Recent high-resolution simulations demonstrate that disks around primordial protostars easily fragment in the accretion phase before the protostars accrete less than a solar mass. To understand why the gravitational instability generally causes the fragmentation so early, we develop a one-dimensional (1D) non-steady model of the circumstellar disk that takes the mass supply from an accretion envelope into account. We also compare the model results to a three-dimensional (3D) numerical simulation performed with a code employing the adaptive mesh refinement. Our model shows that the self-gravitating disk, through which the Toomre $Q$ parameter is nearly constant at $Q \sim 1$, gradually spreads as the disk is fed by the gas infalling from the envelope. We further find that the accretion rate onto the star is an order of magnitude smaller than the mass supply rate onto the disk. This discrepancy makes the disk more massive than the protostar in an early evolutionary stage. Most of the infalling gas is used to extend the outer part of the self-gravitating disk rather than transferred inward toward the star through the disk. We find that similar evolution also occurs in the 3D simulation, where the disk becomes three times more massive than the star before the first fragmentation occurs. Our 1D disk model well explains the evolution of the disk-to-star mass ratio observed in the simulation. We argue that the formation of such a massive disk leads to the early disk fragmentation.
We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostell…
We report results from numerical simulations of star formation in the early universe that focus on the role of subsonic turbulence, and investigate whether it can induce fragmentation of the gas. We find that dense primordial gas is highly susceptible to fragmentation, even for rms turbulent velocity dispersions as low as 20% of the initial sound speed. The resulting fragments cover over two orders of magnitude in mass, ranging from 0.1 to 40 solar masses. However, our results suggest that the details of the fragmentation depend on the local properties of the turbulent velocity field and hence…
It has been shown that the behaviour of primordial gas collapsing in a dark matter minihalo can depend on the adopted choice of 3-body H$_2$ formation rate. The uncertainties in this rate span two orders of magnitude in the current literature, and so it remains a source of uncertainty in our knowledge of population III star formation. Here we investigate how the amount of fragmentation in primordial gas depends on the adopted 3-body rate. We present the results of calculations that follow the chemical and thermal evolution of primordial gas as it collapses in two dark matter minihalos. Our res…
Population III stars form in groups due to the fragmentation of primordial gas. While uniform magnetic fields have been shown to support against fragmentation in present day star formation, it is unclear whether realistic k^3/2 primordial fields can have the same effect. We bypass the issues associated with simulating the turbulent dynamo by introducing a saturated magnetic field at equipartition with the velocity field when the central densities reaches 10-13 g cm-3. We test a range of sink particle creation densities from 10-10-10-8 g cm-3. Within the range tested, the fields did not suppres…
The first stars are known to form in primordial gas, either in minihalos with about $10^6$~M$_\odot$ or so-called atomic cooling halos of about $10^8$~M$_\odot$. Simulations have shown that gravitational collapse and disk formation in primordial gas yield dense stellar clusters. In this paper, we focus particularly on the formation of protostellar binary systems, and aim to quantify their properties during the early stage of their evolution. For this purpose, we combine the smoothed particle hydrodynamics code GRADSPH with the astrochemistry package KROME. The GRADSPH-KROME framework is employ…
The collapse of the primordial gas in the density regime $\sim 10^{8}\hbox{--}10^{10}$ cm$^{-3}$ is controlled by the three-body $\rm H_2$ formation process, in which the gas can cool faster than free-fall time $\hbox{--}$ a condition proposed as the chemothermal instability. We investigate how the heating and cooling rates are affected during the rapid transformation of atomic to molecular hydrogen. With a detailed study of the heating and cooling balance in a 3D simulation of Pop~III collapse, we follow the chemical and thermal evolution of the primordial gas in two dark matter minihaloes. T…
Under rapid cooling from molecular hydrogen, the accretion disks around Population III (PopIII) stars are believed to fragment, resulting in multiple accreting cores. In this paper, we build a theoretical framework for calculating the optical depth of H$_2$ ro-vibrational line cooling based on the vertical structure in these accretion disks. Applying this physically motivated prescription for the optical depth, we find that cooling in the inner disk with $r \lesssim 10 {\rm\ AU}$ is attenuated significantly as a result of high surface density; $PdV$ heating becomes more efficient than cooling,…
We use the moving-mesh code AREPO to investigate the effects of different levels of rotation and turbulence on the fragmentation of primordial gas and the formation of Population III stars. We consider 9 different combinations of turbulence and rotation and carry out 5 different realizations of each setup, yielding one of the largest sets of simulations of Population III star formation ever performed. We find that fragmentation in Population III star-forming systems is a highly chaotic process and show that the outcomes of individual realizations of the same initial conditions often vary signi…
Collapse and fragmentation of uniform filamentary clouds under isotropic far-ultraviolet external radiation are investigated. Especially, impact of photodissociation of hydrogen molecules during collapse is investigated. Dynamical and thermal evolution of collapsing filamentary clouds are calculated by solving virial equation and energy equation with taking into accounts non-equilibrium chemical reactions. It is found that thermal evolution is hardly affected by the external radiation if the initial density is high ($n_0 > 10^2 \mathrm{cm^{-3}}$). On the other hand, if line mass of the filamen…
We present the first 3D simulations to include the effects of dark matter annihilation feedback during the collapse of primordial mini-halos. We begin our simulations from cosmological initial conditions and account for dark matter annihilation in our treatment of the chemical and thermal evolution of the gas. The dark matter is modelled using an analytical density profile that responds to changes in the peak gas density. We find that the gas can collapse to high densities despite the additional energy input from the dark matter. No objects supported purely by dark matter annihilation heating …
We present the implementation of a dust growth and fragmentation module in the public Smoothed Particle Hydrodynamics (SPH) code PHANTOM. This module is made available for public use with this paper. The coagulation model considers locally monodisperse dust size distributions around single values that are carried by the SPH particles. Along with the presentation of the model, implementation and tests, we showcase growth and fragmentation in a few typical circumstellar disc simulations and revisit previous results. The module is also interfaced with the radiative transfer code MCFOST, which fac…
The origin of supermassive black holes (with $\gtrsim\!10^9\,M_{\odot}$) in the early universe (redshift $z \sim 7$) remains poorly understood. Gravitational collapse of a massive primordial gas cloud is a promising initial process, but theoretical studies have difficulty growing the black hole fast enough. We focus on the magnetic effects on star formation that occurs in an atomic-cooling gas cloud. Using a set of three-dimensional magnetohydrodynamic (MHD) simulations, we investigate the star formation process in the magnetized atomic-cooling gas cloud with different initial magnetic field s…
We report results from numerical simulations of star formation in the early universe that focus on the dynamical behavior of metal-free gas under different initial and environmental conditions. In particular we investigate the role of turbulence, which is thought to ubiquitously accompany the collapse of high-redshift halos. We distinguish between two main cases: the birth of Population III.1 stars - those which form in the pristine halos unaffected by prior star formation - and the formation of Population III.2 stars - those forming in halos where the gas is still metal free but has an increa…
The Population III initial mass function (IMF) is currently unknown, but recent studies agree that fragmentation of primordial gas gives a broader IMF than the initially suggested singular star per halo. In this study we introduce sink particle mergers into Arepo, to perform the first resolution study for primordial star formation simulations and present the first Population III simulations to run up to densities of 10-6g cm-3 for hundreds of years after the formation of sink particles. The total number of sinks formed increases with increasing sink particle creation density, without achieving…
We perform a set of cosmological simulations of early structure formation with incorporating baryonic streaming motions. We present a case where a significantly elongated gas cloud with $\sim\!10^4\,$solar masses (${\rm M_\odot}$) is formed in a pre-galactic ($\sim\!10^7\,{\rm M_\odot}$) dark halo. The gas streaming into the halo compresses and heats the massive filamentary cloud to a temperature of $\sim\!10,000\,$Kelvin. The gas cloud cools rapidly by atomic hydrogen cooling, and then by molecular hydrogen cooling down to $\sim\!400\,$Kelvin. The rapid decrease of the temperature and hence o…
The discovery of a low-mass star with such low metallicity as < 4.5x10^{-5} Z_sun reveals the critical role of dust in the formation of extremely metal-poor stars. In this paper we explore the effect of the growth of dust grains through accretion of gaseous refractory elements in very low-metallicity pre-stellar cores on the cloud fragmentation induced by the dust emission cooling. Employing a simple model of grain growth in a gravitationally collapsing gas, we show that Fe and Si grains can grow efficiently at hydrogen densities of ~10^{10}-10^{14} cm^{-3} in the clouds with metal abundances …
We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long, initially sub-critical but accreting filaments. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length scale which is roughly 4 times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength …
We study low-metallicity star formation with a set of high-resolution hydrodynamics simulations for various gas metallicities over a wide range $0$--$10^{-3} \ {\rm Z}_{\bigodot}$. Our simulations follow non-equilibrium chemistry and radiative cooling by adopting realistic elemental abundance and dust size distribution. We examine the condition for the fragmentation of collapsing clouds (cloud fragmentation; CF) and of accretion discs (disc fragmentation; DF). We find that CF is suppressed due to rapid gas heating accompanied with molecular hydrogen formation even with efficient dust cooling f…
The Impact of Fuzzy Dark Matter Dynamics on the Accumulation and Fragmentation of Primordial Gas
Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理学院）；Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik（海德堡大学天文学中心理论天体物理研究所）；Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen（海德堡大学科学计算跨学科中心）
Magnetic fields play an important role in the dynamics of present-day molecular clouds. Recent work has shown that magnetic fields are equally important for primordial clouds, which form the first stars in the Universe. While the primordial magnetic field strength on cosmic scales is largely unconstrained, theoretical models strongly suggest that a weak seed field existed in the early Universe. We study how the amplification of such a weak field can influence the evolution of accretion discs around first stars, and thus affect the primordial initial mass function (IMF). We perform a suite of 3…
We present simulation results for the formation and long-term evolution of a primordial protostellar disk harbored by a first star. Using a 2+1D nonaxisymmetric thin disk numerical simulation, together with a barotropic relation for the gas, we are able to probe ~20 kyr of the disk's evolution. During this time period we observe fragmentation leading to loosely bound gaseous clumps within the disk. These are then torqued inward and accreted onto the growing protostar, giving rise to a burst phenomenon. The luminous feedback produced by this mechanism may have important consequences for the sub…
While the stellar Initial Mass Function (IMF) appears to be close to universal within the Milky Way galaxy, it is strongly suspected to be different in the primordial Universe, where molecular hydrogen cooling is less efficient and the gas temperature can be higher by a factor of 30. In between these extreme cases, the gas temperature varies depending on the environment, metallicity and radiation background. In this paper we explore if changes of the gas temperature affect the IMF of the stars considering fragmentation and accretion. The fragmentation behavior depends mostly on the Jeans mass …
Supermassive stars (SMSs; >10^5 Msun) formed in the first protogalaxies with virial temperature T_vir>10^4 K are expected to collapse into seeds of supermassive black hole (SMBHs) in the high-redshift universe (z>7). Fragmentation of the primordial gas is, however, a possible obstacle to SMS formation. We discuss the expected properties of a compact, metal-free, marginally unstable nuclear protogalactic disk, and the fate of the clumps formed in the disk by gravitational instability. Interior to a characteristic radius R_f=few*10^{-2} pc, the disk fragments into massive clumps with M_c~30 Msun…
We study the formation and long-term evolution of primordial protostellar disks harbored by first stars using numerical hydrodynamics simulations in the thin-disk limit. The initial conditions are specified by pre-stellar cores with distinct mass, angular momentum, and temperature. This allows us to probe several tens of thousand years of the disk's initial evolution, during which we observe multiple episodes of fragmentation leading to the formation of gravitationally bound gaseous clumps within spiral arms. These fragments are torqued inward due to gravitational interaction with the spiral a…
In a low-metallicity gas, rapid cooling by dust thermal emission is considered to induce cloud fragmentation and play a vital role in the formation of low-mass stars (<~ 1 M_sun) in metal-poor environments. We investigate how the growth of dust grains through accretion of heavy elements in the gas phase onto grain surfaces alters the thermal evolution and fragmentation properties of a collapsing gas cloud. We calculate directly grain growth and dust emission cooling in a self-consistent manner. We show that MgSiO3 grains grow sufficiently at gas densities nH = 10^{10}, 10^{12}, and 10^{14} /cc…
A promising supermassive black hole seed formation channel is that of direct collapse from primordial gas clouds. We perform a suite of 3D hydrodynamics simulations of an isolated turbulent gas cloud to investigate conditions conducive to forming massive black hole seeds via direct collapse, probing the impact of cloud metallicity, gas temperature floor and cooling physics on cloud fragmentation. We find there is no threshold in metallicity which produces a sharp drop in fragmentation. When molecular cooling is not present, metallicity has little effect on fragmentation. When molecular cooling…
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.…
Low-metallicity star formation poses a central problem of cosmology, as it determines the characteristic mass scale and distribution for the first and second generations of stars forming in our Universe. Here, we present a comprehensive investigation assessing the relative impact of metals and magnetic fields, which may both be present during low-metallicity star formation. We show that the presence of magnetic fields generated via the small-scale dynamo stabilises the protostellar disc and provides some degree of support against fragmentation. In the absence of magnetic fields, the fragmentat…
Quasars powered by massive black holes (BHs) with mass estimates above a billion solar masses have been identified at redshift 6 and beyond. The existence of such BHs requires almost continuous growth at the Eddington limit for their whole lifetime, of order of one billion years. In this paper, we explore the possibility that positively skewed scale-dependent non-Gaussian primordial fluctuations may ease the assembly of massive BHs. In particular, they produce more low-mass halos at high redshift, thus altering the production of metals and ultra-violet flux, believed to be important factors in…
We investigate the formation and growth of massive black hole (BH) seeds in dusty star-forming galaxies, relying and extending the framework proposed by Boco et al. 2020. Specifically, the latter envisages the migration of stellar compact remnants (neutron stars and stellar-mass black holes) via gaseous dynamical friction towards the galaxy nuclear region, and their subsequent merging to grow a massive central BH seed. In this paper we add two relevant ingredients: (i) we include primordial BHs, that could constitute a fraction $f_{\rm pBH}$ of the dark matter, as an additional component parti…
The thermodynamical evolution of gas during the collapse of the primordial star-forming cloud depends significantly on the initial degree of rotation. However, there is no clear understanding of how the initial rotation can affect the heating and cooling process and hence the temperature that leads to the fragmentation of the gas during Population III star formation. We report the results from three\hbox{-}dimensional, smoothed-particle hydrodynamics (SPH) simulations of a rotating self-gravitating primordial gas cloud with a modified version of the Gadget-2 code, in which the initial ratio of…
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 t…
Radiative feedback from populations II stars played a vital role in early structure formation. Particularly, photons below the Lyman limit can escape the star forming regions and produce a background ultraviolet (UV) flux which consequently may influence the pristine halos far away from the radiation sources. These photons can quench the formation of molecular hydrogen by photo-detachment of $\rm H^{-}$. In this study, we explore the impact of such UV radiation on fragmentation in massive primordial halos of a few times $\rm 10^{7}$~M${_\odot}$. To accomplish this goal, we perform high resolut…
We introduce a prescription for the luminosity from accreting protostars into smoothed particle hydrodynamics simulation, and apply the method to simulations of five primordial minihalos generated from cosmological initial conditions. We find that accretion luminosity delays fragmentation within the halos, but does not prevent it. In halos that slowly form a low number of protostars, the accretion luminosity can reduce the number of fragments that are formed before the protostars start ionising their surroundings. However, halos that rapidly form many protostars become dominated by dynamical p…
