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Despite extensive search efforts, direct observations of the first [Population III (Pop III)] stars have not yet succeeded. Theoretical studies have suggested that late Pop III star formation is still possible in pristine clouds of high-mass galaxies, co-existing with Pop II stars, down to the epoch of reionization. Here, we re-assess this finding by exploring Pop III star formation in six 50 h−1 cMpc simulations performed with the hydrodynamical code dustyGadget. We find that Pop III star formation (∼10−3.4–10−3.2 M⊙ yr−1 cMpc−3) is still occurring down to z ∼ 6–8, i.e. well within the reach of deep JWST surveys. At these epochs, $\gtrsim\!{10}~{{\ \rm per\ cent}}$ of the rare massive galaxies with M⋆ ≳ 3 × 109 M⊙ are found to host Pop III stars, although with a Pop III/Pop II mass fraction $\lesssim\!0.1~{{\ \rm per\ cent}}$ . Regardless of their mass, Pop III-hosting galaxies are mainly found on the main sequence, at high star-formation rates, probably induced by accretion of pristine gas. This scenario is also supported by their increasing star-formation histories and their preferential location in high-density regions of the cosmic web. Pop III stars are found both in the outskirts of metal-enriched regions and in isolated, pristine clouds. In the latter case, their signal may be less contaminated by Pop IIs, although its detectability will strongly depend on the specific line of sight to the source, due to the complex morphology of the host galaxy and its highly inhomogeneous dust distribution.

We estimate the fraction of halos that host supermassive black holes (SMBHs) forming through the direct collapse (DC) scenario by using cosmological N -body simulations combined with a semi-analytic model for galaxy evolution. While in most of earlier studies the occurrence of the DC is limited only in chemically pristine halos, we here suppose that the DC can occur also in halos with metallicity below a threshold value $Z_{\rm th} = 0$--$10^{-3}~{\rm Z}_{\bigodot}$, considering the super-competitive accretion pathway for DC black hole (DCBH) formation. In addition, we consider for the first time the effect of Lyman-Werner (LW) radiation from stars within host halos, i.e., internal radiation. We find that, with low threshold metallicities of $Z_{\rm th} \leq 10^{-4}~{\rm Z}_{\bigodot}$, the inclusion of internal radiation rather reduces the number density of DCBHs from $0.2$--$0.3$ to $0.03$--$0.06~{\rm Mpc}^{-3}$. This is because star formation is suppressed due to self-regulation, and the LW flux emitted by neighboring halos is reduced. Only when $Z_{\rm th}$ is as high as $10^{-3}~{\rm Z}_{\bigodot}$, internal radiation enhances the number density of DCBHs from $0.4$ to $1~{\rm Mpc}^{-3}$, thereby decreasing the threshold halo mass above which at least one DCBH forms from $2\times 10^{9}$ to $9\times 10^{8}~{\rm M}_{\bigodot}$. We also find that halos with $M_{\rm halo} \gtrsim 10^{11}$--$10^{12}~{\rm M}_{\bigodot}$ can host more than one DCBH at $z = 0$. This indicates that the DC scenario alone can explain the observed number of SMBH-hosting galaxies., 17 pages, 12 figures, 2 tables, accepted by MNRAS

Cosmic metallicity evolution possibly creates the diversity of star formation modes at different epochs. Gravitational fragmentation of circumstellar discs provides an important formation channel of multiple star systems, including close binaries. We here study the nature of disc fragmentation, systematically performing a suite of two-dimensional radiation-hydrodynamic simulations, in a broad range of metallicities, from the primordial to the solar values. In particular, we follow relatively long-term disc evolution over 15 kyr after the disc formation, incorporating the effect of heating by the protostellar irradiation. Our results show that the disc fragmentation occurs at all metallicities $1$--$0$ $Z_{\odot}$, yielding self-gravitating clumps. Physical properties of the clumps, such as their number and mass distributions, change with the metallicity due to different gas thermal evolution. For instance, the number of clumps is the largest for the intermediate metallicity range of $10^{-2}$--$10^{-5}$ $Z_{\odot}$, where the dust cooling is effective exclusively in a dense part of the disc and causes the fragmentation of spiral arms. The disc fragmentation is more modest for $1$--$0.1$ $Z_{\odot}$ thanks to the disc stabilization by the stellar irradiation. Such metallicity dependence agrees with the observed trend that the close binary fraction increases with decreasing metallicity in the range of $1$--$10^{-3}$ $Z_{\odot}$., Comment: 17 pages, 16 figures, submitted to MNRAS

Recent theoretical studies have suggested that a magnetic field may play a crucial role in the first star formation in the universe. However, the influence of the magnetic field on the first star formation has yet to be understood well. In this study, we perform three-dimensional magnetohydrodynamic simulations taking into account all the relevant cooling processes and non-equilibrium chemical reactions up to the protostar density, in order to study the collapse of magnetized primordial gas cores with self-consistent thermal evolution. Our results show that the thermal evolution of the central core is hardly affected by a magnetic field, because magnetic forces do not prevent the contraction along the fields lines. We also find that the magnetic braking extracts the angular momentum from the core and suppresses fragmentation depending on the initial strength of the magnetic field. The angular momentum transport by the magnetic outflows is less effective than that by the magnetic braking because the outflows are launched only in a late phase of the collapse. Our results indicate that the magnetic effects become important for the field strength $B> 10^{-8}(n_{\rm H}/1\ \rm cm^{-3})^{2/3}\ \rm G$, where $n_{\rm H}$ is the number density, during the collapse phase. Finally, we compare our results with simulations using a barotropic approximation and confirm that this approximation is reasonable at least for the collapse phase. Nevertheless, self-consistent treatment of the thermal and chemical processes is essential for extending simulations to the accretion phase, in which radiative feedback by protostars plays a crucial role., 18 pages, 15 figures, 2 tables. Accepted for publication in MNRAS

Magnetic fields play such essential roles in star formation as transporting angular momentum and driving outflows from a star-forming cloud, thereby controlling the formation efficiency of a circumstellar disc and also multiple stellar systems. The coupling of magnetic fields to the gas depends on its ionization degree. We calculate the temperature evolution and ionization degree of a cloud for various metallicities of Z/Zsun = 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, and 1. We update the chemical network by reversing all the gas-phase processes and by considering grain-surface chemistry, including grain evaporation, thermal ionization of alkali metals, and thermionic emission from grains. The ionization degree at nH ~ 1e15-1e19 /cm^3 becomes up to eight orders of magnitude higher than that obtained in the previous model, owing to the thermionic emission and thermal ionization of K and Na, which have been neglected so far. Although magnetic fields dissipate owing to ambipolar diffusion or Ohmic loss at nH < 1e15 /cm^3, the fields recover strong coupling to the gas at nH ~ 1e15 /cm^3, which is lower by a few orders of magnitude compared to the previous work. We develop a reduced chemical network by choosing processes relevant to major coolants and charged species. The reduced network consists of 104 (161) reactions among 28 (38) species in the absence (presence, respectively) of ionization sources. The reduced model includes H2 and HD formation on grain surfaces as well as the depletion of O, C, OH, CO, and H2O on grain surfaces., 23 pages, 12 figures, 3 tables, accepted for publication in MNRAS

The direct collapse (DC) is a promising mechanism that provides massive seed black holes (BHs) with ∼105 M⊙ in the early universe. To study a long-term accretion growth of a direct-collapse black hole (DCBH), we perform cosmological radiation-hydrodynamics simulations, extending our previous work where we investigated its formation stage. With a high spatial resolution down below the Bondi radius, we show that the accretion rate on to the BH is far below the Eddington value. Such slow mass growth is partly because of the strong radiative feedback from the accreting BH to the surrounding dense gas. Even after it falls into the first galaxy, the accretion rate is substantially suppressed due to the supernova feedback associated with the intense star formation. Moreover, the BH has a large velocity of ∼100 km s−1 relative to the gas, which further reduces the accretion rate. This large relative velocity stems from the fact that the DCBHs form in metal-free environments typically at ∼1 kpc from the galaxy. The BH accelerates as it approaches the galactic centre due to the gravity. The relative velocity never damps and the BH wanders around the outer galactic region. An analytic estimate predicts that the DCBH formation within ∼100 pc around the galactic centre is necessary to decelerate the BH with dynamical friction before z = 7. Since metal enrichment with Z ∼ 10−5−10−3 Z⊙ is expected there, the formation of DCBHs in the metal-enriched environments is preferable for the subsequent rapid growth.

Supermassive stars (SMSs) with $\sim10^{4-5}~\mathrm{M}_{\odot}$ are candidate objects for the origin of supermassive black holes observed at redshift $z$>6. They are supposed to form in primordial-gas clouds that provide the central stars with gas at a high accretion rate, but their growth may be terminated in the middle due to the stellar ionizing radiation if the accretion is intermittent and its quiescent periods are longer than the Kelvin-Helmholtz (KH) timescales at the stellar surfaces. In this paper, we examine the role of the ionizing radiation feedback based on the accretion history in two possible SMS-forming clouds extracted from cosmological simulations, following their evolution with vertically-integrated two-dimensional hydrodynamic simulations with detailed thermal and chemical models. The consistent treatment of the gas thermal evolution is crucial for obtaining the realistic accretion history, as we demonstrate by performing an additional run with a barotropic equation of state, in which the fluctuation of the accretion rate is artificially suppressed. We find that although the accretion becomes intermittent due to the formation of spiral arms and clumps in gravitationally unstable disks, the quiescent periods are always shorter than the KH timescales, implying that SMSs can form without affected by the ionizing radiation., 14 pages, 11 figures, accepted for publication in MNRAS

Direct collapse black hole (DCBH) formation with mass $\gtrsim 10^{5}~M_{\odot}$ is a promising scenario for the origin of high-redshift supermassive black holes. It has usually been supposed that the DCBH can only form in the primordial gas since the metal enrichment enhances the cooling ability and causes the fragmentation into smaller pieces. What actually happens in such an environment, however, has not been explored in detail. Here, we study the impact of the metal enrichment on the clouds, conducting hydrodynamical simulations to follow the cloud evolution in cases with different degree of the metal enrichment $Z/Z_{\odot}=10^{-6}-10^{-3}$. Below $Z/Z_{\odot}=10^{-6}$, metallicity has no effect and supermassive stars form along with a small number of low-mass stars. With more metallicity $Z/Z_{\odot} \gtrsim 5 \times 10^{-6}$, although the dust cooling indeed promotes fragmentation of the cloud core and produces about a few thousand low-mass stars, the accreting flow preferentially feeds the gas to the central massive stars, which grows supermassive as in the primordial case. We term this formation mode as the {\it super competitive accretion}, where only the central few stars grow supermassive while a large number of other stars are competing for the gas reservoir. Once the metallicity exceeds $10^{-3}~Z_{\odot}$ and metal-line cooling becomes operative, the central star cannot grow supermassive due to lowered accretion rate. Supermassive star formation by the super competitive accretion opens up a new window for seed BHs, which relaxes the condition on metallicity and enhances the seed BH abundance., Comment: 10 pages, 6figures, submitted to MNRAS

In the present-day universe, magnetic fields play such essential roles in star formation as angular momentum transport and outflow driving, which control circumstellar disc formation/fragmentation and also the star formation efficiency. While only a much weaker field has been believed to exist in the early universe, recent theoretical studies find that strong fields can be generated by turbulent dynamo during the gravitational collapse. Here, we investigate the gravitational collapse of a cloud core ($\sim 10^{3}\ \rm cm^{-3}$) up to protostar formation ($\sim 10^{20}\ \rm cm^{-3}$) by non-ideal magnetohydrodynamics (MHD) simulations considering ambipolar diffusion (AD), the dominant non-ideal effects in the primordial-gas. We systematically study rotating cloud cores either with or without turbulence and permeated with uniform fields of different strengths. We find that AD can slightly suppress the field growth by dynamo especially on scales smaller than the Jeans-scale at the density range $10^{10}-10^{14}\ \rm cm^{-3}$, while we could not see the AD effect on the temperature evolution, since the AD heating rate is always smaller than compression heating. The inefficiency of AD makes the field as strong as $10^{3}-10^{5} \rm\ G$ near the formed protostar, much stronger than in the present-day cases, even in cases with initially weak fields. The magnetic field affects the inflow motion when amplified to the equipartition level with turbulence on the Jeans-scale, although disturbed fields do not launch winds. This might suggest that dynamo amplified fields have smaller impact on the dynamics in the later accretion phase than other processes such as ionisation feedback., Comment: 15 pages, 11 figures, 2 tables. Accepted for publication in MNRAS

We study star cluster formation in a low-metallicity environment using three dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we follow the formation and growth of protostellar systems with different metallicities ranging from $10^{-6}$ to $0.1~Z_{\odot}$. The cooling induced by dust grains promotes fragmentation at small scales and the formation of low-mass stars with $M_{*} \sim 0.01$--$0.1~M_{\odot}$ when $Z/Z_{\odot} \gtrsim 10^{-5}$. While the number of low-mass stars increases with metallicity, the stellar mass distribution is still top-heavy for $Z/Z_{\odot} \lesssim 10^{-2}$ compared to the Chabrier initial mass function (IMF). In these cases, star formation begins after the turbulent motion decays and a single massive cloud core monolithically collapses to form a central massive stellar system. The circumstellar disk preferentially feeds the mass to the central massive stars, making the mass distribution top-heavy. When $Z/Z_{\odot}=0.1$, collisions of the turbulent flows promote the onset of the star formation and a highly filamentary structure develops owing to efficient fine-structure line cooling. In this case, the mass supply to the massive stars is limited by the local gas reservoir and the mass is shared among the stars, leading to a Chabrier-like IMF. We conclude that cooling at the scales of the turbulent motion promotes the development of the filamentary structure and works as an important factor leading to the present-day IMF., Comment: 20 pages, 14 figures, accepted for publication in MNRAS

The detections of gravitational waves (GW) by the LIGO/Virgo collaborations provide various possibilities for both physics and astronomy. We are quite sure that GW observations will develop a lot, both in precision and in number, thanks to the continuous work on the improvement of detectors, including the expected new detector, KAGRA, and the planned detector, LIGO-India. On this occasion, we review the fundamental outcomes and prospects of gravitational wave physics and astronomy. We survey the development, focusing on representative sources of gravitational waves: binary black holes, binary neutron stars, and supernovae. We also summarize the role of gravitational wave observations as a probe of new physics.

We investigate the formation of merging binary black holes (BHs) through isolated binary evolution, performing binary population synthesis calculations covering an unprecedentedly wide metallicity range of Population (Pop) I, II, III, and extremely metal-poor (EMP) binary stars. We find that the predicted merger rate density and primary BH mass ($m_1$) distribution are consistent with the gravitational wave (GW) observations. Notably, Pop III and EMP ($< 10^{-2}$ $Z_\odot$) binary stars yield most of the pair instability (PI) mass gap events with $m_1 = 65$--$130$ $M_\odot$. Pop III binary stars contribute more to the PI mass gap events with increasing redshift, and all the PI mass gap events have the Pop III origin at redshifts $\gtrsim 8$. Our result can be assessed by future GW observations in the following two points. First, there are no binary BHs with $m_1=100$--$130$ $M_\odot$ in our result, and thus the $m_1$ distribution should suddenly drop in the range of $m_1=100$--$130$ $M_\odot$. Second, the PI mass gap event rate should increase toward higher redshift up to $\sim 11$, since those events mainly originate from the Pop III binary stars. We find that the following three assumptions are needed to reproduce the current GW observations: a top-heavy stellar initial mass function and the presence of close binary stars for Pop III and EMP binary stars, and inefficient convective overshoot in the main-sequence phase of stellar evolution. Without any of the above, the number of PI mass gap events becomes too low to reproduce current GW observations., 26 pages, 13 figures, 2 tables, ApJ accepted. BSEEMP, a binary population synthesis code used in this paper, is published on github: https://github.com/atrtnkw/bseemp

The recent discovery of high-redshift (z > 6) supermassive black holes (SMBH) favors the formation of massive seed BHs in protogalaxies. One possible scenario is formation of massive stars ~ 1e3-1e4 Msun via runaway stellar collisions in a dense cluster, leaving behind massive BHs without significant mass loss. We study the pulsational instability of massive stars with the zero-age main-sequence (ZAMS) mass Mzams/Msun = 300-3000 and metallicity Z/Zsun = 0-0.1, and discuss whether or not pulsation-driven mass loss prevents massive BH formation. In the MS phase, the pulsational instability excited by the epsilon-mechanism grows in ~ 1e3 yrs. As the stellar mass and metallicity increase, the mass-loss rate increases to < 1e-3 Msun/yr. In the red super-giant (RSG) phase, the instability is excited by the kappa-mechanism operating in the hydrogen ionization zone and grows more rapidly in ~ 10 yrs. The RSG mass-loss rate is almost independent of metallicity and distributes in the range of ~ 1e-3-1e-2 Msun/yr. Conducting the stellar structure calculations including feedback due to pulsation-driven winds, we find that the stellar models of Mzams/Msun = 300-3000 can leave behind remnant BHs more massive than ~ 200-1200 Msun. We conclude that massive merger products can seed monster SMBHs observed at z > 6., 15 pages, 10 figures, accepted for publication in the Astrophysical Journal

Shocks may have been prevalent in the early Universe, associated with virialization and supernova explosions, etc. Here, we study thermal evolution and fragmentation of shock-compressed clouds, by using a one-zone model with detailed thermal and chemical processes. We explore a large range of initial density (1-1e5 /cm^3), metallicity (0-1e-2 Z_sun), UV strength (0-500 times Galactic value), and cosmic microwave background temperature (10 and 30 K). Shock-compressed clouds contract isobarically via atomic and molecular line cooling, until self-gravitating clumps are formed by fragmentation. If the metals are only in the gas-phase, the clump mass is higher than ~ 3 M_sun in any conditions we studied. Although in some cases with a metallicity higher than ~ 1e-3 Z_sun, re-fragmentation of a clump is caused by metal-line cooling, this fragment mass is higher than ~ 30 M_sun. On the other hand, if about half the mass of metals is condensed in dust grains, as in the Galactic interstellar medium, dust cooling triggers re-fragmentation of a clump into sub-solar mass pieces, for metallicities higher than ~ 1e-5 Z_sun. Therefore, the presence of dust is essential in low-mass (< M_sun) star formation from a shock-compressed cloud., 15 pages, 8 figures, accepted for publication in MNRAS

Dust enables low-mass stars to form from low-metallicity gas by inducing fragmentation of clouds via the cooling by its thermal emission. Dust may, however, be evacuated from star-forming clouds due to radiation force from massive stars. We here study the condition for the dust evacuation by comparing the dust evacuation time with the time of cloud destruction due to either expansion of HII regions or supernovae. The cloud destruction time has weak dependence on the cloud radius, while the dust evacuation time becomes shorter for a cloud with the smaller radius. The dust evacuation thus occurs in compact star-forming clouds whose column density is $N_{\rm H} \simeq 10^{24} - 10^{26} ~{\rm cm^{-2}}$. The critical halo mass above which the dust evacuation occurs becomes lower for higher formation redshift, e.g., $\sim 10^{9}~M_{\odot}$ at redshift $z \sim 3$ and $\sim 10^{7}~M_{\odot}$ at $z \sim 9$. In addition, metallicity of the gas should be less than $\sim 10^{-2} ~ Z_{\odot}$. Otherwise the dust attenuation reduces the radiation force significantly. From the dust-evacuated gas, massive stars are likely to form even with metallicity above $\sim 10^{-5}~Z_{\odot}$, the critical value for low-mass star formation due to the dust cooling. This can explain the dearth of ultra-metal poor stars with the metallicity lower than $\sim 10^{-4}~Z_{\odot}$., Comment: 16 pages, 18 figures, accepted for publication in MNRAS

We consider whether the maximum mass of first stars is imposed by the protostellar spin, i.e., by the so-called $\Omega\Gamma$-limit, which requires the sum of the radiation and centrifugal forces at the stellar surface be smaller than the inward pull of the gravity. Once the accreting protostar reaches such a marginal state, the star cannot spin up more and is not allowed to accrete more gas with inward angular momentum flux. So far, however, the effect of stellar radiation on the structure of the accretion disk has not been properly taken into account in discussing the effect of $\Omega\Gamma$-limit on the first star formation. Here, we obtain a series of the steady accretion-disk solutions considering such effect and find solutions without net angular momentum influx to the stars with arbitrary rotation rates, in addition to those with finite angular momentum flows. The accretion of positive angular momentum flows pushes the star beyond the $\Omega\Gamma$-limit, which is allowed only with the external pressure provided by the circumstellar disk. On the other hand, the accretion with no net angular momentum influx does not result in the spin-up of the star. Thus, the existence of the solution with no net angular momentum influx indicates that the protostars can keep growing in mass by accretion even after they reach the $\Omega\Gamma$-limit.

Discovery of high-redshift (z > 6) supermassive black holes (BHs) may indicate that the rapid (or super-Eddington) gas accretion has aided their quick growth. Here, we study such rapid accretion of the primordial gas on to intermediate-mass (10^2 - 10^5 M_sun) BHs under anisotropic radiation feedback. We perform two-dimensional radiation hydrodynamics simulations that solve the flow structure across the Bondi radius, from far outside of the Bondi radius down to a central part which is larger than a circum-BH accretion disc. The radiation from the unresolved circum-BH disc is analytically modeled considering self-shadowing effect. We show that the flow settles into a steady state, where the flow structure consists of two distinct parts: (1) bipolar ionized outflowing regions, where the gas is pushed outward by thermal gas pressure and super-Eddington radiation pressure, and (2) an equatorial neutral inflowing region, where the gas falls toward the central BH without affected by radiation feedback. The resulting accretion rate is much higher than that in the case of isotropic radiation, far exceeding the Eddington-limited rate to reach a value slightly lower than the Bondi one. The opening angle of the equatorial inflowing region is determined by the luminosity and directional dependence of the central radiation. We find that photoevaporation from its surfaces set the critical opening angle of about ten degrees below which the accretion to the BH is quenched. We suggest that the shadowing effect allows even stellar-remnant BHs to grow rapidly enough to become high-redshift supermassive BHs., 19 pages, 12 figures, 8 tables, corrected typos in the appendix

Magnetic fields play such roles in star formation as the angular momentum transport in star-forming clouds, thereby controlling circumstellar disc formation and even binary star formation efficiency. The coupling between the magnetic field and gas is determined by the ionization degree in the gas. Here, we calculate the thermal and chemical evolution of the primordial gas by solving chemical reaction network where all the reactions are reversed. We find that at ~ 10^14-10^18 /cm^3, the ionization degree becomes 100-1000 times higher than the previous results due to the lithium ionization by thermal photons trapped in the cloud, which has been omitted so far. We construct the minimal chemical network which can reproduce correctly the ionization degree as well as the thermal evolution by extracting 36 reactions among 13 species. Using the obtained ionization degree, we evaluate the magnetic field diffusivity. We find that the field dissipation can be neglected for global fields coherent over > a tenth of the cloud size as long as the field is not so strong as to prohibit the collapse. With magnetic fields strong enough for ambipolar diffusion heating to be significant, the magnetic pressure effects to slow down the collapse and to reduce the compressional heating become more important, and the temperature actually becomes lower than in the no-field case., 17 pages, 13 figures, 2 tables, submitted to MNRAS

We study the impact of star-forming minihaloes, and the initial mass function (IMF) of Population III (Pop III) stars, on the Galactic halo metallicity distribution function (MDF) and on the properties of C-enhanced and C-normal stars at [Fe/H]

The formation of SMSs is a potential pathway to seed SMBHs in the early universe. A critical issue for forming SMSs is stellar UV feedback, which may limit the stellar mass growth via accretion. In this paper we study the evolution of an accreting SMS and its UV emissivity under conditions of realistic variable accretion from a self-gravitating circumstellar disc. First we conduct a 2D hydrodynamical simulation to follow the long-term protostellar accretion until the stellar mass exceeds $10^4~M_\odot$. The disc fragments due to gravitational instability, creating a number of small clumps that rapidly migrate inward to fall onto the star. The resulting accretion history is thus highly time-dependent: short episodic accretion bursts are followed by longer, relative quiescent phases. We show that the circumstellar disc for the so-called direct collapse model is more unstable and generates greater variability over shorter timescales than normal Pop III cases. We conduct a post-process stellar evolution calculation using the obtained accretion history. Our results show that, regardless of the strong variability of the accretion rates, the stellar radius monotonically increases with almost constant effective temperature at $T_{\rm eff} \simeq 5000$ K as the stellar mass increases. The resulting UV feedback is too weak to hinder mass accretion due to the low flux of stellar UV photons, thus verifying our implicit assumption of no stellar feedback during the hydrodynamic simulations. The insensitivity of stellar evolution to variable accretion is attributed to the fact that typical timescales of variability, $\lesssim 10^3$ years, are too short to affect the stellar structure. We argue that this evolution will continue until the SMS eventually collapses to produce a massive black hole by the general relativistic instability after the stellar mass reaches $\gtrsim 10^5~M_\odot$., Comment: 9 pages, 6 figures, submitted to MNRAS

Aims. The early evolution of protostellar disks with metallicities in the Z = 1.0 − 0.01 Z⊙ range was studied with a particular emphasis on the strength of gravitational instability and the nature of protostellar accretion in low-metallicity systems. Methods. Numerical hydrodynamics simulations in the thin-disk limit were employed that feature separate gas and dust temperatures, and disk mass-loading from the infalling parent cloud cores. Models with cloud cores of similar initial mass and rotation pattern but distinct metallicity were considered to distinguish the effect of metallicity from that of the initial conditions. Results. The early stages of disk evolution in low-metallicity models are characterized by vigorous gravitational instability and fragmentation. Disk instability is sustained by continual mass-loading from the collapsing core. The time period that is covered by this unstable stage is much shorter in the Z = 0.01 Z⊙ models than in their higher metallicity counterparts thanks to the higher rates of mass infall caused by higher gas temperatures (which decouple from lower dust temperatures) in the inner parts of collapsing cores. Protostellar accretion rates are highly variable in the low-metallicity models reflecting the highly dynamic nature of the corresponding protostellar disks. The low-metallicity systems feature short but energetic episodes of mass accretion caused by infall of inward-migrating gaseous clumps that form via gravitational fragmentation of protostellar disks. These bursts seem to be more numerous and last longer in the Z = 0.1 Z⊙ models than in the Z = 0.01 Z⊙ case. Conclusions. Variable protostellar accretion with episodic bursts is not a particular feature of solar metallicity disks. It is also inherent to gravitationally unstable disks with metallicities up to 100 times lower than solar.

Aims: We explore the long-term evolution of young protoplanetary disks with different approaches to computing the thermal structure determined by various cooling and heating processes in the disk and its surroundings. Methods: Numerical hydrodynamics simulations in the thin-disk limit were complemented with three thermal evolution schemes: a simplified $\beta$-cooling approach with and without irradiation, in which the rate of disk cooling is proportional to the local dynamical time, a fiducial model with equal dust and gas temperatures calculated taking viscous heating, irradiation, and radiative cooling into account, and also a more sophisticated approach allowing decoupled dust and gas temperatures. Results: We found that the gas temperature may significantly exceed that of dust in the outer regions of young disks thanks to additional compressional heating caused by the infalling envelope material in the early stages of disk evolution and slow collisional exchange of energy between gas and dust in low-density disk regions. The outer envelope however shows an inverse trend with the gas temperatures dropping below that of dust. The global disk evolution is only weakly sensitive to temperature decoupling. Nevertheless, separate dust and gas temperatures may affect the chemical composition, dust evolution, and disk mass estimates. Constant-$\beta$ models without stellar and background irradiation fail to reproduce the disk evolution with more sophisticated thermal schemes because of intrinsically variable nature of the $\beta$-parameter. Constant-$\beta$ models with irradiation can better match the dynamical and thermal evolution, but the agreement is still incomplete. Conclusions: Models allowing separate dust and gas temperatures are needed when emphasis is placed on the chemical or dust evolution in protoplanetary disks, particularly in sub-solar metallicity environments., Comment: 19 pages, 21 Figures, accepeted for publication in Astronomy & Astrophysics

Accretion on to seed black holes (BHs) is believed to play a crucial role in formation of supermassive BHs observed at high-redshift (z>6). Here, we investigate the combined effect of gas angular momentum and radiation feedback on the accretion flow, by performing 2D axially symmetric radiation hydrodynamics simulations that solve the flow structure across the Bondi radius and the outer part of the accretion disc simultaneously. The accreting gas with finite angular momentum forms a rotationally-supported disc inside the Bondi radius, where the accretion proceeds by the angular momentum transport due to assumed alpha-type viscosity. We find that the interplay of radiation and angular momentum significantly suppresses accretion even if the radiative feedback is weakened in an equatorial shadowing region. The accretion rate is O(alpha)\sim O(0.01-0.1) times the Bondi value, where alpha is the viscosity parameter. By developing an analytical model, we show that such a great reduction of the accretion rate persists unless the angular momentum is so small that the corresponding centrifugal radius is \lesssim 0.04 times the Bondi radius. We argue that BHs are hard to grow quickly via rapid mass accretion considering the angular momentum barrier presented in this paper., 17 pages, 12 figures, published in MNRAS

We calculate the spectral energy distribution of the first galaxies which contain pre-main-sequence stars by using the stellar evolution code Modules for Experiments in Stellar Astrophysics, the spectra model BT-Settl, and the stellar population synthesis code PEGASE. We calculate the galaxy spectral energy distribution for Salpeter Initial Mass Function. We find that very young first galaxies are bright also in mid-infrared, and the contribution of pre-main-sequence stars can be significant over 0.1 Myr after a star-formation episode.

HD dominates the cooling of primordial clouds with enhanced ionization, e.g. shock-heated clouds in structure formation or supernova remnants, relic HII regions of Pop III stars, and clouds with cosmic-ray (CR) irradiation. There, the temperature decreases to several 10 K and the characteristic stellar mass decreases to $\sim 10\ {\rm M}_{\odot}$, in contrast with first stars formed from undisturbed pristine clouds ($\sim 100\ {\rm M}_{\odot}$). However, without CR irradiation, even weak far ultra-violet (FUV) irradiation suppresses HD formation/cooling. Here, we examine conditions for HD cooling in primordial clouds including both FUV and CR feedback. At the beginning of collapse, the shock-compressed gas cools with its density increasing, while the relic HII region gas cools at a constant density. Moreover, shocks tend to occur in denser environments than HII regions. Owing to the higher column density and the more effective shielding, the critical FUV intensity for HD cooling in a shock-compressed gas becomes $\sim 10$ times higher than in relic HII regions. Consequently, in the shock-compressed gas, the critical FUV intensity exceeds the background level for most of the redshift we consider ($6 \lesssim z \lesssim 15$), while in relic HII regions, HD cooling becomes effective after the CR intensity increases enough at $z \lesssim 10$. Our result suggests that less massive ($\sim 10\ {\rm M}_{\odot}$) Pop III stars may be more common than previously considered and could be the dominant population of Pop III stars., Comment: 15 pages, 12 figures, 1 table, accepted for publication in MNRAS

Fragmentation of protostellar disks controls the growth of protostars and plays a key role in determining the final mass of newborn stars. In this paper, we investigate the structure and gravitational stability of the protostellar disks in the full metallicity range between zero and the solar value. Using the mass-accretion rates evaluated from the thermal evolution in the preceding collapse phase of the pre-stellar cores, we calculate disk structures and their evolution in the framework of the standard steady disks. Overall, with higher metallicity, more efficient cooling results in the lower accretion rate and lower temperature inside the disk: at zero metallicity, the accretion rate is ~ 1e-3Msun/yr and the disk temperature is ~ 1000 K, while at solar metallicity, ~ 1e-6Msun/yr and 10 K. Despite the large difference in these values, the zero- and solar-metallicity disks have similar stability properties: the Toomre parameter for the gravitational stability, which can be written using the ratio of temperatures in the disk and in the envelope as Q ~ (T_disk/T_env)^3/2, is > 1, i.e., marginally stable. At intermediate metallicities of 1e-5--1e-3Zsun, however, the disks are found to be strongly unstable with Q ~ 0.1--1 since dust cooling, which is effective only in the disks due to their high density (> 1e10 cm^-3), makes the temperature in the disks lower than that in the envelopes. This indicates that masses of the individual stars formed as a result of the protostellar disk fragmentation can be significantly smaller than their parent core in this metallicity range. The typical stellar mass in this case would be a few Msun, which is consistent with the observationally suggested mass-scale of extremely metal-poor stars., 15 pages, 8 figures, accepted for publication in MNRAS

The growth of the first super massive black holes (SMBHs) at z > 6 is still a major challenge for theoretical models. If it starts from black hole (BH) remnants of Population III stars (light seeds with mass ~ 100 Msun) it requires super-Eddington accretion. An alternative route is to start from heavy seeds formed by the direct collapse of gas onto a ~ 10^5 Msun BH. Here we investigate the relative role of light and heavy seeds as BH progenitors of the first SMBHs. We use the cosmological, data constrained semi-analytic model GAMETE/QSOdust to simulate several independent merger histories of z > 6 quasars. Using physically motivated prescriptions to form light and heavy seeds in the progenitor galaxies, we find that the formation of a few heavy seeds (between 3 and 30 in our reference model) enables the Eddington-limited growth of SMBHs at z > 6. This conclusion depends sensitively on the interplay between chemical, radiative and mechanical feedback effects, which easily erase the conditions that allow the suppression of gas cooling in the low metallicity gas (Z < Zcr and JLW > Jcr). We find that heavy seeds can not form if dust cooling triggers gas fragmentation above a critical dust-to-gas mass ratio (D > Dcr). In addition, the relative importance of light and heavy seeds depends on the adopted mass range for light seeds, as this dramatically affects the history of cold gas along the merger tree, by both SN and AGN-driven winds., 16 pages, 13 figures, accepted for publication in MNRAS

Direct collapse black holes (DCBHs) are excellent candidates as seeds of supermassive black holes (SMBHs) observed at $z \gsim 6$. The formation of a DCBH requires a strong external radiation field to suppress $\rm H_2$ formation and cooling in a collapsing gas cloud. Such strong field is not easily achieved by first stars or normal star-forming galaxies. Here we investigate a scenario in which the previously-formed DCBH can provide the necessary radiation field for the formation of additional ones. Using one-zone model and the simulated DCBH Spectral Energy Distributions (SEDs) filtered through absorbing gas initially having column density $N_{\rm H}$, we derive the critical field intensity, $J_{\rm LW}^{\rm crit}$, to suppress $\rm H_2$ formation and cooling. For the SED model with $N_{\rm H}=1.3\times10^{25}$ cm$^{-2}$, $8.0\times10^{24}$ cm$^{-2}$ and $5.0\times10^{24}$ cm$^{-2}$, we obtain $J_{\rm LW}^{\rm crit}\approx22$, 35 and 54, all much smaller than the critical field intensity for normal star-forming galaxies ($J_{\rm LW}^{\rm crit}\simgt 1000$). X-ray photons from previously-formed DCBHs build up a high-$z$ X-ray background (XRB) that may boost the $J_{\rm LW}^{\rm crit}$. However, we find that in the three SED models $J_{\rm LW}^{\rm crit}$ only increases to $\approx80$, 170 and 390 respectively even when $\dt{\rho}_\bullet$ reaches the maximum value allowed by the present-day XRB level ($0.22, 0.034, 0.006~M_\odot$yr$^{-1}$Mpc$^{-3}$), still much smaller than the galactic value. Although considering the XRB from first galaxies may further increase $J_{\rm LW}^{\rm crit}$, we conclude that our investigation supports a scenario in which DCBH may be more abundant than predicted by models only including galaxies as external radiation sources., Comment: 18 pages, 14 figures, 5 tables, ApJ in press

We combine the output of hydrodynamical simulations of Population III star cluster formation with stellar evolution models, and calculate the evolution of protostars experiencing variable mass accretion rates due to interactions within a massive disc. We find that the primordial protostars are extended ‘fluffy’ objects for the bulk of their pre-main-sequence lifetimes. Accretion luminosity feedback from such objects is high, but, as shown in previous work, it has a minimal effect on the star cluster. The extended radii of the protostars, combined with the observation of close encounters in the simulations, suggest that mergers will occur in such systems. Furthermore, mass transfer between close protostellar binaries with extended radii could lead to massive tight binaries, which are a possible progenitor of gamma-ray bursts.

The relative importance of metals and dust grains in the formation of the first low-mass stars has been a subject of debate. The recently discovered Galactic halo star SDSS J102915+172927 has a mass less than 0.8 M⊙ and a metallicity of Z= 4.5 × 10−5 Z⊙. We investigate the origin and properties of this star by reconstructing the physical conditions in its birth cloud. We show that the observed elemental abundance trend of SDSS J102915+172927 can be well fitted by the yields of core-collapse supernovae (SNe) with metal-free progenitors of 20 and 35 M⊙. Using these selected SN explosion models, we compute the corresponding dust yields and the resulting dust depletion factor taking into account the partial destruction by the SN reverse shock. We then follow the collapse and fragmentation of a star-forming cloud enriched by the products of these SN explosions at the observed metallicity of SDSS J102915+172927. We find that 0.05–0.1 M⊙ mass fragments, which then lead to the formation of low-mass stars, can occur provided that the mass fraction of dust grains in the birth cloud exceeds 0.01 of the total mass of metals and dust. This, in turn, requires that at least 0.4 M⊙ of dust condense in the first SNe, allowing for moderate destruction by the reverse shock. If dust formation in the first SNe is less efficient or strong dust destruction does occur, the thermal evolution of the SDSS J102915+172927 birth cloud is dominated by molecular cooling, and only ≥8 M⊙ fragments can form. We conclude that the observed properties of SDSS J102915+172927 support the suggestion that dust must have condensed in the ejecta of the first SNe and played a fundamental role in the formation of the first low-mass stars.

We propose a new scenario for supermassive star (SMS;>10^5Msun) formation in shocked regions of colliding cold accretion flows near the centers of first galaxies. Recent numerical simulations indicate that assembly of a typical first galaxy with virial temperature (~10^4K) proceeds via cold and dense flows penetrating deep to the center, where the supersonic streams collide each other to develop a hot and dense (~10^4K, ~10^3/cc) shocked gas. The post-shock layer first cools by efficient Ly alpha emission and contracts isobarically until 8000K. Whether the layer continues the isobaric contraction depends on the density at this moment: if the density is high enough for collisionally exciting H2 rovibrational levels (>10^4/cc), enhanced H2 collisional dissociation suppresses the gas to cool further. In this case, the layer fragments into massive (>10^5Msun) clouds, which collapse isothermally (~8000K) by the Ly alpha cooling without subsequent fragmentation. As an outcome, SMSs are expected to form and evolve eventually to seeds of supermassive black holes (SMBH). By calculating thermal evolution of the post-shock gas, we delimit the range of post-shock conditions for the SMS formation, which can be expressed as: T>6000K/(n/10^4/cc) for n 5000-6000K for n>10^4/cc, depending somewhat on initial ionization degree. We found that metal enrichment does not affect the above condition for metallicity below 10^-3Zsun if metals are in the gas phase, while condensation of several percent of metals into dust decreases this critical value of metallicity by an order of magnitude. Unlike the previously proposed scenario for SMS formation, which postulates extremely strong ultraviolet radiation to quench H2 cooling, our scenario naturally explains the SMBH seed formation in the assembly process of the first galaxies, even without such a strong radiation.

We explore the minimal conditions which enable the formation of metal-enriched solar and subsolar-mass stars. Using a one-zone semi-analytical model, we accurately follow the chemical and thermal evolution of the gas with the aim of understanding how the initial metal and dust content alters the cooling and fragmentation properties, hence the characteristic stellar mass. We find that in the absence of dust grains, gas fragmentation occurs at densities nH∼ [104–105] cm−3 when the metallicity exceeds Z∼ 10−4 Z⊙. The resulting fragmentation masses are ≥10 M⊙. The inclusion of Fe and Si cooling does not affect the thermal evolution as this is dominated by molecular (mostly OH, H2O and CO) cooling even for metallicities as large as Z= 10−2 Z⊙. The presence of dust is the key driver for the formation of low-mass stars. We focus on three representative core-collapse supernova (SN) progenitors (a Z= 0 star with 20 M⊙ and two Z= 10−4 Z⊙ stars with 20 and 35 M⊙), and consider the effects of reverse shocks of increasing strength: these reduce the depletion factors, fdep=Mdust/(Mdust+Mmet), alter the shape of the grain size distribution function and modify the relative abundances of grain species and metal species in the gas phase. We find that the lowest metallicity at which fragmentation occurs is Z= 10−6 Z⊙ for gas pre-enriched by the explosion of a 20 M⊙ primordial SN (fdep≥ 0.22) and/or by a 35 M⊙, Z= 10−4 Z⊙ SN (fdep≥ 0.26); it is ∼1 dex larger, when the gas is pre-enriched by a Z= 10−4 Z⊙, 20 M⊙ SN (fdep≥ 0.04). Cloud fragmentation depends on the depletion factor and it is suppressed when the reverse shock leads to a too large destruction of dust grains. These features are all consistent with the existence of a minimum dust-to-gas ratio, , above which fragmentation is activated. We derive a simple analytic expression for , which depends on the total grain cross-section per unit mass of dust; for grain composition and properties explored in the present study, . When the dust-to-gas ratio of star-forming clouds exceeds this value, the fragmentation masses range between 0.01 and 1 M⊙, thus enabling the formation of the first low-mass stars.

We study effects of external ionization by cosmic rays (CRs) and X-rays on the thermal evolution of primordial clouds under strong far-ultraviolet (FUV) radiation. A strong FUV radiation dissociates H2 and quenches its cooling. Even in such an environment, a massive cloud with Tvir>10^4 K can contract isothermally at 8000 K by Lyman alpha cooling. This cloud collapses monolithically without fragmentation, and a supermassive star (>10^5 Msun) is believed to form at the center, which eventually evolves to a supermassive black hole (SMBH). However, candidates of FUV sources, including star-forming galaxies, are probably sources of strong CRs and X-rays, as well. We find that the external ionization promotes H2 production and elevates the threshold FUV intensity Jcr needed for the SMBH formation for CR energy density U_CR>10^-14 erg/cm^3 or X-ray intensity J_X>10^-24 erg/s/cm^2/sr/Hz at 1 keV. The critical FUV flux increases in proportion to U_CR^{1/2} (J_X^{1/2}) in the high CR (X-ray, respectively) limit. With the same value of FUV intensity at the Lyman limit (13.6 eV), the H^- photodissociation rate, with threshold of 0.755 eV, increases and the H2 molecules decrease with decreasing effective temperature of the FUV sources T*. The lower value of T* thus results in the lower critical FUV flux at 13.6 eV. Using an empirical relation between intensities of FUV and CR/X-ray from nearby star-forming galaxies, we find that external ionization effect remarkably enhances the critical FUV flux for sources with T* as high as 10^5 K and composed of stars with

In low-metallicity environments, massive stars are more easily formed than in the solar neighborhood. In this article, we see the following examples of low-mass star formation. We first describe the first star formation in the universe and argue that they are typically ordinary-sized massive stars, rather than very massive (> 100M⊙) ones. Next, we see how the metal-enrichment changes the thermal evolution of gas, thereby causing the shift of characteristic stellar mass towards lower mass. Finally, we discuss the possibility of forming supermassive stars in some special conditions in young galaxies.

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

We investigate the effects of the Cosmic Microwave Background (CMB) radiation field on the collapse of prestellar clouds. Using a semi-analytic model to follow the thermal evolution of clouds with varying initial metallicities and dust contents at different redshifts, we study self-consistently the response of the mean Jeans mass at cloud fragmentation to metal line-cooling, dust-cooling and the CMB. In the absence of dust grains, at redshifts z 10 and the fragmentation mass scales are always > 100s of Msun, independent of the initial metallicity. When dust grains are present, sub-solar mass fragments are formed at any redshift for metallicities Z > 10^{-6} Zsun because dust-cooling remains relatively insensitive to the presence of the CMB. When Z > 10^{-3} Zsun, heating of dust grains by the CMB at z > 5 favors the formation of larger masses, which become super-solar when Z > 10^{-2} Zsun and z > 10. Finally, we discuss the implications of our result for the interpretation of the observed abundance patterns of very metal-poor stars in the galactic halo.

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.

We consider the fragmentation mass scale of low-metallicity clouds based on their thermal evolution. Then we present the protostellar evolution in the main accretion phase, and discuss the upper limit on the stellar mass by the stellar feedback.

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

First protostellar cores are young stellar objects in the earliest evolutionary stage. They are hydrostatic objects formed soon after the central portions of star-forming cores become optically thick to dust emission. We consider their characteristics in the emitted radiation, and discuss their evolution with increasing mass of the cores. Particular attention is paid to detailed radiative and chemical processes in the postshock relaxation layer located at the surface of the core, where the majority of radiation is emitted. Most of the radiation is originally emitted in the dust continuum in mid-infrared wavelength (~10-30 micron), which reprocessed to far-infrared with ~100-200 micron. Although some fraction (~0.1) of the radiation energy is emitted in the H2O lines at the accretion shock, most is absorbed and reemitted in the dust continuum in the envelope. The H2O lines account for at most ~1/100 of the observed luminosity. If a cavity is present in the envelope due to outflow or rotation, the dust and H2O line emission in the mid-infrared wavelength from the shock can be observed directly, or as a reflection nebula. Among forthcoming observational facillities, SPICA is the most suitable for detecting either direct or processed radiation from first-core objects., To appear in PASJ vol.59

Observations of quasars at $ z > 6$ suggest the presence of black holes with a few times $\rm 10^9 ~M_{\odot}$. Numerous models have been proposed to explain their existence including the direct collapse which provides massive seeds of $\rm 10^5~M_{\odot}$. The isothermal direct collapse requires a strong Lyman-Werner flux to quench $\rm H_2$ formation in massive primordial halos. In this study, we explore the impact of trace amounts of metals and dust enrichment. We perform three dimensional cosmological simulations for two halos of $\rm > 10^7~M_{\odot}$ with $\rm Z/Z_{\odot}= 10^{-4}-10^{-6}$ illuminated by an intense Lyman Werner flux of $\rm J_{21}=10^5$. Our results show that initially the collapse proceeds isothermally with $\rm T \sim 8000$ K but dust cooling becomes effective at densities of $\rm 10^{8}-10^{12} ~cm^{-3}$ and brings the gas temperature down to a few 100-1000 K for $\rm Z/Z_{\odot} \geq 10^{-6}$. No gravitationally bound clumps are found in $\rm Z/Z_{\odot} \leq 10^{-5}$ cases by the end of our simulations in contrast to the case with $\rm Z/Z_{\odot} = 10^{-4}$. Large inflow rates of $\rm \geq 0.1~M_{\odot}/yr$ are observed for $\rm Z/Z_{\odot} \leq 10^{-5}$ similar to a zero-metallicity case while for $\rm Z/Z_{\odot} = 10^{-4}$ the inflow rate starts to decline earlier due to the dust cooling and fragmentation. For given large inflow rates a central star of $\rm \sim 10^4~M_{\odot}$ may form for $\rm Z/Z_{\odot} \leq 10^{-5}$., Accepted for publication in ApJ, comments are still welcome

We perform a large set of cosmological simulations of early structure formation and follow the formation and evolution of 1540 star-forming gas clouds to derive the mass distribution of primordial stars. The star formation in our cosmological simulations is characterized by two distinct populations, the so-called Population III.1 stars and primordial stars formed under the influence of far ultraviolet (FUV) radiation (Population III.2D stars). In this work, we determine the stellar masses by using the dependences on the physical properties of star-forming cloud and/or the external photodissociating intensity from nearby primordial stars, which are derived from the results of two-dimensional radiation hydrodynamic simulations of protostellar feedback. The characteristic mass of the Pop III stars is found to be a few hundred solar masses at z ~ 25, and it gradually shifts to lower masses with decreasing redshift. At high redshifts z > 20, about half of the star-forming gas clouds are exposed to intense FUV radiation and thus give birth to massive Pop III.2D stars. However, the local FUV radiation by nearby Pop III stars becomes weaker at lower redshifts, when typical Pop III stars have smaller masses and the mean physical separation between the stars becomes large owing to cosmic expansion. Therefore, at z < 20, a large fraction of the primordial gas clouds host Pop III.1 stars. At z =< 15, the Pop III.1 stars are formed in relatively cool gas clouds due to efficient radiative cooling by H_2 and HD molecules; such stars have masses of a few x 10 Msun. Since the stellar evolution and the final fate are determined by the stellar mass, Pop III stars formed at different epochs play different roles in the early universe., 22 pages, 19 figures, published in MNRAS

We investigate the role of the H_2^+ channel on H_2 molecule formation during the collapse of primordial gas clouds immersed in strong radiation fields which are assumed to have the shape of a diluted black-body spectra with temperature T_rad. Since the photodissociation rate of H_2^+ depends on its level population, we take full account of the vibrationally-resolved H_2^+ kinetics. We find that in clouds under soft but intense radiation fields with spectral temperature T_rad < 7000 K, the H_2^+ channel is the dominant H_2 formation process. On the other hand, for harder spectra with T_rad > 7000 K, the H^- channel takes over H_2^+ in the production of molecular hydrogen. We calculate the critical radiation intensity needed for supermassive star formation by direct collapse and examine its dependence on the H_2^+ level population. Under the assumption of local thermodynamic equilibrium (LTE) level population, the critical intensity is underestimated by a factor of a few for soft spectra with T_rad < 7000 K. For harder spectra, the value of the critical intensity is not affected by the level population of H_2^+. This result justifies previous estimates of the critical intensity assuming LTE populations since radiation sources like young and/or metal-poor galaxies are predicted to have rather hard spectra., 9 pages, 6 figures, submitted to MNRAS

We study dissipation process of magnetic fields in the metallicity range $0-1 Z_{\odot}$ for contracting prestellar cloud cores. By solving non-equilibrium chemistry for important charged species including charged grains, we evaluate the drift velocity of the magnetic-field lines with respect to the gas. We find that the magnetic flux dissipates in the density range $10^{12}{\rm cm^{-3}} \lesssim n_{\rm H} \lesssim 10^{17}{\rm cm^{-3}}$ for the solar-metallicity case at the scale of the core, which is assumed to be the Jeans scale. The dissipation density range becomes narrower for lower metallicity. The magnetic field is always frozen to the gas below metallicity $\lesssim 10^{-7}-10^{-6}Z_\odot$, depending on the ionization rate by cosmic rays and/or radioactivity. With the same metallicity, the dissipation density range becomes wider for lower ionization rate. The presence of such a dissipative regime is expected to cause various dynamical phenomena in protostellar evolution such as the suppression of jet/outflow launching and fragmentation of the circumstellar disks depending on the metallicity., Comment: 13 pages, 7 figures, ApJ accepted

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 analytically investigate the formation of an HII region in the accreting envelope of a newborn star. Special care is taken to examine the role of ionizing radiation force. This effect modifies velocity and density distributions and thereby affects the expansion of the HII region. As a result, the upper limit of the stellar mass imposed by the growth of an HII region around a forming star is increased by a larger factor than the previous estimate. In particular, for a star forming out of metal-free gas, this mechanism does not impose a firm upper limit on its mass., Comment: 14 pages, 3 figures. MNRAS in press

We review formation process of the first stars. After forming by fragmentation of a first . object, a primordial prestellar core (∼ 10 3 M O .) collapses in a self-similar fashion until the formation of a protostar at the number density of about 10 2 2 cm - 3 . The end product of the protostellar collapse is a tiny protostar (∼ 10- 3 M O .) surrounded by a large amount of gravitationally unstable matter (∼ 10 3 M⊙).Subsequently, the protostar grows in mass by orders of magnitude owing to accretion of the ambient matter. The accretion rate M is very high (10 - ( 2 - 3 ) M O ./Yr) for the first stars, because of high prestellar temperature (> 300K) owing to H 2 cooling in the primordial gas. During the accretion phase, there are a few distinctive evolutionary stages; the adiabatic accretion phase (M, 4 x 10 - 3 M O . /yr),depending on the value of the accretion rate. Under a realistic accretion rate proposed by Abel et al. [Science 295 (2002), 93]. the actual evolution resembles the case of small M. Since the protostar is shrouded by an optically thick envelope throughout the main accretion phase, the hot stellar surface is not visible from outside until the protostellar mass grows to about 5003M O .. During this period, the effective temperature remains about 6000K for a wide range of the luminosity.

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.