lik comts and astroids, thr ar ndognous sourcs that considr Earth s watr could hav cam dirctly from th solar nbula, whr trrstrial plants wr bing formd. Stimpfl t al. (2004) hav xamind th rol of physisorption by modlling th adsorption of watr at 1000 K, 700 K, and 500 K using a Mont Carlo simulation. Thir rsults suggst that grains accrtd to Earth could hav adsorbd 1 3 Earth ocans of watr and th fficincy of adsorption of watr incrass as tmpratur dcrass. Howvr, thr ar issus with rtntion of watr as th grains collid and grow to mak plants, as wll D/H ratio discrpancy with trrstrial watr, sinc th D/H ratio of th nbula is 6 tims smallr than Earth s watr valu. Howvr Campins, Swindl & Kring (2004) pointd out that th procss involvd in plantary accrtion, dgassing and th volution of a hydrosphr and atmosphr ar complx and may hav fractionatd th chmical and isotopic signatur of th sourc(s) of watr. Gnda & Ikoma (2007) proposd that
Compound modl to xplain watr s origins of Earth-lik plants 3 th assumption that th D/H ratio of watr on th Earth has rmaind unchangd for th past 4.5 Gyr must b rviwd, sinc th D/H ratio of watr could hav changd during th formation and volution of th Earth s ocan. In this papr, w tackl th qustion of th origins of trrstrial plants watr by incorporating all ths principal proposd sourcs in an analytical modl which is tstd with numrical simulations. W ar motivatd by th ida that probably Earth s watr had not just on sourc and it can b bttr xplaind via a combination of an absorbd componnt, a componnt of astroids and a comtary componnt. Rsults ar analysd using known D/H ratio valus in ordr to idntify possibl rlativ contributions from ach sourc. Sction 2 dscribs th compound modl, which incorporats astroids and local adsorption of watr. Sction 3 dscribs th initial conditions for numrical simulations and Sction 4 prsnts th rsults of ths. Sction 5 discusss rsults adding analyss of a comtary contribution. Sction 6 prsnts th conclusions of th whol work. 2 MODEL Th modl ralistically dscribs th bginning of lat-stag plantary accrtion and is basd on availabl information for th Solar Systm. Howvr, it is intndd to b asily xpandd for any plantary systm. It incorporats an ndognous and an xognous sourc of watr and uss D/H ratio as a discriminator. Th ndognous sourc is adsorption onto grains (Stimpfl t al. 2004) and th xognous sourc is astroids (Raymond t al. 2004), as dfind in th prvious sction. Comts ar considrd in a postriori analysis. Th nxt sub-sctions dscrib how mass, watr and D/H ratio valus ar initially attributd. 2.1 Mass W us a mass distribution modl as in Raymond t al. (2004), whr th mass is dividd btwn mbryos and plantsimals. W assum that oligarchic growth has takn plac in th innr Solar Systm. A two-tird surfac dnsity is usd, which rflcts an incras in surfac dnsity du to th condnsation of watr immdiatly past th snow lin. Σ 1 and Σ snow ar th surfac dnsity at 1 and 5 AU, rspctivly. { ( Σ r ) 3/2 1 Σ(r) = 1AU, r > snowlin ( Σ r ) 3/2 (1) snow 5AU, r < snowlin 2.1.1 Embryos Each mbryo mass is dtrmind by a smi-major axis function. Th prvious phas to oligarchic growth (runaway phas) nds whn th mbryo has mrgd with vry availabl plantsimal in its surroundings, laving an annulus of clard matrial in th solar nbula calld th fding zon. Th fding zon of a plantary mbryo is an annulus with width comparabl to th mbryo s Hill radius (R H ) and radius a. Th mass insid that is givn by: M = 2πaR HΣ (2) whr Σ is th surfac dnsity in solids givn by th Equation 1. Rplacing th Hill radius in Equation 2 and solving for M w can obtain th mbryo mass at th bginnig of oligarchic growth, givn by: ( ) 2πΣa 2 3/2 M mbryo = (3) (3M ) 1/3 Simulations of th formation of mbryos from plantsimals (Kokubo & Ida 2000) show that thy typically form with sparations of 5 10 mutual Hill radii dfind as: R H,m = ( ) ( ) 1/3 a1 + a 2 M 1 + M 2 2 3M Plantary mbryos ar thrfor spacd btwn 0.5 2.5 AU for a random numbr (btwn 5 and 10) of mutual Hill radii. 2.1.2 Plantsimals Btwn th Snow Lin (2.5 AU in th Solar Systm) and 4.0 AU w assum th mass in plantsimals, rprsnting carbonacous chondrits astroids. Th plantsimal mass is fixd at 1 M and 200 of thm ar distributd as N r 1/2, corrsponding to th annular mass in a disc with surfac dnsity proportional to r 3/2, according to Equation 1. 2.1.3 Giant Plant On Jupitr-lik plant is usd to influnc th accrtion dynamics. It has th sam position, mass, smi-major axis and ccntricity of Jupitr. 2.2 Watr Th watr contnt of plantsimals and plantary mbryos in a givn plantary systm dpnds in a complx way upon a rang of factors including th mass and volutionary charactristics of th protoplantary disc, ovrall mtallicity of th molcular cloud clump from which th star is forming, and th positions, masss and timings of formation of th systm s giant plants (Raymond t al. 2004). Hr w us a biphasic modl that considrs th most rcnt thoris about sourcs of watr for trrstrial plants. For mbryos, w us an initial watr contnt dfind by an ndognous thory modl (Stimpfl t al. 2004) that dpnds on th tmpratur gradint profil in th solar nbula. Fig. 1 shows th tmpratur gradint throughout th disc of matrial whr th plants would form in th Solar Systm. Exploring th co-rlation btwn tmpratur and distanc, and thn th co-rlation btwn distanc and watr contnt suscptibl to b absorbd by mbryos in th innr Solar Systm (Stimpfl t al. 2004), w hav th quation: W = 10a 7 (5) whr W is th watr contnt absorbd (in O ) by trrstrial masss and a is th smi-major axis in AU. (4)
4 K. d Souza Torrs and O. C. Wintr 10000 Tmpratur (K) 1000 100 10 0.1 1 10 100 Distanc (AU) Figur 1. Tmpratur gradint in th solar nbula (Clark, 1998). For th plantsimals w us a watr contnt rprsntativ of carbonacous chondrits (5 pr cnt by mass), as in Raymond t al. (2004). 2.3 D/H Ratio In principl, it should b possibl to dtrmin th main sourcs and rlativ contributions to Earth s watr if thy hav distinct chmical and isotopic signaturs. Signaturs that ar usd as discriminators includ th D/H ratio, th ratio of nobl gass and th isotopic composition of th highly sidrophil lmnt osmium. Among thm, th D/H ratio discriminator is th on for which most data on diffrnt clstial bodis ar availabl. Th D/H ratio of th solar nbula gas is stimatd from obsrvations of CH 4 in Jupitr and Saturn to b a low 2.1 ± 0.4 x 10 5 (Tabl 1, Lllouch t al. (2001)). Jupitr and Saturn likly obtaind most of thir hydrogn dirctly from th solar nbula. Th D/H ratios wr masurd from watr in thr comts - Hally, Hyakutak and Hal-Bopp (Tabl 1) - and thy ar all about twic th valu for trrstrial watr, and about fiftn tims th valu for th solar nbula gas. Carbonacous chondrits hav th highst watr abundanc of all mtorits and thir D/H ratios rang from 1.2 x 10 4 to 3.2 x 10 4. Ths valus ar illustratd in Fig. 2. Using ths data, w ar abl to giv th initial D/H ratio valus for mbryos and particls. Initially, mbryos ar considrd to hav som locally absorbd watr (as dscribd in prvious sub-sction) and this watr rcivs a D/H ratio valu lik th protosolar nbula. Particls rciv a mdian valu (2.2 x 10 4 ) among D/H ratio valus of carbonacous chondrits. In an a postriori analysis, comts rciv a mdian valu (3.1 x 10 4 ) ovr th thr known valus. All th modl s quations wr implmntd using th softwar Mathmatica to crat th initial conditions fils for th numrical simulations, as dscribd in th nxt sction. Figur 2. Th D/H ratio in H2O in thr comts, mtorits, Earth (Vinna standard man ocan watr - VSMOW), protosolar H 2, and Mars. CC = carbonacous chondrits, LL3-IW = intrstllar watr in Smarkona, LL3-PS = protostllar watr in Smarkona. (Drak t al., 2006) 3 NUMERICAL SIMULATIONS W run all th simulations for 200 Myrs (Raymond t al. 2004) using a modifid vrsion of Mrcury (Chambrs 1999). Mrcury is a gnral-purpos softwar packag for doing N- body intgrations and w rprogrammd it to includ watr contnt. Th hybrid intgrator is usd, which uss a scondordr mixd variabl sympltic algorithm whn objcts ar sparatd by mor than 1 Hill radii, and a Burlisch-Stor mthod for closr ncountrs. W us a 5 days tim-stp. Collisions consrv linar momntum and do not tak fragmntation into account. Ths simulation wr run on dsktop PCs, ach taking about 1 month of CPU tim on an 800 MHz machin. W us thr valus of surfac dnsity at 1 AU (Σ 1 ), th minimum mass solar nbula (6 g/cm 2 ) xpctd for th innr Solar Systm, th maximum valu xpctd (10 g/cm 2 ), and an intrmdiat valu (8 g/cm 2 ). Each surfac dnsity is simulatd thr tims, with slightly diffrnt configurations. Fig. 3 sums up th initial conditions for on simulation. All th othr simulations follow th sam pattrn, with mbryos initially Moon to Mars sizd. Fig. 4 shows som snapshots of on of th simulations. 4 RESULTS Tabl 2 summarizs final mbryos data of all simulations. Th columns ar nam, surfac dnsity, simulation numbr, final smi-major axis, final ccntricity, final mass (in trrstrial masss), prcntag of astroidal mass, final watr (in trrstrial ocans), prcntag of astroidal watr and final D/H ratio of th surviving mbryos. Th work of Morbidlli t al. (2000), as wll as arlir authors (.g. Wthrill (1996)), showd that plantary accrtion is a stochastic procss, spcially if much of th mass is containd in a small numbr of larg mbryos (Raymond, Quinn & Lunin 2007). Th contnt of watr dlivrd to any givn trrstrial plant, and its sourc rgion, can vary
Compound modl to xplain watr s origins of Earth-lik plants 5 0 Myr 0.1 Myr 5 5 0 0-5 1 Myr -5 10 Myrs 5 0 5 0-5 30 Myrs -5 200 Myrs 5 0 5 0-5 -5 Log(Watr/Mass) -5.3-4.7-4.2-3.7-3.2-2.7-2.2-1.7-1.2 - Figur 4. Snapshots for on of th simulations; surfac dnsity of 8 g/cm 2 at 1 AU. widly. If this viw is valid, thn it implis that trrstrial plants around othr stars may diffr gratly in trms of watr amounts, and th timing of formation and location of giant plants from on systm to anothr could play an important rol in this variation (Lunin t al. 2003). Ths simulations produc diffrnt configurations which supports this pictur of potntially larg variations in watr abundanc. In th nxt sub-sctions ach main paramtr, mass, watr and D/H ratio, is analysd sparatly. 4.1 Mass Fig. 5 shows th total mass, initial and final, of mbryos and plantsimals in all th simulations. Considrabl mass is lost in th simulations by jctions or collisions with star or th giant plant. That is du to cumulativ prturbations of mbryos and gravitational influnc of th giant plant. Most of th rstant mass is usd to form proto-plants. In all th following figurs th surfac dnsitis ar rprsntd as shown in Fig. 6. Fig. 7 shows mass distribution in a x graph. Largr mbryos ar concntratd btwn 0.5 and 1.5 AU, in lowr ccntricitis. Mass distribution paks around 1.3 AU (Fig. 8) and it could rprsnts a mass quilibrium zon of th systm, whr plants ar likly to form with mor mass. If it happns, thr would b implications
6 K. d Souza Torrs and O. C. Wintr Tabl 2. Final data of survivors. a Body Σ 1 Sim a f f Mass(M ) %M Ast Watr(O ) %W Ast D/H EM53 6 1 1.2422 0.2820 238 0 0.1605 0 2.10E-05 EM54 6 1 1.9297 0.2624 475 0 0.3201 0 2.10E-05 EM25 6 2 0.6575 310 0.5652 5.33 8.0421 80 1.79E-04 EM35 6 2 2.0172 0.1276 0.4703 4.27 8.4141 51 1.22E-04 EM37 6 2 1.1913 311 0.5905 0 3.5568 0 2.10E-05 EM16 6 3 0.6472 0.1795 0.5424 0 0.7057 0 2.10E-05 EM49 6 3 1.2701 631 0.6212 3.24 8.5152 50 1.21E-04 EM53 6 3 1.6453 313 0.1944 0 2.0790 0 2.10E-05 EM67 6 3 1.7909 76 384 26.20 2.4267 88 1.96E-04 EM77 6 3 2.4302 0.1840 0.1200 25.12 7.5152 85 1.90E-04 EM33 8 1 1.4725 0.1197 0.1877 0 1.5848 0 2.10E-05 EM54 8 1 0.9237 0.2661 523 19.22 2.5411 84 1.88E-04 EM58 8 1 2.4472 117 902 0 075 0 2.10E-05 EM61 8 1 2.9343 0.1197 478 0 0.6050 0 2.10E-05 EM64 8 1 2.6261 0.8908 500 0 0.6954 0 2.10E-05 EM65 8 1 1.9094 939 0.1703 11.80 6.3617 67 1.54E-04 EM6 8 2 0.6684 961 0.7238 4.17 8.4873 75 1.71E-04 EM22 8 2 2.2660 316 482 0 403 0 2.10E-05 EM41 8 2 1.1374 728 0.7132 4.23 11.3468 56 1.33E-04 EM51 8 2 1.7585 0.1300 0.3598 5.59 7.0762 60 1.41E-04 EM57 8 2 2.2332 0.5756 555 18.10 2.6511 80 1.81E-04 EM62 8 2 3.0464 0.1223 592 16.97 2.7931 76 1.73E-04 EM36 8 3 1.4107 438 0.5882 0 4.8500 0 2.10E-05 EM37 8 3 2.1633 0.4128 309 0 0.1206 0 2.10E-05 EM47 8 3 2.1017 0.6323 365 0 0.2449 0 2.10E-05 EM55 8 3 0.8039 0.1472 0.7190 1.40 5.2529 41 2E-04 EM68 8 3 2.1167 0.1941 0.2357 12.79 9.4650 68 1.56E-04 EM4 10 1 0.71 0.1492 0.9635 4 5.8516 36 9.36E-05 EM49 10 1 1.4076 783 0.8596 4.68 14.2830 60 1.40E-04 EM60 10 1 2.6466 0.5187 718 0 508 0 2.10E-05 EM42 10 2 1.406 279 1.2113 3.32 2818 43 6E-04 EM10 10 3 0.5015 0.1399 0.2756 3.65 2.2885 93 2.07E-04 EM44 10 3 1.2858 608 1.2597 3.19 17.0530 50 1.21E-04 EM50 10 3 2.2788 476 595 0 0.5853 0 2.10E-05 EM65 10 3 2.3168 0.2354 18 0 2.4830 0 2.10E-05 a Columns ar: mbryo nam, surfac dnsity, simulation numbr, final smi-major axis, final ccntricity, final mass (in trrstrial masss), prcntag of astroidal mass, final watr (in trrstrial ocans), prcntag of astroidal watr and final D/H ratio of th surviving mbryos. for habitabl plant formation around solar typ stars, sinc this zon includs th habitabl zon (HZ) of th Solar Systm (s Sction 5 for mor about HZ). It would imply that trrstrial plants ar likly to b formd in th HZ of solar typ stars with masss clos to that of Earth. Thr is also a mass pak around 4 pr cnt of astroidal mass (Fig. 9). A disc with an incrasd surfac dnsity of solid matrial will form a smallr numbr of mor massiv trrstrial plants with largr watr amounts than lowr mass discs, du to strongr slf-scattring among protoplants (Raymond t al. 2004, 2007). That would xplain why just th highst surfac dnsity valu (Σ 1 = 10g/cm 2 ) producd mbryos with mass > 0.8M and, gnrally, mor watr contnt. Most of th largst mbryos ar formd clos to thir initial position (Fig. 10) which suggsts a corrlation btwn biggr mass and lowr migration. 4.2 Watr Th final contnt of watr will dpnd not only on astroidal contribution but also on th watr locally absorbd, bfor th simulations gt startd (as dscribd in Sction 2). Som mbryos gt lowr watr contnt than Earth s minimum limit (1 O ), but it is xpctd trrstrial plants gt diffrnt mass and watr amounts, as is sn in th Solar Systm nowadays. Th systm watr is initially abundant (up to 450 O ) but with th mass loss (Fig. 5), also most of th watr is lost. No mbryo gts mor watr than th maximum xpctd for Earth (50 O, Ab t al. (2000)). Final watr distribution can b sn in th colors of Fig. 8 and Fig. 9. Both mbryos with most watr in th systm ar around 1.3 AU and possss 4 pr cnt of astroidal watr. Thr is also watr concntration btwn 0.5 and 1.5 AU, in lowr ccntricitis, as can b sn in Fig. 11. Fig. 12 shows also a strong corrlation btwn watr and low migration. Embryos formd in th innr part of th systm with
Compound modl to xplain watr s origins of Earth-lik plants 7 3.0 2.5 Astroids D/H Ratio * 2,1 x 10-5 * 2,2 x 10-4 0.8 2.0 0.6 Watr (O ) 1.5 0.5 Embryos 0.4 0.2 0.5 1.5 2.0 2.5 3.0 3.5 5 6 0 0.40 0.50 0.60 0.70 0.80 0.90 1.1 1.2 1.3 1.4 Figur 3. Initial conditions for on of th simulations; surfac dnsity of 8 g/cm 2 in 1 AU. Figur 7. Final smi-major axis vrsus ccntricity showing mass distribution. Total 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 0.8 0.6 0.4 0.2 Initial - Embryos Initial - Plantsimals Final - Embryos Final - Plantsimals Sim6-1 Sim6-2 Sim6-3 Sim8-1 Sim8-2 Sim8-3 Sim10-1 Sim10-2 Sim10-3 1.4 1.2 0.8 0.6 0.4 0.2 0.5 1.5 2.0 2.5 3.0 3.5 Watr (O ) 0 2.0 4.0 6.0 8.0 10 12 14 16 18 20 22 Figur 5. Initial and final total mass of mbryos and plantsimals in all th simulations. Figur 8. Final smi-major axis vrsus final mass showing watr distribution. vry low migration (Fig. 10) and high astroidal prcntag of watr (.g. EM25, Σ 1 = 6g/cm 2, simulation 2 and EM10, Σ 1 = 10g/cm 2, simulation 3) show that watr dlivry by ic bodis coming from byond th snow lin can b vry fficint. That is confirmd also by othr simulations, for xampl, Raymond t al. (2004) and Morbidlli t al. (2000). 6 g/cm 2 8 g/cm 2 10 g/cm 2 Figur 6. Lgnd for th following figurs. Each symbol rprsnts on surfac dnsity group in th simulations. 4.3 D/H Ratio Th final D/H ratio of th surviving mbryos is, in ths simulations, compltly rlatd to th astroidal watr prcntag. Th prcntag of astroidal watr to rach th Earth s watr D/H ratio is givn for Equation 6, with K rprsnting th prcntag of astroidal watr. Th quation givs K 64 pr cnt. K (DH ast) + (1 K) (DH nb ) = DH Earth (6) whr DH ast = 2.2 x 10 4, DH nb = 2.1 x 10 5 and DH Earth = 1.49 x 10 4, th astroidal D/H ratio usd hr, th nbular D/H ratio and th Earth s watr D/H ratio, rspctivly. Som of th surviving mbryos acquir prcntag of astroidal watr clos to this valu, but not with th xact on (Tabl 2). Fig. 13 shows final D/H ratio of survivors watr vrsus final mass. Colors show also th final watr
8 K. d Souza Torrs and O. C. Wintr 1.4 1.2 0.8 0.6 0.4 0.2 0 5 10 15 20 25 30 % Astroidal Mass Watr(O ) 0 2.0 4.0 6.0 8.0 10 12 14 16 18 20 22 0.8 0.6 0.4 0.2 0.5 1.5 2.0 2.5 3.0 3.5 Watr (O ) 0 2.0 4.0 6.0 8.0 10 12 14 16 18 20 22 Figur 9. Final prcntag of astroidal mass vrsus final mass showing watr distribution. Figur 11. Final smi-major axis vrsus ccntricity showing watr distribution. 3.0 2.5 3.0 2.5 Initial Smimajor Axis (AU) 2.0 1.5 0.5 Initial Smimajor Axis (AU) 2.0 1.5 0.5 0.5 1.5 2.0 2.5 3.0 Final Smimajor Axis (AU) 0 0.40 0.50 0.60 0.70 0.80 0.90 1.1 1.2 1.3 1.4 0.5 1.5 2.0 2.5 3.0 Final Smimajor Axis (AU) Watr (O ) 0 2.0 4.0 6.0 8.0 10 12 14 16 18 20 22 Figur 10. Final smi-major axis vrsus initial smi-major axis showing mass distribution. Figur 12. Final vrsus initial smi-major axis showing watr distribution. contnt. What is rmarkabl is most of th mbryos around th Earth s D/H ratio valu hav around 10 O of final watr contnt, what is th amount of watr xpctd for Earth (Drak & Campins 2006). In th Tabl 2 w can s som mbryos (EM37, Σ 1 = 6g/cm 2, simulation 2 EM36, Σ 1 = 6g/cm 2, simulation 3) got mor than half Earth s mass and considrabl watr contnt without astroidal contribution. Th D/H ratio of ths mbryos watr will b th sam of th nbula gas, 6 x lowr than Earth s watr D/H ratio. Gnda & Ikoma (2007) argu that th D/H ratio of Earth s watr is not immutabl, and likly highr today than it was primordially. In ths cass, not only an astroidal contribution but also a comtary contribution could b lss important to complt Earth s watr. Sction 5 brings mor discussions about th D/H ratio of mbryos watr formd in th HZ of th simulatd systms. 5 COMETS AND FINAL ANALYSES A comtary contribution to Earth s watr is not unlikly, although not xpctd as so rlvant any mor. Goms t al. (2005) calculatd th contnt of comtary matrial dlivrd at th Lat Havy Bombardmnt (LHB) as about 6 pr cnt of 1 O. It is consistnt with uppr limits of comtary contribution calculatd basd in D/H ratio masurmnts by Morbidlli t al. (2000). Tabl 3 summarizs mbryos data formd insid th HZ of th simulatd systms, that xtnds from 0.9 to 1.5 AU (Raymond t al. 2007). It shows which prcntag of comtary watr would b ncssary to incras th D/H ratio of ths mbryos watr to th Earth s valu (xcpting EM54, 8 g/cm 2, simulation 1, that has highr valu). Final mass and watr contnt wr updatd accordingly. It is possibl to s from th tabl that adding 6 O of comtary watr (with a comtary D/H ratio) according to
Compound modl to xplain watr s origins of Earth-lik plants 9 D/H Ratio 2.0x10-4 1.5x10-4 x10-4 5.0x10-5 Earth 0.2 0.4 0.6 0.8 1.2 1.4 Watr (O ) 0 2.0 4.0 6.0 8.0 10 12 14 16 18 20 22 Figur 13. Final mass vrsus D/H ratio showing watr distribution. Goms t al. (2005) would not chang considrably th D/H ratio of most of th final mbryos formd in th HZ of ths simulatd systms. For mbryos with non or vry low watr astroidal prcntag, mor comtary watr is ndd (about 44 pr cnt, according to this modl). Som studis considr that likly, ignoring a rmarkabl astroidal contribution. Ipatov & Mathr (2006) argu that, from a dynamical viwpoint, th probability of JFC s collid with Earth would b nough to complt Earth s ocans. Othr studis (.g. Own & Bar- Nun (2001), Drak & Campins (2006)) basd on nobl gass ratios and osmium isotopic composition to show th possibility of low astroidal contribution. In this cas a comtary contribution up to 50 pr cnt would b possibl. Howvr, according to gochmical invstigations, (Chaussidon 2007) it is unlikly that Earth has non or vry low astroidal contribution in its watr. Most of th rst of th mbryos in Tabl 3 nd about 5-15 pr cnt of comtary watr to rach th D/H ratio of Earth s watr. That involvs an uppr limitd a littl highr than som prvious works ( 10 pr cnt by Morbidlli t al. (2000), up to 12 pr cnt by Dloul, Robrt & Doukhan (1998)) but would b in accordanc with by Own & Bar- Nun (2000) (up to 15 pr cnt), giving rlvanc for locally absorbd watr contnt. which is insid th HZ of th systms. Highr valus of mass and watr contnt ar rlatd with low migration. Embryos formd in th habitabl zon of th systms ar analysd considring a comtary contribution for thir watr. Som mbryos formd with no astroidal watr contribution, and for ths would b ncssary about 44 pr cnt of a comtary contribution to mak th D/H ratio of Earth s watr. In th simulations w assumd that all collisions wr prfctly inlastic, and th watr amounts of th rsultd plant would b qual to th sum of th watr amounts of th impacting bodis. As pointd out by Haghighipour & Raymond (2007), this is an assumption that sts an uppr limit for th watr budgt of trrstrial plants, and ignors th loss of watr du to th impact. Th simulations prsntd ar also low rsolution and th rsults may not rval dtaild charactristics of th final plantary systms. Howvr, as shown by Agnor, Canup & Lvison (1999) and Chambrs (2001), such intgrations can produc th main gnral proprtis of th final assmbly of th plantary bodis. Numrical simulations ar always limitd by th fact that th spd of computation simulations varis as N 2, whr N is th numbr of involvd objcts (Haghighipour & Raymond 2007). Dspit its limitations, our study shows a compound modl incorporating main thoris producs xpctd rsults for watr contnt and mass for trrstrial plants and bttr xplains th D/H ratio of Earth s watr, whras any individual sourc of watr fails. Such low-rsolution small numbr of simulations do not prov a thory, but improv prvious and rcnt studis about watr origins for trrstrial plants. Rsults of th modl and analyss basing in D/H ratio masurmnts show th most likly rlativs contributions for Earth s watr involvs 35 pr cnt of absorbd watr, 50 60 pr cnt of astroidal watr and 5 15 pr cnt of comtary watr. ACKNOWLEDGEMENTS Th authors ar gratful to CAPES (Coordnação d Aprfiçoamnto d Pssoal d Nívl Suprior), CNPq (Conslho Nacional d Dsnvolvimnto Cintífico Tcnológico) and FAPESP (Fundação d Amparo a Psquisa do Estado d São Paulo) for supporting this rsarch. This papr has bn typst from a TEX/ L A TEX fil prpard by th author. 6 CONCLUSIONS W prsntd rsults of 9 numrical simulations, projctd to invstigat possibl sourcs of trrstrial plants watr and possibl rlativ contributions to Earth s watr. W propos a compound modl that incorporats th main rcnt thoris of local absorption and astroids, adding comts at final analysis. W bas our rsarch on th likly assumption that Earth s watr had mor than on sourc, and w us known D/H ratio masurmnts of diffrnt clstial bodis to discuss possibl sourcs. Final mbryos hav thir mass, watr contnt and D/H ratio analysd and compard with Earth s valus. Biggr mbryos with mor watr ar concntratd around 1.3 AU, REFERENCES Ab Y., Ohtani E., Okuchi T., Rightr K., Drak M., 2000, Watr in th Early Earth. Origin of th arth and moon, ditd by R.M. Canup and K. Rightr and 69 collaborating authors. Tucson: Univrsity of Arizona Prss., p.413-433, pp 413 433 Agnor C. B., Canup R. M., Lvison H. F., 1999, Icarus, 142, 219 Bockl-Morvan D., Gautir D., Lis D. C., Young K., Kn J., Phillips T., Own T., Crovisir J., Goldsmith P. F., Brgin E. A., Dspois D., Woottn A., 1998, Icarus, 133, 147
10 K. d Souza Torrs and O. C. Wintr Tabl 3. Data of survivors in HZ, with th prcntag of comtary watr to rach th D/H ratio of Earth s watr. a Body Σ 1 Sim a f f Mass(M ) %M Ast Watr(O ) %W Ast % W Comt EM53 6 a 1.2422 0.2820 238 0 0.2882 0 44 EM37 6 b 1.1913 311 0.5912 0 6.3856 0 44 EM49 6 c 1.2701 631 0.6215 3.24 9.9944 50 15 EM33 8 a 1.4725 0.1197 0.1880 0 2.8452 0 44 EM41 8 b 1.1374 728 0.7135 4.23 12.4690 56 9 EM36 8 c 1.4107 438 0.5891 0 8.7073 0 44 EM49 10 a 1.4076 783 0.8598 4.68 15.0827 60 5 EM42 10 b 1.406 279 1.2126 3.32 25.4522 43 21 EM44 10 c 1.2858 608 1.2604 3.19 2153 50 15 a Columns ar: mbryo nam, surfac dnsity, simulation numbr, final smi-major axis, ccntricity, mass, prcntag of astroidal mass, watr, prcntag of astroidal watr and prcntag of comtary watr to rach VSMOW. Boss A. P., 1998, Annual Rviw of Earth and Plantary Scincs, 26, 53 Campins H., Swindl T. D., Kring D. A., 2004, J. Sckbach (d.) Origin, Evolution and Biodivrsity of Microbial Lif in th Univrs, p. 569 Chambrs J. E., 1999, MNRAS, 304, 793 Chambrs J. E., 2001, Icarus, 152, 205 Chaussidon M., 2007, Formation of th Solar Systm: a Chronology Basd on Mtorits. Lcturs in Astrobiology, p. 45 Dauphas N., Robrt F., Marty B., 2000, Icarus, 148, 508 Dloul E., Robrt F., Doukhan J. C., 1998, GCA, 62, 3367 Drak M. J., Campins H., 2006, in Danila L., Sylvio Frraz M., Angl F. J., ds, Astroids, Comts, Mtors Vol. 229 of IAU Symposium, Origin of watr on th trrstial plants. pp 381 394 Drak M. J., Rightr K., 2002, Natur, 416, 39 Drouart A., Dubrull B., Gautir D., Robrt F., 1999, Icarus, 140, 129 Ebrhardt P., Rbr M., Krankowsky D., Hodgs R. R., 1995, AAP, 302, 301 Encrnaz T., 2006, Sarching for Watr in th Univrs. Sarching for Watr in th Univrs, by T. Encrnaz. ISBN 978-0-387-34174-3. Brlin: Springr, 2006. Gnda H., Ikoma M., 2007, ArXiv -prints, accptd to Icarus (6 Sp 2007), 709 Goms R., Lvison H. F., Tsiganis K., Morbidlli A., 2005, Natur, 435, 466 Haghighipour N., Raymond S. N., 2007, Th Astrophysical Journal, 666, 436 Hrsant F., Gautir D., Huré J.-M., 2001, Th Astrophysical Journal, 554, 391 Hornr J., Mousis O., Hrsant F., 2007, Earth Moon and Plants, 100, 43 Ipatov S. I., Mathr J. C., 2006, in Europan Plantary Scinc Congrss 2006 Migration of Intrplantary Dust and Comts. p. 197 Jssbrgr E. K., Kissl J., Rah J., 1989, Th composition of comts. Origin and Evolution of Plantary and Satllit Atmosphrs, pp 167 191 Kokubo E., Ida S., 2000, Icarus, 143, 15 Lcuyr C., Gillt P., Robrt F., 1998, Chm. Gol., 145, 249 Lllouch E., Bézard B., Foucht T., Fuchtgrubr H., Encrnaz T., d Graauw T., 2001, AAP, 370, 610 Lunin J. I., 2006, Origin of Watr Ic in th Solar Systm. Mtorits and th Early Solar Systm II, pp 309 319 Lunin J. I., Chambrs J., Morbidlli A., Lshin L. A., 2003, Icarus, 165, 1 Mch K. J., 2007, in Amrican Astronomical Socity Mting Abstracts Vol. 210 of Amrican Astronomical Socity Mting Abstracts, Watr in Habitabl Worlds: An Ovrviw. p. 71 Mir R., Own T. C., Jwitt D. C., Matthws H. E., Snay M., Bivr N., Bockl-Morvan D., Crovisir J., Gautir D., 1998, Scinc, 279, 1707 Morbidlli A., Chambrs J., Lunin J. I., Ptit J. M., Robrt F., Valscchi G. B., Cyr K. E., 2000, Mtoritics and Plantary Scinc, 35, 1309 Mousis O., Gautir D., Bocklé-Morvan D., Robrt F., Dubrull B., Drouart A., 2000, Icarus, 148, 513 O Brin D. P., Morbidlli A., Lvison H. F., 2006, Icarus, 184, 39 Own T. C., Bar-Nun A., 2000, Volatil Contributions from Icy Plantsimals. Origin of th arth and moon, ditd by R.M. Canup and K. Rightr and 69 collaborating authors. Tucson: Univrsity of Arizona Prss., p.459-471, pp 459 471 Own T. C., Bar-Nun A., 2001, Origins of Lif and Evolution of th Biosphr, 31, 435 Raymond S. N., Quinn T., Lunin J. I., 2004, Icarus, 168, 1 Raymond S. N., Quinn T., Lunin J. I., 2005, Icarus, 177, 256 Raymond S. N., Quinn T., Lunin J. I., 2007, Astrobiology, 7, 66 Rightr K., Drak M. J., Scott E. R. D., 2006, Compositional Rlationships Btwn Mtorits and Trrstrial Plants. Mtorits and th Early Solar Systm II, pp 803 828 Schmidt B. E., Brown R. H., Laurtta D. S., 2005 Comts: Nw Viws on th D-H Story. p. A102 Stimpfl M., Laurtta D. S., Drak M. J., 2004, Mtoritics amp Plantary Scinc, vol. 39, Supplmnt. Procdings of th 67th Annual Mting of th Mtoritical Socity, August 2-6, 2004, Rio d Janiro, Brazil, abstract no.5218,
39, 5218 Swindl T. D., Kring D. A., 2001, in Elvnth Annual V. M. Goldschmidt Confrnc Implications of Nobl Gas Budgts for th Origin of Watr on Earth and Mars. p. 3785 Wirich J. R., Brown R. H., Laurtta D. S., 2004, in Bulltin of th Amrican Astronomical Socity Vol. 36 of Bulltin of th Amrican Astronomical Socity, Comtary D/H Fractionation during Sublimation. p. 1143 Wthrill G. W., 1996, Icarus, 119, 219 Compound modl to xplain watr s origins of Earth-lik plants 11