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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

We study star cluster formation at low metallicities of $Z/Z_\odot=10^{-4}$--$10^{-1}$ using three-dimensional hydrodynamics simulations. Particular emphasis is put on how the stellar mass distribution is affected by the cosmic microwave background radiation (CMB), which sets the temperature floor to the gas. Starting from the collapse of a turbulent cloud, we follow the formation of a protostellar system resolving $\sim$au scale. In relatively metal-enriched cases of $Z/Z_\odot \gtrsim 10^{-2}$, where the mass function resembles the present-day one in the absence of the CMB, high temperature CMB suppresses cloud fragmentation and reduces the number of low-mass stars, making the mass function more top-heavy than in the cases without CMB heating at $z\gtrsim10$. In lower-metallicity cases with $Z/Z_\odot \lesssim 10^{-3}$, where the gas temperature is higher than the CMB value due to inefficient cooling, the CMB has only a minor impact on the mass distribution, which is top-heavy regardless of the redshift. In cases either with a low metallicity of $Z/Z_\odot \lesssim 10^{-2}$ or at a high redshift $z\gtrsim10$, the mass spectrum consists of a low-mass Salpeter-like component, peaking at $0.1~M_\odot$, and a top-heavy component with $10$--$50~M_\odot$, with the fraction in the latter increasing with increasing redshift. In galaxies forming at $z\gtrsim10$, the major targets of the future instruments including JWST, CMB heating makes the stellar mass function significantly top-heavy, enhancing the number of supernova explosions by a factor of $1.4$ ($2.8$) at $z=10$ ($20$, respectively) compared to the prediction by Chabrier initial mass function when $Z/Z_\odot=0.1$., 18 pages, 12 figures, MNRAS submitted

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

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

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

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

Growth of the black holes (BHs) from the seeds to supermassive BHs (SMBHs, $\sim\!10^9\,M_\odot$) is not understood, but the mass accretion must have played an important role. We performed two-dimensional radiation hydrodynamics simulations of line-driven disc winds considering the metallicity dependence in a wide range of the BH mass, and investigated the reduction of the mass accretion rate due to the wind mass loss. Our results show that denser and faster disc winds appear at higher metallicities and larger BH masses. The accretion rate is suppressed to $\sim\! 0.4$--$0.6$ times the mass supply rate to the disc for the BH mass of $M_{\rm BH}\gtrsim 10^5\,M_{\odot}$ in high-metallicity environments of $Z\gtrsim Z_\odot$, while the wind mass loss is negligible when the metallicity is sub-solar ($\sim 0.1Z_\odot$). By developing a semi-analytical model, we found that the metallicity dependence of the line force and the BH mass dependence of the surface area of the wind launch region are the cause of the metallicity dependence ($\propto\! Z^{2/3}$) and BH mass dependencies ($\propto\! M_{\rm BH}^{4/3}$ for $M_{\rm BH}\leq 10^6\,M_\odot$ and $\propto\! M_{\rm BH}$ for $M_{\rm BH}\geq 10^6\,M_\odot$) of the mass-loss rate. Our model suggests that the growth of BHs by the gas accretion effectively slows down in the regime $\gtrsim 10^{5}M_\odot$ in metal-enriched environments $\gtrsim Z_\odot$. This means that the line-driven disc winds may have an impact on late evolution of SMBHs., 11 pages, 7 figures, accepted for publication in MNRAS

Observations of hyper-luminous quasars at $z>6$ reveal the rapid growth of supermassive black holes (SMBHs $>10^9 \rm M_{\odot}$) whose origin is still difficult to explain. Their progenitors may have formed as remnants of massive, metal free stars (light seeds), via stellar collisions (medium-weight seeds) and/or massive gas clouds direct collapse (heavy seeds). In this work we investigate for the first time the relative role of these three seed populations in the formation of $z>6$ SMBHs within an Eddington-limited gas accretion scenario. To this aim, we implement in our semi-analytical data-constrained model a statistical description of the spatial fluctuations of Lyman-Werner (LW) photo-dissociating radiation and of metal/dust enrichment. This allows us to set the physical conditions for BH seeds formation, exploring their relative birth rate in a highly biased region of the Universe at $z>6$. We find that the inclusion of medium-weight seeds does not qualitatively change the growth history of the first SMBHs: although less massive seeds ($ 15$., (21 pages, 18 figures, 2 tables. Accepted for publication in MNRAS)

We perform high-resolution cosmological hydrodynamic simulations to study the formation of the first galaxies that reach the masses of $10^{8-9}~h^{-1}~M_\odot$ at $z=9$. The resolution of the simulations is high enough to resolve minihaloes and allow us to successfully pursue the formation of multiple Population (Pop) III stars, their supernova (SN) explosions, resultant metal-enrichment of the inter-galactic medium (IGM) in the course of the build-up of the system. Metals are ejected into the IGM by multiple Pop III SNe, but some of the metal-enriched gas falls back onto the halo after $\gtrsim 100~\rm Myr$. The star formation history of the first galaxy depends sensitively on the initial mass function (IMF) of Pop III stars. The dominant stellar population transits from Pop III to Pop II at $z\sim 12-15$ in the case of power-law Pop III IMF, ${\rm d}n/{\rm d}M \propto M^{-2.35}$ with the mass range $10-500~M_\odot$. At $z\lesssim 12$, stars are stably formed in the first galaxies with a star formation rate of $\sim 10^{-3}$-$10^{-1}~M_\odot/{\rm yr}$. In contrast, for the case with a flat IMF, gas-deprived first galaxies form due to frequent Pop III pair-instability SNe, resulting in the suppression of subsequent Pop II star formation. In addition, we calculate UV continuum, Ly$\alpha$- and H$\alpha$-line fluxes from the first galaxies. We show that the James Webb Space Telescope will be able to detect both UV continuum, Ly$\alpha$ and H$\alpha$ line emission from first galaxies with halo mass $\gtrsim 10^{9}~M_\odot$ at $z \gtrsim 10$., Comment: 14 pages, 15 figures, accepted for publication in MNRAS

Recent gravitational wave (GW) observations by LIGO/Virgo show evidence for hierarchical mergers, where the merging BHs are the remnants of previous BH merger events. These events may carry important clues about the astrophysical host environments of the GW sources. In this paper, we present the distributions of the effective spin parameter ($\chi_\mathrm{eff}$), the precession spin parameter ($\chi_\mathrm{p}$), and the chirp mass ($m_\mathrm{chirp}$) expected in hierarchical mergers. Under a wide range of assumptions, hierarchical mergers produce (i) a monotonic increase of the average of the typical total spin for merging binaries, which we characterize with ${\bar \chi}_\mathrm{typ}\equiv \overline{(\chi_\mathrm{eff}^2+\chi_\mathrm{p}^2)^{1/2}}$, up to roughly the maximum $m_\mathrm{chirp}$ among first-generation (1g) BHs, and (ii) a plateau at ${\bar \chi}_\mathrm{typ}\sim 0.6$ at higher $m_\mathrm{chirp}$. We suggest that the maximum mass and typical spin magnitudes for 1g BHs can be estimated from ${\bar \chi}_\mathrm{typ}$ as a function of $m_\mathrm{chirp}$. The GW data observed in LIGO/Virgo O1--O3a prefers an increase in ${\bar \chi}_\mathrm{typ}$ at low $m_\mathrm{chirp}$, which is consistent with the growth of the BH spin magnitude by hierarchical mergers, at $\sim 2 \sigma$ confidence. A Bayesian analysis suggests that 1g BHs have the maximum mass of $\sim 15$--$30\,M_\odot$ if the majority of mergers are of high-generation BHs (not among 1g-1g BHs), which is consistent with mergers in active galactic nucleus disks and/or nuclear star clusters, while if mergers mainly originate from globular clusters, 1g BHs are favored to have non-zero spin magnitudes of $\sim 0.3$. We also forecast that signatures for hierarchical mergers in the ${\bar \chi}_\mathrm{typ}$ distribution can be confidently recovered once the number of GW events increases to $\gtrsim O(100)$., Comment: 20 pages, 10 figures, accepted 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 astrophysical origin of gravitational wave (GW) transients is a timely open question in the wake of discoveries by LIGO/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the eccentricity distribution of BH mergers in AGN disks. We find that eccentricity is mainly due to binary-single (BS) interactions, which lead to most BH mergers in AGN disks having a significant eccentricity at $0.01\,\mathrm{Hz}$, detectable by LISA. If BS interactions occur in isotropic-3D directions, then $8$--$30\%$ of the mergers in AGN disks will have eccentricities at $10\,\mathrm{Hz}$ above $e_{10\,\rm Hz}\gtrsim 0.03$, detectable by LIGO/Virgo/KAGRA, while $5$--$17\%$ of mergers have $e_{10\,\rm Hz}\geq 0.3$. On the other hand, if BS interactions are confined to the AGN-disk plane due to torques from the disk, with 1-20 intermediate binary states during each interaction, or if BHs can migrate to $\lesssim10^{-3}\,\mathrm{pc}$ from the central supermassive black hole, then $10$--$70\%$ of the mergers will be highly eccentric ($e_{10\,\rm Hz} \geq 0.3$), consistent with the possible high eccentricity in GW190521., 9 pages, 3 figures, accepted in ApJL

We study the formation of very metal-poor stars under protostellar radiative feedback effect. We use cosmological simulations to identify low-mass dark matter halos and star-forming gas clouds within them. We then follow protostar formation and the subsequent long-term mass accretion phase of over one million years using two-dimensional radiation-hydrodynamics simulations. We show that the critical physical process that sets the final mass is formation and expansion of a bipolar HII region. The process is similar to the formation of massive primordial stars, but radiation pressure exerted on dust grains also contributes to halting the accretion flow in the low-metallicity case. We find that the net feedback effect in the case with metallicity $Z = 10^{-2}~Z_{\odot}$ is stronger than in the case with $Z \sim 1~Z_{\odot}$. With decreasing metallicity, the radiation pressure effect becomes weaker, but photoionization heating of the circumstellar gas is more efficient owing to the reduced dust attenuation. In the case with $Z = 10^{-2}~Z_{\odot}$, the central star grows as massive as 200 solar-masses, similarly to the case of primordial star formation. We conclude that metal-poor stars with a few hundred solar masses can be formed by gas accretion despite the strong radiative feedback., 18 pages, 13 figures, accepted for publication in MNRAS

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

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]

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.

One of the major goals of next-generation space-borne and ground-based telescopes is to detect and characterize the first galaxies that were in place in the first few hundred million years after the big bang. We study the spectral energy distribution (SED) of the first galaxies and discuss the prospects for detection and identification. We consider very young star-forming galaxies at $z=15$ and incorporate the contribution from pre-main-sequence (PMS) stars. Unlike in the present-day galaxies, primordial protostars are not embedded in dusty gas clouds, and hence the light from them can be visible at a wide range of wavelengths. We use MESA code to follow the PMS evolution and use the BT-Settl model to calculate the SED of individual PMS stars. We show that PMS stars contribute to boost the flux in the mid-infrared, and that the galaxy SED at very early evolutionary phases is overall redder than at later phases. The infrared flux contribution is comparable to that caused by emission lines powered by massive stars. We argue that the contribution from PMS stars is important for characterizing young galaxies in the early Universe and also for target selection with future deep galaxy surveys., 5 pages, 4 figures, published online in MNRAS letters

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

Supermassive stars (SMSs) with mass $\sim10^{5}~\rm{M}_{\odot}$ are promising candidates for the origin of supermassive black holes observed at redshift $\gtrsim6$. They are supposed to form as a result of rapid accretion of primordial gas, although it can be obstructed by the time variation caused by circum-stellar disc fragmentation due to gravitational instability. To assess the occurrence of fragmentation, we study the structure of marginally gravitationally unstable accretion discs, by using a steady one-dimensional thin disc model with detailed treatment of chemical and thermal processes. Motivated by two SMS formation scenarios, i.e., those with strong ultraviolet radiation background or with large velocity difference between the baryon and the dark matter, we consider two types of flows, i.e., atomic and molecular flows, respectively, for a wide range of the central stellar mass $10-10^5~\rm{M}_{\odot}$ and the accretion rate $10^{-3}-1~\rm{M}_{\odot}~\rm{yr}^{-1}$. In the case of a mostly atomic gas flowing to the disc outer boundary, the fragmentation condition is expressed as the accretion rate being higher than the critical value of $10^{-1}~\rm{M}_{\odot}~\rm{yr}^{-1}$ regardless of the central stellar mass. On the other hand, in the case of molecular flows, there is a critical disc radius outside of which the disc becomes unstable. Those conditions appears to be marginally satisfied according to numerical simulations, suggesting that disc fragmentation can be common during SMS formation., 17 pages, 10 figures, accepted for publication in MNRAS

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 investigate the upper stellar mass limit set by radiative feedback by the forming star with various accretion rates and metallicities. To this end, we numerically solve the structures of both a protostar and its surrounding accretion envelope assuming a spherical symmetric and steady flow. The optical depth of the dust cocoon, a dusty part of the accretion envelope, differs among the direct light from the stellar photosphere and the diffuse light re-emitted as dust thermal emission. As a result, varying the metallicity qualitatively changes the way that the radiative feedback suppresses the accretion flow. With a fixed accretion rate of $10^{-3}M_{\odot} {\rm yr^{-1}}$, the both direct and diffuse lights jointly operate to prevent the mass accretion at $Z \gtrsim 10^{-1}Z_{\odot}$. At $Z \lesssim 10^{-1}Z_{\odot}$, the diffuse light is no longer effective, and the direct light solely limits the mass accretion. At $Z \lesssim 10^{-3}Z_{\odot}$, the HII region formation plays an important role in terminating the accretion. The resultant upper mass limit increases with decreasing metallicity, from a few $\times~10~M_\odot$ to $\sim 10^3~M_\odot$ over $Z = 1Z_{\odot} - 10^{-4}~Z_\odot$. We also illustrate how the radiation spectrum of massive star-forming cores changes with decreasing metallicity. First, the peak wavelength of the spectrum, which is located around $30 \mu {\rm m}$ at $1Z_{\odot}$, shifts to $< 3 \mu {\rm m}$ at $Z \lesssim 0.1 Z_\odot$. Second, a characteristic feature at $10 \mu \rm{m}$ due to the amorphous silicate band appears as a dip at $1Z_{\odot}$, but changes to a bump at $Z \lesssim 0.1 Z_{\odot}$. Using these spectral signatures, we can search massive accreting protostars in nearby low-metallicity environments with up-coming observations., Comment: 21 pages, 20 figures, accepted for publication in MNRAS

Fragmentation of filaments into dense cores is thought to be an important step in forming stars. The bar-mode instability of spherically collapsing cores found in previous linear analysis invokes a possibility of re-fragmentation of the cores due to their ellipsoidal (prolate or oblate) deformation. To investigate this possibility, here we perform three-dimensional self-gravitational hydrodynamics simulations that follow all the way from filament fragmentation to subsequent core collapse. We assume the gas is polytropic with index \gamma, which determines the stability of the bar-mode. For the case that the fragmentation of isolated hydrostatic filaments is triggered by the most unstable fragmentation mode, we find the bar mode grows as collapse proceeds if \gamma < 1.1, in agreement with the linear analysis. However, it takes more than ten orders-of-magnitude increase in the central density for the distortion to become non-linear. In addition to this fiducial case, we also study non-fiducial ones such as the fragmentation is triggered by a fragmentation mode with a longer wavelength and it occurs during radial collapse of filaments and find the distortion rapidly grows. In most of astrophysical applications, the effective polytropic index of collapsing gas exceeds 1.1 before ten orders-of-magnitude increase in the central density. Thus, supposing the fiducial case of filament fragmentation, re-fragmentation of dense cores would not be likely and their final mass would be determined when the filaments fragment., Comment: 13 pages, 11 figures, 4 tables, submitted to MNRAS

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

Supermassive stars (SMS; ~ 10^5 M_sun) formed from metal-free gas in the early Universe attract attention as progenitors of supermassive black holes observed at high redshifts. To form SMSs by accretion, central protostars must accrete at as high rates as ~ 0.1-1 M_sun/yr. Such protostars have very extended structures with bloated envelopes, like super-giant stars, and are called super-giant protostars (SGPSs). Under the assumption of hydrostatic equilibrium, SGPSs have density inverted layers, where the luminosity becomes locally super-Eddington, near the surface. If the envelope matter is allowed to flow out, however, a stellar wind could be launched and hinder the accretion growth of SGPSs before reaching the supermassive regime. We examine whether radiation-driven winds are launched from SGPSs by constructing steady and spherically symmetric wind solutions. We find that the wind velocity does not reach the escape velocity in any case considered. This is because once the temperature falls below ~ 10^4 K, the opacity plummet drastically owing to the recombination of hydrogen and the acceleration ceases suddenly. This indicates that, in realistic non-steady cases, even if outflows are launched from the surface of SGPSs, they would fall back again. Such a "wind" does not result in net mass loss and does not prevent the growth of SGPSs. In conclusion, SGPSs will grow to SMSs and eventually collapse to massive BHs of ~ 10^5 M_sun, as long as the rapid accretion is maintained., 11 pages, 13 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 present coupled stellar evolution (SE) and 3D radiation-hydrodynamic (RHD) simulations of the evolution of primordial protostars, their immediate environment, and the dynamic accretion history under the influence of stellar ionizing and dissociating UV feedback. Our coupled SE-RHD calculations result in a wide diversity of final stellar masses covering 10 Msun $\lesssim M_* \lesssim$ 1000 Msun. The formation of very massive ($\gtrsim$ 250 Msun) stars is possible under weak UV feedback, whereas ordinary massive (a few x 10 Msun) stars form when UV feedback can efficiently halt the accretion. This may explain the peculiar abundance pattern of a Galactic metal-poor star recently reported by Aoki et al. (2014), possibly the observational signature of very massive precursor primordial stars. Weak UV feedback occurs in cases of variable accretion, in particular when repeated short accretion bursts temporarily exceed 0.01 Msun/yr, causing the protostar to inflate. In the bloated state, the protostar has low surface temperature and UV feedback is suppressed until the star eventually contracts, on a thermal adjustment timescale, to create an HII region. If the delay time between successive accretion bursts is sufficiently short, the protostar remains bloated for extended periods, initiating at most only short periods of UV feedback. Disk fragmentation does not necessarily reduce the final stellar mass. Quite the contrary, we find that disk fragmentation enhances episodic accretion as many fragments migrate inward and are accreted onto the star, thus allowing continued stellar mass growth under conditions of intermittent UV feedback. This trend becomes more prominent as we improve the resolution of our simulations. We argue that simulations with significantly higher resolution than reported previously are needed to derive accurate gas mass accretion rates onto primordial protostars., 28 pages, 27 figures, accepted for publication in ApJ. Movies are available at https://www.youtube.com/playlist?list=PLy0BOLTBcHhb-Q6cG8hwmjUEvTzcH4AMF

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.