Protostar Formation in the Early Universe
aa r X i v : . [ a s t r o - ph ] A ug Protostar Formation in the Early Universe
Naoki Yoshida, Kazuyuki Omukai, Lars Hernquist Department of Physics, Nagoya University, Furocho, Chikusa, Nagoya, Aichi 464-8602, Japan National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan Harvard-Smithsonian Center for Astrophysics,60 Garden Street, Cambridge, MA02138 ∗ To whom correspondence should be addressed; E-mail: [email protected].
Science, 321, 669 (2008)The nature of the first generation of stars in the Universe remainslargely unknown. Observations imply the existence of massive pri-mordial stars early in the history of the universe, and the standardtheory for the growth of cosmic structure predicts that structuresgrow hierarchically through gravitational instability. We have devel-oped an ab initio computer simulation of the formation of primordialstars that follows the relevant atomic and molecular processes ina primordial gas in an expanding universe. The results show thatprimeval density fluctuations left over from the Big Bang can drivethe formation of a tiny protostar with a mass of just one percent thatof the Sun. The protostar is a seed for the subsequent formation ofa massive primordial star.
Large ground-based telescopes have discovered distant astronomical objects such asgalaxies and quasars (
1, 2 ) that were in place when the Universe was less than 1 billion1ears old, or about 5% of its current age. Moreover, these studies have shown thatother luminous objects must have been present even earlier. For example, the mostdistant known quasar, SDSS-J1148, contains substantial amounts of heavy elements suchas carbon, oxygen, and iron as well as dust grains ( ). These heavy elements are not ofcosmic origin, but must have been formed earlier in massive stars before being expelled bysupernovae and stellar winds, and then incorporated into the material that later condensedto produce this quasar.Recently, stars with extremely low heavy element content were discovered in the haloof our Galaxy (
4, 5 ). The observed elemental abundance patterns indicate several possi-bilities for the nature of their ancestors (
6, 7 ). One interesting scenario is that supernovaexplosions of massive primordial stars enriched the parent gas clouds, from which thesehalo stars were born.Theoretical analyses hold promise for revealing the process of primordial star forma-tion for two main reasons: (i) the initial conditions, as determined cosmologically, arewell-established, so that statistically equivalent realizations of a standard model universecan be accurately generated, and (ii) the important basic physics such as gravitation,hydrodynamics, and atomic and molecular processes in a hydrogen-helium gas are un-derstood. Other complications that plague investigations of star formation in the localUniverse, such as the presence of strong magnetic fields or heavy elements, can be ne-glected at these early times.Here, we report super-computer simulations of the development of cosmic structurein the early Universe and the formation of primordial stars. Our simulations achieve adynamic range in spatial scale of ∼ , resolving small-scale structures having sizes of afraction of a solar radius ( ∼ cm) within cosmological volumes hundreds of kiloparsecsin length ( ∼ cm). The smallest length scale, the so-called local Jeans length set by the2ction of gravity and hydrodynamic pressure, is fully resolved throughout the simulationvolume at all times.We do not assume any a priori equation of state for the gas. The thermal and chem-ical evolution of the gas is determined fully by molecular and atomic processes, whichare treated in a direct, self-consistent manner. The spatial resolution and the accurateimplementations of the physical processes allow us to follow the collapse of a gas to stellardensities, and thus our calculations offer a detailed picture of how the first cosmologicalobjects – primordial protostars – form from chemically pristine gas.We set up cosmological initial conditions such that the statistical properties of thedensity and velocity fields are matched to those given by the standard model of theUniverse ( ), according to which the energy density is dominated by dark energy and colddark matter. We follow the gravitational collapse of dark matter and the hydrodynamicsof primordial gas through simulations of cosmic structure formation. Below, we providedetails on one simulation, which followed the evolution of dark matter and gas in a cube200 comoving kiloparsecs on a side. We focus our attention on a gravitationally bounddark matter halo which formed in this volume at an epoch when the cosmological redshiftwas z = 14 (Fig. 1). The mass of this halo, a half million solar masses, and the physicalconditions within it are particularly conducive for it to host a primordial star (
9, 10, 11 ).The gas within this halo had a temperature of ∼ ∼ − in number fraction) had already formed, enabling efficient radiativecooling.Through the action of radiative cooling, a star-forming gas cloud collected in the hostdark halo. We tracked the subsequent thermal and chemical evolution of the primordialgas cloud for more than 20 decades in density up to the epoch of protostar formation.We accounted for: (i) the chemistry at both low and high densities, including molecular3ydrogen formation, (ii) transfer of molecular line photons and accompanying radiativecooling, (iii) transfer of collisionally-induced continuum radiation and resulting radiativecooling. In the final phase of the collapse, the temperature increased adiabatically as aresult of the absence of radiative and chemical cooling. This continued until the con-traction of the central part was halted by strong thermal pressure. At this time, stronghydrodynamic shocks formed, marking the moment of the formation of a protostar. Wecould not follow the evolution after this epoch accurately without implementing radiativeeffects from the post-shock high temperature gases, and thus we stopped the simulationat this point.The structure in and around the newly formed protostar wass rather complex (Fig. 1D). At this time, there were substantial variations in density and temperature even in theinnermost 10 solar-radii region. Clearly, the primordial protostar was not simply a spheresurrounded by a single accretion shock.The cloud evolution was dictated by several important physical processes: First, a fullymolecular cloud with mass ∼ M ⊙ formed ( ) when the gas density was sufficientlyhigh ( > cm − ) that three-body chemical reactions converted nearly all the hydrogeninto molecules. Efficient cooling by rovibrational transitions of hydrogen molecules causedthe first small dip at a radius of R ∼ cm in the radial temperature profile (Fig. 2).When the dense, molecular part contracted further, it became optically thick to hydrogenmolecular rovibrational lines, and then the efficiency of radiative cooling saturated (dot-dashed lines in Fig. 2). At still higher densities, frequent collisions between hydrogenmolecules led to efficient emission of continuum radiation via collision-induced emission.By this rapid cooling occurring at densities greater than ∼ cm − , a small central partwith ∼ . M ⊙ cooled efficiently to form a flattened disk-like structure. In the flattenedgas cloud, radiation escaped preferentially in the direction where contraction was fastest,4ecause the velocity gradient was large and also the continuum optical depth was smallin this direction [supporting online material (SOM) text and Fig. S1, S2]. This combinedeffect of gravitational contraction and direction-dependent radiative cooling acceleratedthe deformation of the cloud core to a disk structure. The disk structure had a radius of ∼ cm and a mass of ∼ . M ⊙ , where the cooling time and the local dynamical timeare comparable. While the innermost portion further contracted slowly, spiral densitywaves were excited, yielding two arms (see the bottom-right panel of Fig. 1).When the central density reached n ∼ cm − , the gas became completely opticallythick to continuum radiation, and at this point radiative cooling no longer operatedefficiently (long dashed lines in Fig. 2). Further collapse and the associated dynamicalheating triggered full-scale dissociation of hydrogen molecules in the central part (seealso Fig. 3). After most of the hydrogen molecules were collisionally dissociated, the gascould not lose its thermal energy either radiatively or by dissociating molecules. Theresulting effective equation of state became progressively more stiff, making the gas cloudresist gravitational deformation and fragmentation (
14, 15 ). The gas then contractedadiabatically, and its temperature quickly increased above several thousand Kelvin, whilethe density exceeded n ∼ cm − . The strong thermal pressure finally stopped thegravitational collapse and hydrodynamic shocks were generated (solid lines in Fig. 2). Wedefine a constant density, atomic gas core as a protostar that is pressure-supported. Atthe final output time, a protostar formed with a mass of just 0.01 solar masses. It hadan initial radius of ∼ × cm, similar to that of present-day protostars in theoreticalcalculations ( ). The central particle number density of the protostar was ∼ cm − and the temperature was well above 10,000 K.At the time of protostar formation, the central temperature was so high that almost allthe molecules were collisionally dissociated within an enclosed mass of 0.01 M ⊙ (Fig. 3).5 slight degree of ionization was also seen in the innermost high-pressure part of theatomic core. There was a small variation in the atomic hydrogen fraction at ∼ . M ⊙ ; asmall fraction of hydrogen molecules were dissociated when the gas temperature reached ∼
12, 17 ), but the molecular fraction increased again when the density increasedand efficient continuum cooling brought the gas temperature temporarily below 2000 K(see the second temperature dip at R ∼ cm in Fig. 2).The protostar accretes the ambient gas in a complicated way (Fig. 3 bottom). In thedirection vertical to the disk plane, gas falling in at a velocity exceeding 10 km/sec wassuddenly stopped at the location of a shock at M enclosed ∼ . M ⊙ . Fig. 3 also showsthe degree of rotational support of the gas, defined as f rot = ( L/r ) /v Kep , where L is thespecific angular momentum of the gas within radius r , and v Kep is the Keplerian velocityat that radius.Within a mass of ∼ . M ⊙ , two spiral arms rotated rapidly, and the outer part( ∼ . − . M ⊙ ) appeared nearly centrifugally supported, whereas the central part hadgravitationally collapsed. The central core lost part of its angular momentum via grav-itational torques exerted by non-axisymmetric perturbations. The newly-born protostarwas supported by both thermal pressure and rotation. The overall velocity structure ischaracteristic of a collapsing gas with an initially slow rotation, as reported in previousstudies of both present-day and primordial star-formation (
18, 19 ).A long-standing question is whether a primordial gas cloud such as that studied hereexperiences vigorous fragmentation by thermal instability during its evolution. In oursimulation, a single small proto-stellar core formed first and the central part did notfragment into multiple objects before protostar formation. At all phases, the locallyestimated growth time for isobaric perturbations was longer than, or only comparable to,the local dynamical time for collapse. Hence, the cloud core did not fragment by thermal6nstability, but instead its collapse accelerated.It has been suggested that the central part of primordial gas clouds may break up intosmaller clumps later during the subsequent accretion phase (
20, 19 ). We have examineda core fragmentation model of ( ) by measuring Ω t dyn where Ω is the mean angularvelocity and t dyn = 1 / √ πGρ is the local dynamical time. The central ∼ . M ⊙ portionhad a value of Ω t dyn = 0 .
25, which is large and close to the critical value for fragmentation.Thus the formation of multiple stellar systems may be possible, although not very likely,during later accretion phases.The instantaneous gas mass accretion rate at the time of protostar formation was aslarge as 0.01-0.1 solar masses per year within the innermost 10 M ⊙ . If the gas in theinner portion accreted efficiently, the protostar would quickly grow to be as massive as10 solar masses within a thousand years ( ). Even if multiple stellar seeds formed, therewould be at least one main accreting protostar. A detailed proto-stellar calculation for asimilarly large accretion rate predicts that the mass of the star when it lands on the mainsequence will be ∼ M ⊙ (
22, 13 ).Feedback effects, in particular those from ionizing photons emitted by the protostar,work to evaporate the surrounding gas and to halt gas accretion. A semi-analytic cal-culation including this radiative feedback and the effect of rotation shows that the finalstellar mass can still be greater than a few tens of solar masses in a reasonable parameterspace of the model ( ). If instead mass accretion is unimpeded throughout the star’sevolution, the final stellar mass can be very large, possibly exceeding a few hundred solarmasses (
22, 21 ). Such very massive stars ionize a large volume of the surrounding gas.Because of the different thermal evolution of an initially ionized gas ( ), second gener-ation primordial stars formed under such conditions are predicted to be several tens ofsolar masses (
25, 26 ). Therefore, in either case, our model provides a viable scenario for7he early chemical enrichment in the Universe by massive primordial stars ( ), which isnecessary for the formation of later populations of ordinary stars.The basic properties of the particular star-forming cloud we simulate, such as physicalsize and mass, are characteristic for cosmological primordial gas clouds, and the objectis indeed similar in many aspects to those found in previous works (
10, 11, 27 ). The finalevolution of the central high-density part will likely be affected by its angular momentumcontent ( ). However, because the bulk of the cloud core is assembled from material withlow angular momentum ( ), it generally has a slow initial spin, and thus the evolutionof prestellar gas is expected to be similar to what is presented here. Our simulationthus offers a complete picture of how a primordial protostar may have formed from tinycosmological density fluctuations. Primordial star formation for different cosmologicalmodels has been explored ( ). The particle properties of dark matter may be anotherimportant factor in star-formation in the early universe. References and Notes
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00 parsec 5 parsec10 astronomical unit25 solar−radii(A) cosmological halo (B) star−forming cloud(C) fully molecular part(D) new−born protostar
Fig. 1: Projected gas distribution around the protostar. Shown regions are, from top-left,clockwise, (A) the large-scale gas distribution around the cosmological halo (300 pc on aside), (B) a self-gravitating, star-forming cloud (5 pc on a side), (C) the central part ofthe fully molecular core (10 astronomical units on a side), and (D) the final protostar (25solar-radii on a side). We use the density-weighted temperature to color (D), to show thecomplex structure of the protostar. 11 R [cm]10 nu m be r den s i t y [ c m - ] R [cm]100100010000 t e m pe r a t u r e [ K ] Fig. 2: Evolution of spherically-averaged radial density profile (top) and temperatureprofile (bottom) around the protostar. Epochs are shown when the central core becameoptically thick to molecular lines (dot-dashed lines), when cooling by collision-inducedemission kicked-in (short dashed lines), when the core became optically thick to contin-uum (long dashed lines), and when full-scale dissociation was completed and a pressure-supported core formed (solid lines). 12 enc /M O • )0.00010.00100.01000.10001.0000 s pe c i e s f r a c t i on HII HIH2 -4 -3 -2 -1 0 1 2 log(M enc /M O • )-5051015 i n f a ll v e l o c i t y [ k m / s e c ] r o t a t i on s uppo r t f rot V vertical V mid planemid plane