Kazuyuki Omukai

First Stars, Very Massive Black Holes, and Metals

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 ?10-4 Z?, when a transition to efficient cooling-driven fragmentation producing 1 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 top-heavy 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 22.1, and for case 2, ~3 ? 105, a very negligible fraction of the initial stars produce the metals and the transition redshift occurs at zf 5.4. 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.

Formation of Primordial Stars in a ΛCDM Universe

We study the formation of the first generation of stars in the standard cold dark matter model. We use a very high resolution cosmological hydrodynamic simulation that achieves a dynamic range of ~1010 in length scale. With accurate treatment of atomic and molecular physics, including the effect of molecular line opacities and cooling by collision-induced continuum emission, it allows us to study the chemothermal evolution of primordial gas clouds to densities up to ρ ~ 2 × 10-8 g cm-3 (nH ~ 1016 cm-3) without assuming any a priori equation of state, an improvement of 6 orders of magnitude over previous three-dimensional calculations. We study the evolution of a primordial star-forming gas cloud in the cosmological simulation in detail. The cloud core becomes marginally unstable against chemothermal instability when the gas cooling rate is increased owing to three-body molecule formation. However, since the core is already compact at that point, runaway cooling simply leads to fast condensation to form a single protostellar seed. During the final dynamical collapse, small angular momentum material collapses faster than the rest of the gas and selectively sinks inward. Consequently, the central regions have little specific angular momentum, and rotation does not halt collapse. We, for the first time, obtain an accurate gas mass accretion rate within a 10 M☉ innermost region around the protostar. We carry out protostellar evolution calculations using the obtained accretion rate. The resulting mass of the first star when it reaches the zero-age main sequence is MZAMS ~ 100 M☉, and less (60 M☉) for substantially reduced accretion rates.

Thermal and Fragmentation Properties of Star-forming Clouds in Low-Metallicity Environments

The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai, 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 to 10-3 Z☉ and density ≈105 cm-3. Early on, CMB radiation prevents the gas temperature from falling below TCMB, 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 ≡ (b - a)/a > NL ~ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at = NL. Given these assumptions and the initial (Gaussian) distribution of , we compute the fragment mass distribution as a function of metallicity. We find that (1) for Z = 0, all fragments are very massive, 103 M☉, consistent with previous studies; (2) for Z > 10-6 Z☉ a few clumps go through an additional high-density (1010 cm-3) fragmentation phase driven by dust cooling, leading to low-mass fragments; (3) 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; (4) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0.01 < Z/Z☉ < 0.1; and (5) for 0.1 Z☉, the two peaks merge into a single-peaked mass function, which might be regarded as the precursor of the ordinary Salpeter-like initial mass function.

FORMATION OF THE FIRST STARS BY ACCRETION

The process of star formation from metal-free gas is investigated by following the evolution of accreting protostars with emphasis on the properties of massive objects. The main aim is to establish the physical processes 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 sensitively on the mass accretion rate and its time variation. Even in the rather idealized case in which star formation is mainly determined by acc, the characteristic mass scale of the first stars is rather uncertain. We find that there is a critical mass accretion rate crit 4 × 10-3 M☉ yr-1 that separates solutions with acc crit) where the maximum mass limit decreases as acc increases. In the latter case, the protostellar luminosity reaches the Eddington limit before the onset of hydrogen burning at the center via the CN cycle. This phase is followed by a rapid and dramatic expansion of the radius, possibly leading 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 (~10-2 M☉ yr-1) and decreases rapidly in the high-mass regime (M* 90 M☉), the evolution follows the case of acc < crit and accretion can continue unimpeded 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 presence of heavy elements with abundances in the range Z = 5 × 10-5 to 5 × 10-3 Z☉. The main evolutionary features of protostars are similar to those of metal-free objects, except that the value of crit increases for metal-enriched protostars. Since the accretion rate is lower in a slightly polluted environment, the condition acc < crit is expected to be more easily met. We find that for metallicities below ~10-2 Z☉, where radiation forces onto dust grains in the flow are negligible, a slightly metal-rich gas favors continued accretion and the formation of very massive stars.The process of star formation from metal-free gas is investigated by following the evolution of accreting protostars with emphasis on the properties of massive objects. The main aim is to establish the physical processes 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 sensitively on the mass accretion rate and its time variation. Even in the rather idealized case in which star formation is mainly determined by dot{M}acc, the characteristic mass scale of the first stars is rather uncertain. We find that there is a critical mass accretion rate dot{M}crit = 4 10^{-3} Msun/yr that separates solutions with dot{M}acc>100 Msun can form, provided there is sufficient matter in the parent clouds, from others (dot{M}acc>dot{M}crit) where the maximum mass limit decreases as dot{M}acc increases. In the latter case, the protostellar luminosity reaches the Eddington limit before the onset of hydrogen burning at the center via the CN-cycle. This phase is followed by a rapid and dramatic expansion of the radius, possibly leading to reversal of the accretion flow when the stellar mass is about 100Msun. (abridged)

Protostar Formation in the Early Universe

The nature of the first generation of stars in the universe remains largely unknown. Observations imply the existence of massive primordial stars early in the history of the universe, and the standard theory for the growth of cosmic structure predicts that structures grow hierarchically through gravitational instability. We have developed an ab initio computer simulation of the formation of primordial stars that follows the relevant atomic and molecular processes in a primordial gas in an expanding universe. The results show that primeval density fluctuations left over from the Big Bang can drive the formation of a tiny protostar with a mass 1% that of the Sun. The protostar is a seed for the subsequent formation of a massive primordial star.

Protostellar Feedback Halts the Growth of the First Stars in the Universe

Simulations suggest that most of the first stars in the universe might have been less massive than previously thought. The first stars fundamentally transformed the early universe by emitting the first light and by producing the first heavy elements. These effects were predetermined by the mass distribution of the first stars, which is thought to have been fixed by a complex interplay of gas accretion and protostellar radiation. We performed radiation-hydrodynamics simulations that followed the growth of a primordial protostar through to the early stages as a star with thermonuclear burning. The circumstellar accretion disk was evaporated by ultraviolet radiation from the star when its mass was 43 times that of the Sun. Such massive primordial stars, in contrast to the often-postulated extremely massive stars, may help explain the fact that there are no signatures of the pair-instability supernovae in abundance patterns of metal-poor stars in our galaxy.

One Hundred First Stars : Protostellar Evolution and the Final Masses

We perform a large set of radiation hydrodynamic simulations of primordial star formation in a fully cosmological context. Our statistical sample of 100 First Stars shows that the first generation of stars has 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 that 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 protostars 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 of 100 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.

Protostellar Collapse with Various Metallicities

The thermal and chemical evolution of gravitationally collapsing protostellar clouds is investigated, focusing attention on their dependence on metallicity. Calculations are carried out for a range of metallicities spanning the local interstellar value to zero. During the time when clouds are transparent to continuous radiation, the temperatures are higher for those with lower metallicity, reflecting lower radiative ability. However, once the clouds become opaque, in the course of the adiabatic contraction of the transient cores, their evolutionary trajectories in the density-temperature plane converge to a unique curve that is determined by only physical constants. The trajectories coincide with each other thereafter. Consequently, the size of the stellar core at the formation is the same regardless of the gas composition of the parent cloud.

Formation of Primordial Protostars

The evolution of collapsing metal-free protostellar clouds is investigated for various masses and initial conditions. We perform hydrodynamical calculations for spherically symmetric clouds, taking into account radiative transfer of the molecular hydrogen lines and the continuum as well as the chemistry of molecular hydrogen. The collapse is found to proceed almost self-similarly, like the Larson-Penston similarity solution. In the course of the collapse, efficient three-body processes transform atomic hydrogen in an inner region of ~1 M☉ entirely into molecular form. However, hydrogen in the outer part remains totally atomic, although there is an intervening transitional layer of several solar masses, where hydrogen is in partially molecular form. No opaque transient core is formed, although clouds become optically thick to H2 collision-induced absorption continuum, since H2 dissociation follows successively. When the central part of the cloud reaches stellar densities (~10-2 g cm-3), a very small hydrostatic core (~5 × 10-3 M☉) is formed and subsequently grows in mass as the ambient gas accretes onto it. The mass accretion rate is estimated to be 3.7 × 10-2 M☉ yr-1 (M*/M☉)-0.37, where M* is the instantaneous mass of the central core, by using a similarity solution that reproduces the evolution of the cloud before the core formation.

Evolution of Massive Protostars with High Accretion Rates

Formation of massive stars by accretion requires a high accretion rate of 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 of , which is presumed in the standard scenario for low-mass star formation. With the high accretion rate of , 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-1, 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-1 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.