Kazuyuki Omukai and Francesco Palla- Formation of the First Stars by Accretion

FORMATION OF THE FIRST STARS BY ACCRETION Kazuyuki Omukai 1 and Francesco Palla 2 Recei ved 2002November 19; acce pted2003 Febr uary7 ABSTRACT The process of star formation from metal-free gas is investigated by following the evolution of accreting pro tos tar s with emp has is on the pro perties of mas sive obj ect s. The mai n aim i s to establ ish the phy sical proc- esses that determine the upper mass limit of the first stars. Although the consensus is that massive stars were commonly formed in the first cosmic structures, our calculations show that their actual formation depends sensitivel y on the massaccr et ion rate and its time variation. Even in the ra ther idealized case in whichstarfor- mation is mainly determined by _ M M acc , the characteristic mass scale of the first stars is rather uncertain. We find that there is a critical mass accretion rate _ M M crit ’ 4 Â 10 À3 M yr À1 that separates solutions with _ M M acc < _ M M crit in which objects with mass 4100 M can form, provided there is sufficient matter in the parent clouds, from others ( _ M M acc > _ M M crit ) where the maximum mass limit decreases as _ M M acc increases. In the latter case, the pro tostel lar luminosit y reaches the Eddingto n limit bef ore theonset of hyd rog en burnin g at the cen- ter via the C N cycle. This phas e is follo wed b y a rapi d an d dr amat ic ex pansi on o f the radi us, poss ibly leadin g to reversal of the accretion flow when the stellar mass is about 100 M . Under a realistic time-dependent accretion rate that starts at high values ( $10 À2 M yr À1 ) and decreases rapidly in the high-mass regime (M Ã e90 M ), the evolution foll ows the cas e of _ M M acc < _ M M crit and accret ion can continue unimp eded by radiation forces. Thus, the maximum mass is set by consideration of stellar lifetimes rather than by protostellar evolution. In this case, the upper limit can be as high as $600 M . We consider also the sensitivity of the results to the presenc e of heavy elemen ts with abun dances in the range Z ¼ 5 Â 10 À5 to 5 Â 10 À3 Z . The main evolutionary features of protostars are similar to those of metal-free objects, except that the value of _ M M crit increases for metal-enriched protostars. Since the accretion rate is lower in a slightly polluted environ- ment, the condit ion _ M M acc < _ M M crit is ex pec te d to be more ea si ly met. We find that for me tall icit ies below $10 À2 Z , where radiation forces onto dust grains in the flow are negligible, a slightly metal-rich gas favors continued acc ret ion and theformation of ver y massiv e stars. Subject headings: cosmology : theor y — earl y unive rse — galaxies : forma tion — stars: formation 1. INTRODUCTION The problem of the characteristic mass of the first stars that formed in the universe is still largely unsolved. Recent theoretical and numerical studies are revealing in leaps and bounds the physical state of star-forming regions within the first cosmic structures. In the framework of cold dark matter cosmology, smaller objects tend to collapse earlier. In these models, a moderately rare object of $3 overdensity collapses and virializesat abo ut z $ 30.Howeve r, only suffi- cie ntl y mas siv e obj ect s can cool in a Hubble time and become luminous by forming stars. The minimum cooling mass at z $ 30 is M min $ 10 6 M and is a decreasing func- tion of the collapse redshif t (e.g. , Haiman, Thoul, & Loeb 1996; Tegmark et al. 1997; Fuller & Couchman 2000). After virialization, objects more massive than M min , called ‘‘ first objects,’’ can collapse gravitationally owing to molecular hyd rog en coolin g (e. g., Palla,Sal pet er, & Stahler 1983, her e- aft er PSS 83) and fra gment int o hig h-d ens ity clu mps . Accord ing to numeri cal studies, the mas s scale of these clumps is rather high, on the order of 10 3 M (Abel, Bryan, & Norman 2000, 2002; Bromm, Coppi, & Larson 1999, 2002; Tsuribe & Inutsuka 2001). However, the formation of fragments of lower mass, down to d1 M , is also possible (e.g., Yoshii & Saio 1986; Uehara et al. 1996; Nakamura & Umemura 199 9, 200 1, 200 2; Ueh ara & Inuts uka 200 0; Omukai 2001). Indeed, the recent discovery of HE 0107À 5240, a star of 0.8 M in the galactic halo with virtually no metals (½Fe=H ¼À5:3), attests to the ability of very metal- poor gas clouds to give birth to low-mass stars (Christ lieb et al . 20 02). Afte r frag menta tion, the evolu tion of gravi tati onally unstable clumps proceeds in a highly nonhomologous fash- ion, with the central parts collapsing first. This runaway phase is induced by cooling provided by H 2 line radiation at densities nd10 14 cm À3 , and by H 2 collision-induced emis- sion at higher densities. The resulting gas temperature is nearly constant at several 10 2 K, and the innermost region of $1 M becomes fully molecular owing to the three-body reaction (PSS83). At densities n $ 10 16 cm À3 , the cloud becomes optically thick to collision-induced absorption and H 2 dissociation works as an effective cooling agent. Finally, witho ut furt her cooli ng mecha nism, at n ’ 10 22 cm À3 , a sma ll hyd ros tatic cor e of mass $10 À3 M is for med (Omukai & Nishi 1998), similar to the conditions found in studies of the collapse of clouds of standard solar composi- tion, i.e., the stellar (or second) core according to Larson (1969). In the pri mor dia l clouds des cri bed by the numeri calsimu- lat ion s, the outco me of the runaway col lap se is a tin y ($10 À3 M ) protostar, surrounded by a large amount of res erv oir gas ($10 3 M ). As a re sult , the pr ot os tar can gr ow by several orders of magnitude in mass by accreting the envelo pe matt er. Th e mass accreti on rate onto the protostar is determined by the radial density distribution at the time 1 Div isi on of The ore tical Ast rophysics , Nat ion al Ast ron omica l Observator y, Mitaka, Tokyo 181-8588, Japan; omukai@th .nao.ac.jp. 2 INAF–Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Florence, Italy; [email protected]. The Astrophys ical Journal, 589 :677 –687,2003June 1 #2003.The Ameri can Astrono micalSociety . All rightsreserved.Printedin U.S.A. 677

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Kazuyuki Omukai and Francesco Palla- Formation of the First Stars by Accretion