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The collapse of dense cores with different metallicities is studied by hydrodynamical calculations coupled with detailed chemical and radiative processes. For this purpose, we construct a simple chemical network with non-equilibrium reactions among 15 chemical species, which reproduces the abundance of important molecular coolants by more detailed network very well. The evolution is followed until the formation of a hydrostatic protostar at the center. In a lower-metallicity gas cloud, the temperature during the collapse remains high owing to less efficient cooling. Using the temperature evolution at the center as a function the density, we discuss the possibility of fragmentation during the dust-cooling phase. The critical metallicity for the fragmentation is 10^{-5}Z_sun assuming moderate elongation of the cloud cores at the onset of this phase. From the density and velocity distributions at the time of protostar formation, we evaluate the mass accretion rate in the subsequent accretion phase. Using these accretion rates, we also calculate the evolution of the protostars under the assumption of stationary accretion flow. Finally, we discuss possible suppression of fragmentation by heating of the ambient gas by protostellar radiation, which is considered important in the contemporary star formation. We argue that it is negligible for, ApJ in press

Mass accretion onto (proto-)stars at high accretion rates > 10^-4 M_sun/yr is expected in massive star formation. We study the evolution of massive protostars at such high rates by numerically solving the stellar structure equations. In this paper we examine the evolution via disk accretion. We consider a limiting case of "cold" disk accretion, whereby most of the stellar photosphere can radiate freely with negligible backwarming from the accretion flow, and the accreting material settles onto the star with the same specific entropy as the photosphere. We compare our results to the calculated evolution via spherically symmetric accretion, the opposite limit, whereby the material accreting onto the star contains the entropy produced in the accretion shock front. We examine how different accretion geometries affect the evolution of massive protostars. For cold disk accretion at 10^-3 M_sun/yr the radius of a protostar is initially small, about a few R_sun. After several solar masses have accreted, the protostar begins to bloat up and for M \simeq 10 M_sun the stellar radius attains its maximum of 30 - 400 R_sun. The large radius about 100 R_sun is also a feature of spherically symmetric accretion at the same accreted mass and accretion rate. Hence, expansion to a large radius is a robust feature of accreting massive protostars. At later times the protostar eventually begins to contract and reaches the Zero-Age Main-Sequence (ZAMS) for M \simeq 30 M_sun, independent of the accretion geometry. For accretion rates exceeding several 10^-3 M_sun/yr the protostar never contracts to the ZAMS. The very large radius of several 100s R_sun results in a low effective temperature and low UV luminosity of the protostar. Such bloated protostars could well explain the existence of bright high-mass protostellar objects, which lack detectable HII regions., 20 pages, 16 figures

The final mass of a newborn star is set at the epoch when the mass accretion onto the star is terminated. We study the evolution of accreting protostars and the limits of accretion in low-metallicity environments under spherical symmetry. Accretion rates onto protostars are estimated via the temperature evolution of prestellar cores with different metallicities. The derived rates increase with decreasing metallicity, from at Z = Z ☉ to 10–3 M ☉ yr–1 at Z = 0. With the derived accretion rates, the protostellar evolution is numerically calculated. We find that, at lower metallicity, the protostar has a larger radius and reaches the zero-age main sequence (ZAMS) at higher stellar mass. Using this protostellar evolution, we evaluate the upper stellar mass limit where the mass accretion is hindered by radiative feedback. We consider the effects of radiation pressure exerted on the accreting envelope, and expansion of an H II region. The mass accretion is finally terminated by radiation pressure on dust grains in the envelope for Z 10–3 Z ☉ and by the expanding H II region for lower metallicity. The mass limit from these effects increases with decreasing metallicity from M * 10 M ☉ at Z = Z ☉ to 300 M ☉ at Z = 10–6 Z ☉. The termination of accretion occurs after the central star arrives at the ZAMS at all metallicities, which allows us to neglect protostellar evolution effects in discussing the upper mass limit by stellar feedback. The fragmentation induced by line cooling in low-metallicity clouds yields prestellar cores with masses large enough that the final stellar mass is set by the feedback effects. Although relaxing the assumption of spherical symmetry will alter feedback effects, our results will be a benchmark for more realistic evolution to be explored in future studies.

If a significant fraction of metals is in dust, star-forming cores with metallicity higher than a critical value ~10^{-6}-10^{-5}Z_sun are able to fragment by dust cooling, thereby producing low-mass cores. Despite being above the critical metallicity, a metallicity range is found to exist around 10^{-5}-10^{-4}Z_sun where low-mass fragmentation is prohibited. In this range, three-body H_2 formation starts at low (~100K) temperature and thus the resulting heating causes a dramatic temperature jump, which makes the central part of the star-forming core transiently hydrostatic and thus highly spherical. With little elongation, the core does not experience fragmentation in the subsequent dust-cooling phase. The minimum fragmentation mass is set by the Jeans mass just before the H_2 formation heating, and its value can be as high as ~10M_sun. For metallicity higher than ~10^{-4}Z_sun, H_2 formation is almost completed by the dust-surface reaction before the onset of the three-body reaction, and low-mass star formation becomes possible. This mechanism might explain the higher characteristic mass of metal-poor stars than in the solar neighborhood presumed from the statistics of carbon-enhanced stars., 4 pages, 3 figures, ApJ Letters in press

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< dot{M}crit in which objects with mass >> 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), 34 pages, 12 figures. ApJ, in press

We investigate the formation by accretion of massive primordial protostars in the range 10 to 300 Msun. The high accretion rate used in the models (4.4 x 10^{-3} Msun/yr) causes the structure and evolution to differ significantly from those of both present-day protostars and primordial zero-age main sequence stars. After an initial expansion of the radius (for < 12 Msun), the protostar undergoes an extended phase of contraction (up to 60 Msun). The stellar surface is not visible throughout most of the main accretion phase, since a photosphere is formed in the infalling envelope. Also, significant nuclear burning does not take place until a protostellar mass of about 80 Msun. As the interior luminosity approaches the Eddington luminosity, the protostellar radius rapidly expands, reaching a maximum around 100 Msun. Changes in the ionization of the surface layers induce a secondary phase of contraction, followed by a final swelling due to radiation pressure when the stellar mass reaches about 300 Msun. This expansion is likely to signal the end of the main accretion phase, thus setting an upper limit to the protostellar mass formed in these conditions., 11 pages and 4 figures. ApJL accepted

Thermal and chemical evolution of primordial gas clouds irradiated with far-ultraviolet (FUV; < 13.6 eV) radiation is investigated. In clouds irradiated by intense FUV radiation, sufficient hydrogen molecules to be important for cooling are never formed. However, even without molecular hydrogen, if the clouds are massive enough, they start collapsing via atomic hydrogen line cooling. Such clouds continue to collapse almost isothermally owing to successive cooling by H^{-} free-bound emission up to the number density of 10^{16} cm^{-3}. Inside the clouds, the Jeans mass eventually falls well below a solar mass. This indicates that hydrogen molecules are dispensable for low-mass primordial star formation, provided fragmentation of the clouds occurs at sufficiently high density., 32 pages and 9 figures. ApJ, in press

The formation of supermassive stars (SMSs) via rapid mass accretion and their direct collapse into black holes (BHs) is a promising pathway for sowing seeds of supermassive BHs in the early universe. We calculate the evolution of rapidly accreting SMSs by solving the stellar structure equations including nuclear burning as well as general relativistic (GR) effects up to the onset of the collapse. We find that such SMSs have less concentrated structure than fully-convective counterpart, which is often postulated for non-accreting ones. This effect stabilizes the stars against GR instability even above the classical upper mass limit $\gtrsim 10^5~M_\odot$ derived for the fully-convective stars. The accreting SMS begins to collapse at the higher mass with the higher accretion rate. The collapse occurs when the nuclear fuel is exhausted only for cases with $\dot M \lesssim 0.1~M_\odot~{\rm yr}^{-1}$. With $\dot{M} \simeq 0.3 - 1~M_\odot~{\rm yr}^{-1}$, the star becomes GR-unstable during the helium-burning stage at $M \simeq 2 - 3.5~\times 10^5~M_\odot$. In an extreme case with $10~M_\odot~{\rm yr}^{-1}$, the star does not collapse until the mass reaches $\simeq 8.0\times 10^5~M_\odot$, where it is still in the hydrogen-burning stage. We expect that BHs with roughly the same mass will be left behind after the collapse in all the cases., Comment: 5 pages, 3 figures, accepted for publication in ApJL

Supermassive stars (SMSs) forming via very rapid mass accretion (Mdot >~ 0.1 Msun/yr) could be precursors of supermassive black holes observed beyond redshift of about 6. Extending our previous work, we here study the evolution of primordial stars growing under such rapid mass accretion until the stellar mass reaches 10^{4 - 5} Msun. Our stellar evolution calculations show that a star becomes supermassive while passing through the "supergiant protostar" stage, whereby the star has a very bloated envelope and a contracting inner core. The stellar radius increases monotonically with the stellar mass, until =~ 100 AU for M_* >~ 10^4 Msun, after which the star begins to slowly contract. Because of the large radius the effective temperature is always less than 10^4 K during rapid accretion. The accreting material is thus almost completely transparent to the stellar radiation. Only for M_* >~ 10^5 Msun can stellar UV feedback operate and disturb the mass accretion flow. We also examine the pulsation stability of accreting SMSs, showing that the pulsation-driven mass loss does not prevent stellar mass growth. Observational signatures of bloated SMSs should be detectable with future observational facilities such as the James Webb Space Telescope. Our results predict that an inner core of the accreting SMS should suffer from the general relativistic instability soon after the stellar mass exceeds 10^5 Msun. An extremely massive black hole should form after the collapse of the inner core., 14 pages, 13 figures, accepted for publication in ApJ

The recently discovered gravitational wave sources GW190521 and GW190814 have shown evidence of BH mergers with masses and spins that could be outside of the range expected from isolated stellar evolution. These merging objects could have undergone previous mergers. Such hierarchical mergers are predicted to be frequent in active galactic nuclei (AGN) disks, where binaries form and evolve efficiently by dynamical interactions and gaseous dissipation. Here we compare the properties of these observed events to the theoretical models of mergers in AGN disks, which are obtained by performing one-dimensional $N$-body simulations combined with semi-analytical prescriptions. The high BH masses in GW190521 are consistent with mergers of high-generation (high-g) BHs where the initial progenitor stars had high metallicity, 2g BHs if the original progenitors were metal-poor, or 1g BHs that had gained mass via super-Eddington accretion. Other measured properties related to spin parameters in GW190521 are also consistent with mergers in AGN disks. Furthermore, mergers in the lower mass gap or those with low mass ratio as found in GW190814 and GW190412 are also reproduced by mergers of 2g-1g or 1g-1g objects with significant accretion in AGN disks. Finally, due to gas accretion, the massive neutron star merger reported in GW190425 can be produced in an AGN disk., 12 pages, 4 figures, accepted in ApJ