The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai (2000), updated to include deuterium chemistry and the effects of cosmic microwave background (CMB) radiation. HD-line cooling dominates the thermal balance of clouds when Z ∼ 10 −5 − 10 −3 Z ⊙ and density ≈ 10 5 cm −3 . Early on, CMB radiation prevents the gas temperature to fall below T CM B , although this hardly alters the cloud thermal evolution in low-metallicity gas. From the derived temperature evolution, we assess cloud/core fragmentation as a function of metallicity from linear perturbation theory, which requires that the core elongation E ≡ (b − a)/a > E NL ∼ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at E = E NL . Given these assumptions and the initial (gaussian) distribution of E we compute the fragment mass distribution as a function of metallicity. We find that: (i) For Z = 0, all fragments are very massive, 10 3 M ⊙ , consistently with previous studies; (ii) for Z > 10 −6 Z ⊙ a few clumps go through an additional high density ( 10 10 cm −3 ) fragmentation phase driven by dustcooling, leading to low-mass fragments; (iii) The mass fraction in low-mass fragments is initially very small, but at Z ∼ 10 −5 Z ⊙ it becomes dominant and continues to grow as Z is increased; (iv) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0.01 < Z/Z ⊙ < 0.1. (v) For 0.1Z ⊙ , the two peaks merge into a singly-peaked mass function which might be regarded as the precursor of the ordinary Salpeter-like IMF.

Primordial stars are formed from a chemically pristine gas consisting of hydrogen and helium. They are believed to have been born at some early epoch in the history of the Universe and to have enriched the interstellar medium with synthesized heavy elements before the emergence of ordinary stellar populations. We study the formation of the first generation of stars in the standard cold dark matter model. We follow the gravitational collapse and thermal evolution of primordial gas clouds within early cosmic structures using very high-resolution, cosmological hydrodynamic simulations. Our simulation achieves a dynamic range of ∼ 10 10 in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to ρ ∼ 2 × 10 −8 g cm −3 (n H ∼ 10 16 cm −3 ) without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. We implement an extensive chemistry network for hydrogen, helium and deuterium. All the relevant atomic and molecular cooling and heating processes, including cooling by collision-induced continuum emission, are implemented. For calculating optically thick H 2 cooling at high densities, we use the Sobolev method (Sobolev 1960) and evaluate the molecular line opacities for a few hundred lines. We validate the accuracy of the method by performing a spherical collapse test and comparing the results with those of accurate one-dimensional calculations that treat the line radiative transfer problem in a fully self-consistent manner.We then perform a cosmological simulation adopting the standard ΛCDM model. Dense gas clumps are formed at the centers of low mass (∼ 10 5−6 M ⊙ ) dark matter halos at redshifts z ∼ 20, and they collapse gravitationally when the cloud mass exceeds a few hundred solar masses. To examine possible gas fragmentation owing to thermal instability, we compute explicitly the growth rate of isobaric perturbations. We show that the cloud core does not fragment in either the low-density (n H ∼ 10 10 cm −3 ) or high-density (∼ 10 15 cm −3 ) regimes, where gas cooling rate is increased owing to three-body molecule formation and collision-induced emission, respectively. The cloud core becomes marginally unstable against chemo-thermal instability in the low-density regime. However, since the core is already compact at that point and correspondingly the sound-crossing time as well as the free-fall time are short, or comparable to the perturbation growth timescale, it does not fragment. Run-away cooling simply leads to fast condensation of the core to form a single proto-stellar seed. We also show that the core remains stable against gravitational deformation and fragmentation throughout the evolution. We trace in Lagrangian space the gas elements that end up at the center of the cloud, and study the evolution of the specific angular momentum. We show that, during the final dynamical collapse, small angular momentum material collapses faster...

We perform a large set of radiation hydrodynamics simulations of primordial star formation in a fully cosmological context. a Our statistical sample of 100 First Stars show that the first generation of stars have a wide mass distribution M popIII = 10 ∼ 1000 M ⊙ . We first run cosmological simulations to generate a set of primordial star-forming gas clouds. We then follow protostar formation in each gas cloud and the subsequent protostellar evolution until the gas mass accretion onto the protostar is halted by stellar radiative feedback. The accretion rates differ significantly among the primordial gas clouds which largely determine the final stellar masses. For low accretion rates the growth of a protostar is self-regulated by radiative feedback effects and the final mass is limited to several tens of solar masses. At high accretion rates the protostar's outer envelope continues to expand and the effective surface temperature remains low; such protostars do not exert strong radiative feedback and can grow in excess to one hundred solar masses. The obtained wide mass range suggests that the first stars play a variety of roles in the early universe, by triggering both core-collapse supernovae and pair-instability supernovae as well as by leaving stellar mass black holes. We find certain correlations between the final stellar mass and the physical properties of the star-forming cloud. These correlations can be used to estimate the mass of the first star from the properties of the parent cloud or of the host halo, without following the detailed protostellar evolution.

Formation of massive stars by accretion requires a high accretion rate ofṀ * > 10 −4 M ⊙ /yr to overcome the radiation pressure barrier of the forming stars. Here, we study evolution of protostars accreting at such high rates, by solving the structure of the central star and the inner accreting envelope simultaneously. The protostellar evolution is followed starting from small initial cores until their arrival at the stage of the Zero-Age Main Sequence (ZAMS) stars. An emphasis is put on evolutionary features different from those with a low accretion rate ofṀ * ∼ 10 −5 M ⊙ /yr, which is presumed in the standard scenario for low-mass star formation. With the high accretion rate ofṀ * ∼ 10 −3 M ⊙ /yr, the protostellar radius becomes very large and exceeds 100 R ⊙ . Unlike the cases of low accretion rates, deuterium burning hardly affects the evolution, and the protostar remains radiative even after its ignition. It is not until the stellar mass reaches ≃ 40 M ⊙ that hydrogen burning begins and the protostar reaches the ZAMS phase, and this ZAMS arrival mass increases with the accretion rate. These features are similar to those of the first star formation in the universe, where high accretion rates are also expected, rather than to the present-day low-mass star formation. At a very high accretion rate of > 3 × 10 −3 M ⊙ /yr, the total luminosity of the protostar becomes so high that the resultant radiation pressure inhibits the growth of the protostars under steady accretion before reaching the ZAMS stage. Therefore, the evolution under the critical accretion rate 3 × 10 −3 M ⊙ /yr gives the upper mass limit of possible pre-main-sequence stars at ≃ 60 M ⊙ . The upper mass limit of MS stars is also set by the radiation pressure onto the dusty envelope under the same accretion rate at ≃ 250 M ⊙ . We also propose that the central source enshrouded in the Orion KL/BN nebula has effective temperature and luminosity consistent with our model, and is a possible candidate for such protostars growing under the high accretion rate.

Recent studies suggest that the initial mass function (IMF) of the first stars (Population III) is likely to have been extremely top-heavy, unlike what is observed at present. We propose a scenario to generate fragmentation to lower masses once the first massive stars have formed and derive constraints on the primordial IMF. We estimate the mass fraction of pair-unstable supernovae (SN ), shown to be the dominant sources of the first heavy elements. These metals enrich the surrounding gas up to %10 À4 Z , when a transition to efficient cooling-driven fragmentation producing d1 M clumps occurs. We argue that the remaining fraction of the first stars ends up in %100 M VMBHs (very massive black holes). If we further assume that all these VMBHs are likely to end up in the centers of galactic nuclei constituting the observed supermassive black holes (SMBHs), then %6% of the first stars contributed to the initial metal enrichment and the IMF remained topheavy down to a redshift z % 18:5%. Interestingly, this is the epoch at which the cool metals detected in the Ly forest at z % 3 must have been ejected from galaxies. At the other extreme, if none of these VMBHs has as yet ended up in SMBHs, we expect them to be either (1) en route toward galactic nuclei, thereby accounting for the X-ray-bright off-center sources detected locally by ROSAT, or (2) the dark matter candidate composing the entire baryonic halos of galaxies. For case 1 we expect all but a negligible fraction of the primordial stars to produce metals, causing the transition at the maximum possible redshift of e22.1, and for case 2, $3 Â 10 5 , a very negligible fraction of the initial stars produce the metals and the transition redshift occurs at z f e5:4. In this paper, we present a framework (albeit one that is not stringently constrained at present) that relates the first episode of star formation to the fate of their remnants at late times. Clearly, further progress in understanding the formation and fragmentation of Population III stars within the cosmological context will provide tighter constraints in the future. We conclude with a discussion of several hitherto unexplored implications of a high-mass-dominated star formation mode in the early universe.