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The thermal evolution of low metallicity gas during the protostellar collapse is described. By using this result, the fragmentation mass scale is evaluated. Particular attention is paid to the critical metallicity where transition from very massive to low‐mass star formation occurs. For this transition, metals must be in a form of dust. Its cooling enables low‐mass fragmentataion for metallicity higher than [M/H] = −6–−51. However, there is a pocket in the metallicity range −5≲[M/H]≲−4 where the low‐mass fragmentation is prohibited by sudden heat injection due to three‐body H2 formation. This may explain observed scarcity of ultra metal‐poor stars in this metallicity range, as well as a clear cutoff at metallicity of [M/H]≃−4, provided that the dust is already present in such low metallicity environments.

We use cosmological hydrodynamic simulations with unprecedented resolution to study the formation of primordial stars in an ionized gas at high redshifts. Our approach includes all the relevant atomic and molecular physics to follow the thermal evolution of a prestellar gas cloud to very high densities of ~10^{18} cm^{-3}. We locate a star-forming gas cloud within a reionized region in our cosmological simulation. The first run-away collapse is triggered when the gas cloud's mass is ~40 Msun. We show that the cloud core remains stable against chemo-thermal instability and also against gravitational deformation throughout its evolution. Consequently, a single proto-stellar seed is formed, which accretes the surrounding hot gas at the rate ~10^{-3} Msun/year. We carry out proto-stellar evolution calculations using the inferred accretion rate. The resulting mass of the star when it reaches the zero-age main sequence is M_ZAMS ~40 Msun. We argue that, since the obtained M_ZAMS is as large as the mass of the collapsing parent cloud, the final stellar mass should be close to this value. Such massive, rather than exceptionally massive, primordial stars are expected to cause early chemical enrichment of the Universe by exploding as black hole-forming super/hypernovae, and may also be progenitors of high redshift gamma-ray bursts. The elemental abundance patterns of recently discovered hyper metal-poor stars suggest that they might have been born from the interstellar medium that was metal-enriched by supernovae of these massive primordial stars., Revised version. To appear in ApJL

We study the formation of the first generation of stars in the standard cold dark matter model, using a very high-resolution hydordynamic simulations. Our simulation achieves a dynamic range of 10^{10} in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to n = 10^{16}/cc without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. All the relevant atomic and molecular cooling and heating processes, including cooling by collision-induced continuum emission, are implemented. For calculating optically thick H2 cooling at high densities, we use the Sobolev method. To examine possible gas fragmentation owing to thermal instability, we compute explicitly the growth rate of isobaric perturbations. We show that the cloud core does not fragment in either the low-density or high-density regimes. We also show that the core remains stable against gravitational deformation and fragmentation. We obtain an accurate gas mass accretion rate within a 10 Msun innermost region around the protostar. The protostar is accreting the surrounding hot gas at a rate of 0.001-0.01 Msun/yr. From these findings we conclude that primordial stars formed in early minihalos are massive. We carry out proto-stellar evolution calculations using the obtained accretion rate. The resulting mass of the first star is M_ZAMS = 60-100 Msun, with the exact mass dependent on the actual accretion rate., 27 pages, 13 embedded figures. Revised version

The protostellar jets driven by the formation of the first stars are studied by using MHD nested grid simulations. Starting from a slowly rotating spherical cloud of 5.1 times 10^4 Msun permeated by a uniform magnetic field, we follow the evolution from the central number density n = 10^3 cm^-3 to n simeq 10^23 cm^-3. We calculate four models that differ in initial magnetic field strengths and angular velocities. In all models, protostars of simeq 10^-3 Msun are formed at n simeq 10^22 cm^-3 in accordance with one-dimensional calculations. By this epoch, the magnetic flux density is amplified by 10 orders of magnitude from the initial value. Consequently, the formed protostar possesses the magnetic field of \sim 10^6 G that is much larger than the flux density of the present counterparts, reflecting the fact that the dissipation of a magnetic field is ineffective in primordial gas clouds. If the initial magnetic field B > 10^-9 (n/10^3 cm^-3)^2/3 G, the protostellar jet is launched and its velocities reaches \sim 70 km s^-1 by the time the protostellar mass becomes (4-6) times 10^-3 Msun, and a fraction (3-10%) of the accreting matter is blown off from the central region. Owing to the interaction of these ejecta with surrounding matter, expanding bow shocks are created at both heads of the jet. If this jet continues to sweep out the surrounding gas that otherwise accretes onto the central star or circumstellar disk, the final mass of the first star can be substantially reduced. In addition, dense post-shock regions behind the bow shocks are expected to promote the chemical reactions (formation of H_2 and HD), and this provides possible environments for subsequent low-mass star formation in the early universe., 12 pages, 2 figures, Submitted to ApJL, For high resolution figures see this http://www2.scphys.kyoto-u.ac.jp/~machidam/primordial/MS20707v1.pdf

Dynamical collapse and fragmentation of low-metallicity cloud cores is studied using three-dimensional hydrodynamical calculations, with particular attention devoted whether the cores fragment in the dust-cooling phase or not. The cores become elongated in this phase, being unstable to non-spherical perturbation due to the sudden temperature decrease. In the metallicity range of 10^{-6}-10^{-5}Z_sun, cores with an initial axis ratio >2 reach a critical value of the axis ratio (>30) and fragment into multiple small clumps. This provides a possible mechanism to produce low-mass stars in ultra-metal-poor environments., 4 pages, 3 figures, ApJ Letters in press

We examine observational characteristics of multi-phase turbulent flows in the diffuse interstellar medium (ISM) using a synthetic radiation field of atomic and molecular lines. We consider the multi-phase ISM which is formed by thermal instability under the irradiation of UV photons with moderate visual extinction $A_V\sim 1$. Radiation field maps of C$^{+}$, C$^0$, and CO line emissions were generated by calculating the non-local thermodynamic equilibrium (nonLTE) level populations from the results of high resolution hydrodynamic simulations of diffuse ISM models. By analyzing synthetic radiation field of carbon lines of [\ion{C}{2}] 158 $\mu$m, [\ion{C}{1}] $^3P_2-^3P_1$ (809 GHz), $^3P_1-^3P_0$ (492 GHz), and CO rotational transitions, we found a high ratio between the lines of high- and low-excitation energies in the diffuse multi-phase interstellar medium. This shows that simultaneous observations of the lines of warm- and cold-gas tracers will be useful in examining the thermal structure, and hence the origin of diffuse interstellar clouds., Comment: 16 pages, 10 figures : accepted for publication in ApJ. PDF version with high resolution figures is available (http://yso.mtk.nao.ac.jp/~ymasako/paper/ms_hires.pdf)

We study formation of molecules in primordial prestellar clumps and evaluate the line luminosities to assess detectability by next-generation facilities. If the initial H_2 fraction is sufficiently high, HD becomes an important coolant in the clumps. The luminosity from such HD cooling clumps is lower than that from H_2 cooling ones because of lower temperature ( Li + H_2. LiH does not become an important coolant in any density range. The luminous emission lines from the prestellar cores include H_2 rovibrational lines: 1-0 Q(1), 1-0 O(3), 1-0 O(5), and pure rotational lines: 0-0 S(3), 0-0 S(4), 0-0 S(5). The next-generation facilities SPICA and JWST are able to detect H_2 emission in a large pre-galactic cloud that forms metal-free stars at a high rate of \sim 10^3 M_s/yr at redshift z, 32 pages, 13 figures, 3 tables, accepted PASJ

We study the evolution of gas in HII regions around the first stars after the death of the exciting stars. If the first star in a small halo dies without supernova (SN), subsequent star formation is possible in the same halo. We thus investigate the effect of ionization of the gas on subsequent star formation within small halos in the early universe using one-dimensional hydrodynamics with spherical symmetry along with non-equilibrium primordial gas chemistry. We find that the enhanced electron fraction facilitates the formation of molecular hydrogen at the cores of these halos. The low temperature circumstances produced by the H_2 cooling is suitable for HD formation and the resultant cooling further drops the temperature below 100 K. Consequently, low-mass stars with primordial abundances can form even in a small halo. After accreting the interstellar metals, these stars might resemble low-mass ultra metal-poor stars discovered in the present Galactic halo., 9 pages, 6 figures, accepted for publication in MNRAS

We evaluate the broadband afterglow emission of very high redshift gamma-ray bursts (GRBs) using standard relativistic blastwave models with both forward and reverse shock components. For a broad range of parameters, a generic property for GRBs at redshifts $z \sim$ 5--30 is that the emission peaks in the millimeter to far-infrared bands with milli-Jansky flux levels, first at a few hours after the burst due to the reverse shock, and then again for several days afterwards with somewhat lower flux due to the forward shock. The radio, submillimeter and infrared continuum emission should be readily detectable out to $z \ga 30$ by the Atacama Large Millimeter Array (ALMA), Extended Very Large Array (EVLA), Square Kilometer Array (SKA) and other facilities. For relatively bright bursts, spectroscopic measurements of molecular and atomic absorption lines due to ambient protostellar gas may be possible. Utilizing models of primordial protostellar clouds, we show that under certain conditions, appreciable absorption may be caused by HD rotational transitions even in metal-free environments. After sufficient metal enrichment, absorption from CO rotational transitions and [OI] fine-structure transitions can also become strong. With appropriate observing strategies in combination with optical telescopes, ALMA and/or SKA may be able to detect such lines, offering a unique probe of physical conditions in individual Pop III and early Pop II star forming regions. We also remark on potential near-infrared absorption features due to electronic transitions of H$_2$., MNRAS, in press; 16 pages, 11 figures

We study the H2 cooling emission of forming galaxies, and discuss their observability using the future infrared facility SAFIR. Forming galaxies with mass >10^11 Msun emit most of their gravitational energy liberated by contraction in molecular hydrogen line radiation, although a large part of thermal energy at virialization is radiated away by the H Ly alpha emission. For more massive objects, the degree of heating due to dissipation of kinetic energy is so great that the temperature does not drop below 10^4 K and the gravitational energy is emitted mainly by the Ly alpha emission. Therefore, the total H2 luminosity attains the peak value of about 10^42 ergs/s for forming galaxies whose total mass 10^11 Msun. If these sources are situated at redshift z=8, they can be detected by rotational lines of 0-0S(3) at 9.7 micron and 0-0S(1) at 17 micron by SAFIR. An efficient way to find such H2 emitters is to look at the Ly alpha emitters, since the brightest H2 emitters are also luminous in the Ly alpha emission., 20 pages, 7 figures, ApJ accepted

Recent studies suggest that the initial mass function (IMF) of the first stars was likely to be extremely top-heavy, unlike what is observed at present. We propose a scenario to generate fragmentation to lower masses once the first massive stars have formed and derive constraints on the primordial IMF. We estimate the mass fraction of pair-unstable supernovae, shown to be the dominant sources of the first heavy elements. These metals enrich the gas up to about $10^{-5}$ solar metallicity, when a transition to efficient cooling-driven fragmentation occurs producing 1 solar mass clumps. We argue that the remaining fraction of the first stars ends up in 100 solar mass VMBHs (Very Massive Black Holes). We obtain constraints on the fraction of first stars that contribute to the initial metal enrichment and the transition redshift for primordial IMF away from a top-heavy one, by making various assumptions about the fate of these VMBHs at late times. We conclude with a discussion of several hitherto unexplored implications of a high-mass dominated star formation mode in the early Universe., revised version, Fig. 4 modified, abbreviated abstract, matches accepted version in ApJ, ApJ in press

The thermal and chemical evolution of gravitationally collapsing protostellar clouds is investigated, focusing attention on their dependence on metallicity. Calculations are carried out for a range of metallicities spanning the local interstellar value to zero. During the time when clouds are transparent to continuous radiation, the temperatures are higher for those with lower metallicity, reflecting lower radiative ability. However, once the clouds become opaque, in the course of the adiabatic contraction of the transient cores, their evolutionary trajectories in the density-temperature plane converge to a unique curve that is determined by only physical constants. The trajectories coincide with each other thereafter. Consequently, the size of the stellar core at the formation is the same regardless of the gas composition of the parent cloud., Comment: 30 pages. The Astrophysical Journal, 533, in press

We study the H2 photodissociation regions around OB stars in primordial gas clouds whose virial temperatures are between a few hundred and a few thousand Kelvin. In such small objects, a single O star can photodissociate a mass equal to that of the cloud itself. As a result, the clouds deplete their molecular coolant and cannot cool in a free-fall time, and subsequent star formation is totally quenched. This indicates that stars do not form efficiently in small objects and that these objects contribute little to the reionization of the universe., 9 pages. ApJ, 518, in press

The contraction processes of metal-free molecular clouds of starlike mass (or cloud cores) are investigated. We calculate radiative transfer of the H_2 lines and examine quasi-static contraction with radiative cooling. Comparing two time-scales, the free-fall time t_ff and the time-scale of quasi-static contraction t_qsc (nearly equal to t_cool, the cooling time) of these cores, we find that the ratio of the two time-scales t_ff/t_qsc, i.e., the efficiency of cooling, becomes larger with contraction even under the existence of cold and opaque envelopes. In particular, for fragments of primordial filamentary clouds, for which t_ff is nearly equal to t_qsc at the fragmentation epoch, they collapse dynamically in the free-fall time-scale. This efficiency of cooling is unique to line cooling., 13 pages, 8 Postscript figures, uses ptptex

We investigate the thermal and dynamical evolution of primordial gas clouds in the universe after decoupling. Comparing the time-scale of dynamical evolution with that of fragmentation, we can estimate the typical fragmentation scale. We propose the following scenario of the formation process of first luminous objects consisting of large number stars. First, by pancake collapse of the overdensity regions in the expanding universe or collision between clouds in potential wells, quasi-plane shocks form. If the shock-heated temperature is higher than about $10^4$ K, the postshock gas cools down to several hundred K by \Hbun line cooling, and the shock-compressed layer fragments into filamentary clouds. The filamentary cloud collapses dynamically once more and fragments into cloud cores. Finally, a primordial star forms in a cloud core. We show that the minimum mass of the first star is essentially determined by the Chandrasekhar mass. Also, we investigate the dynamical collapse of cloud cores by numerical simulation and show that the evolution paths of the central regions of the cores depend only very weakly on the total core mass. After mass accretion, a massive star may be formed in a core, since the estimated mass accretion rate is very large. In such a case, it may be possible for many massive stars form almost simultaneously. Then the clouds can be luminous objects. On the other hand, if the shock-heated temperature is lower, effective star formation is delayed significantly., Comment: PTP Tex file 23 pages, 10 figures

The evolution of collapsing metal free protostellar clouds is investigated for various masses and initial conditions. We perform hydrodynamical calculations for spherically symmetric clouds taking account of radiative transfer of the molecular hydrogen lines and the continuum, as well as of chemistry of the molecular hydrogen. The collapse is found to proceed almost self-similarly like Larson-Penston similarity solution. In the course of the collapse, efficient three-body processes transform atomic hydrogen in an inner region of $\sim 1 M_{\sun}$ entirely into molecular form. However, hydrogen in the outer part remains totally atomic although there is an intervening transitional layer of several solar masses, where hydrogen is in partially molecular form. No opaque transient core is formed although clouds become optically thick to H$_{2}$ collision-induced absorption continuum, since H$_{2}$ dissociation follows successively. When the central part of the cloud reaches stellar densities ($\sim 10^{-2} {\rm g cm^{-3}}$), a very small hydrostatic core ($\sim 5 \times 10^{-3} M_{\sun}$) is formed and subsequently grows in mass as the ambient gas accretes onto it. The mass accretion rate is estimated to be $3.7 \times 10^{-2} M_{\sun} {\rm yr^{-1}} (M_{\ast}/M_{\sun})^{-0.37}$, where $M_{\ast}$ is instantaneous mass of the central core, by using a similarity solution which reproduces the evolution of the cloud before the core formation., Comment: 20 pages, 5 Postscript figures, uses AAS LaTeX

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

We study effects of the fully ionized initial state, or pre-ionization, on the subsequent thermal evolution of low-metallicity clouds under various intensities of the external far-ultraviolet(FUV) and cosmic-ray(CR) fields. The pre-ionization significantly affects the thermal and dynamical evolution of metal-free clouds without FUV/CRs by way of efficient HD formation. On the other hand, the pre-ionization effect on the thermal evolution is limited in very low-density regime for more metal-enriched clouds ([Z/H] >~ -4) or those under modest FUV (>10^{-3}) or CR field (>0.1 of the present-day Galactic disk levels). In any case, for >10^8 cm^{-3}, neither the initial ionization state nor the irradiating FUV strength affect the thermal evolution. The dust cooling is an important mechanism for making sub-solar mass fragments in low-metallicity gas. Since this fragmentation occurs at the temperature minimum by the dust cooling at >10^{10} cm^{-3}, this process is not vulnerable either to initial ionization state or external radiation., 11 pages, 5 figures, PASJ accepted

The standard theory of cosmic structure formation posits that the present-day rich structure of the universe developed through gravitational amplification of tiny matter density fluctuations left over from the Big Bang. Recent observations of the cosmic microwave background, large-scale structure, and distant supernovae determined the energy content of the universe and the basic statistics of the initial density field with great accuracy. It has become possible to make accurate predictions for the formation and nonlinear growth of structure through early to the present epochs. We review recent progress in the theory of structure formation in the early universe. Results from state-of-the-art computer simulations are presented. Finally, we discuss prospects for future observations of the first generation of stars, black holes, and galaxies.

We examined observational characteristics of multi-phase turbulent flows in the diffuse interstellar medium (ISM) by calculating atomic and molecular carbon lines. Radiation field maps of C+, C0, and CO line emissions were generated by calculating the non-local thermodynamic equilibrium (nonLTE) level populations and high resolution hydrodynamic simulations of diffuse ISM. By analyzing synthetic line emission, we found a high ratio between the lines of high- and low-excitation energies in the diffuse multi-phase interstellar medium. Our results shows that simultaneous observations of the lines of warm- and cold-gas tracers will be useful in examining the thermal structure, and hence the origin of diffuse interstellar clouds.

The formation of stars in proto-galactic clouds can be viewed as two step processes i.e. the fragmentation of proto-galactic clouds and evolution of these fragments into stars. We consider here the latter process, the contraction of protosteller clouds (∼ 1M⊙) which consist of primordial gas. We investigate cooling processes by calculating the radiative transfer of H2 rotational/vibrational lines. We consider clouds in hydrostatic equilibrium as initial conditions. Comparing two timescales, the freefall time and the timescale of quasi-static contraction (∼ tcool, the cooling time) of these clouds, we find that as the clouds contract, the ratio of two timescales tff/tqsc, i.e. the efficiency of cooling, becomes larger even under the existence of cold and opaque envelope. Especially for the fragments of primordial filamentary clouds (tff ∼ tqsc initially), they collapse dynamically in the freefall timescale. This efficiency of cooling is utterly peculiar to the line cooling.

The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai (2000), updated to include deuterium chemistry and the effects of cosmic microwave background (CMB) radiation. HD-line cooling dominates the thermal balance of clouds when Z \~ 10^{-5}-10^{-3} Z_sun and density ~10^{5} cm^{-3}. Early on, CMB radiation prevents the gas temperature to fall below T_CMB, although this hardly alters the cloud thermal evolution in low-metallicity gas. From the derived temperature evolution, we assess cloud/core fragmentation as a function of metallicity from linear perturbation theory, which requires that the core elongation E := (b-a)/a > E_NL ~ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at E = E_NL. Given these assumptions and the initial (gaussian) distribution of E we compute the fragment mass distribution as a function of metallicity. We find that: (i) For Z=0, all fragments are very massive, > 10^{3}M_sun, consistently with previous studies; (ii) for Z>10^{-6} Z_sun a few clumps go through an additional high density (> 10^{10} cm^{-3}) fragmentation phase driven by dust-cooling, leading to low-mass fragments; (iii) The mass fraction in low-mass fragments is initially very small, but at Z ~ 10^{-5}Z_sun it becomes dominant and continues to grow as Z is increased; (iv) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0.01 < Z/Z_sun < 0.1. (v) For > 0.1Z_sun, the two peaks merge into a singly-peaked mass function which might be regarded as the precursor of the ordinary Salpeter-like IMF., 38 pages, 16 figures, ApJ in press

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