arXiv subjects

Kazuyuki Sugimura

Publications and source records attributed to Kazuyuki Sugimura.

At least 19 recordsLinked to original sources

arXiv2025

An Explicit M1 Radiation-hydrodynamics Scheme for 3D Protostellar Evolution

We present a radiation-hydrodynamics (RHD) scheme that enables 3D simulations resolving both protostellar interiors and their surrounding accretion flows within a single framework, to clarify how a protostar evolves while interacting with the accretion flow. The method builds on an explicit two-moment M1 closure scheme with a reduced speed of light approximation (RSLA) for massively parallel computation. Our scheme introduces a complementary non-RSLA radiation component that dominates in optically thick regions. This hybrid treatment restores physical energy conservation inside protostars, which would otherwise be violated under the RSLA, while retaining the advantage of large time steps. To overcome the limitation of the conventional M1 closure in solving radiative transfer in extremely optically thick regions inside protostars and across steep optical-depth gradients near their surfaces, we incorporate the optical-depth information of neighboring cells into the radiative transfer calculation. We further evolve photon-number densities in addition to radiation energy densities to reconstruct an effective local spectrum on the fly without resorting to costly multi-frequency transport. We implement this scheme in the adaptive mesh refinement code SFUMATO and verify its validity through a series of test calculations. As an application, we follow the early evolution of a massive protostar formed at high redshift, within a full cosmological context. The results reveal a continuous structure connecting the swollen protostar and its surrounding disk, which cannot be captured in conventional 1D models. This RHD scheme opens a path to studies of protostellar evolution and its interaction with the accretion flow in realistic 3D environments.

astro-ph.SR↗

arXiv2025

Neural-Network Chemical Emulator for First-Star Formation: Robust Iterative Predictions over a Wide Density Range

We present a neural-network emulator for the thermal and chemical evolution in Population III star formation. The emulator accurately reproduces the thermochemical evolution over a wide density range spanning 21 orders of magnitude (10$^{-3}$-10$^{18}$ cm$^{-3}$), tracking six primordial species: H, H$_2$, e$^{-}$, H$^{+}$, H$^{-}$, and H$_2^{+}$. To handle the broad dynamic range, we partition the density range into five subregions and train separate deep operator networks (DeepONets) in each region. When applied to randomly sampled thermochemical states, the emulator achieves relative errors below 10% in over 90% of cases for both temperature and chemical abundances (except for the rare species H$_2^{+}$). The emulator is roughly ten times faster on a CPU and more than 1000 times faster for batched predictions on a GPU, compared with conventional numerical integration. Furthermore, to ensure robust predictions under many iterations, we introduce a novel timescale-based update method, where a short-timestep update of each variable is computed by rescaling the predicted change over a longer timestep equal to its characteristic variation timescale. In one-zone collapse calculations, the results from the timescale-based method agree well with traditional numerical integration even with many iterations at a timestep as short as 10$^{-4}$ of the free-fall time. This proof-of-concept study suggests the potential for neural network-based chemical emulators to accelerate hydrodynamic simulations of star formation.

astro-ph.GA↗

arXiv2025

Unveiling the Ionized and Neutral ISM at z > 10 : The Origin of [O III] /[C II] Ratios from a Sub-parsec Resolution Radiative Transfer Simulation

Recent multi-wavelength observations by JWST and ALMA are unveiling both ionized and neutral ISM components in high-redshift ($z>6$) galaxies. In this work, we investigate the origin of rest-frame far-infrared [OIII]88 $\mu$m and [CII]158 $\mu$m emission by performing zoom-in cosmological simulations of dwarf-galaxy progenitors at $z=9-13$. Our simulations incorporate on-the-fly radiative transfer at sub-pc ($\sim$ 0.1 pc) resolution, allowing us to resolve the multi-phase ISM. We compute emission lines on a cell-by-cell basis, taking into account local temperature, density, metallicity, radiation field strength, column density, and spectral hardness of radiation bins. We find that [OIII] predominantly arises from centrally located ionizing bubbles with temperatures of $\sim (1-5)\times 10^4\,\mathrm{K}$ and high ionization parameters of $\log U_{\mathrm{ion}} \simeq -1.5$. In contrast, [CII] is produced in the surrounding dense neutral regions at $\sim 5\times 10^3\,\mathrm{K}$, which are heated by strong FUV radiation ($G/G_0 \sim 10^{3-5}$) from the central stellar clusters. This spatial arrangement leads to large local variations in [OIII]/[CII], ranging from $\sim$ 100 to 0.01. Our galaxy reproduces the global ratio [OIII]/[CII]$\sim5-30$, consistent with recent ALMA detections at $z>6$ without invoking enhanced O/C abundance ratios. We further derive that [OIII]/[CII] linearly scales with the mass and density ratios of ionized to neutral gas, $M_{\rm HII}/M_{\rm HI}$ and $n_{\rm HII}/n_{\rm HI}$ and show that the [OIII]/[CII] ratio typically changes from 5.7 to 0.3 from high-z to low-z. For future synergies of JWST and ALMA, we derived $M_{\rm HII}/M_{\rm HI}$ for observed $z >6$ galaxies using ${\rm H}\beta$ and [CII] and show the validity of our scaling relations.

astro-ph.GA↗

arXiv2025

Seeding Cores: A Pathway for Nuclear Star Clusters from Bound Star Clusters in the First Billion Years

We model the formation of star clusters in a dwarf galaxy progenitor during the first $700 ~{\rm Myr}$ of cosmic history using a cosmological radiation-hydrodynamic simulation with a sub-grid star formation efficiency (SFE) model calibrated from AU-scale radiation-MHD simulations of molecular clouds with varying mass, density, and metallicity. In comparison to a constant SFE model, our model yields more bursty star formation, a more abundant massive star cluster population, and overall a higher stellar mass. Clouds reach SFEs up to $80\%$, forming bound star clusters (densities $\sim10^{2-4} ~{\rm M_\odot\:pc^{-2}}$, radii $\lesssim 3~{\rm pc}$) resembling those observed by the James Webb Space Telescope (JWST) in strongly lensed galaxies. Star clusters follow a flat power-law mass function ${\rm d}N/{\rm d}\log M \propto M^\Gamma$ with slope $\Gamma \sim -0.4$. The most massive star clusters ($10^{4-5} ~{\rm M_\odot}$) grow through mergers and have metallicity spreads of $0.05 - 0.1$ dex that roughly scale with mass. The second burst of star formation produce loosely bound star clusters with higher metallicities: $-1.95 < \log(Z/{\rm Z_\odot}) < -1.50$ at lower SFEs ($2 - 20\%$). At $z \sim 8.7$, a nuclear star cluster (NSC) is seeded, growing $83\%$ of its mass ($ 2.4 \times 10^5 ~{\rm M_\odot}$, $20\%$ of the galaxy's stellar mass) through mergers with pre-existing clusters and the rest through in-situ star formation. The early formation of NSCs has interesting implications for seeding supermassive black holes and the population of $\textit{little red dots}$ recently discovered by JWST at $z \gtrsim 5$

astro-ph.GA↗

arXiv2024

Violent starbursts and quiescence induced by FUV radiation feedback in metal-poor galaxies at high-redshift

JWST observations of galaxies at $z\gtrsim 8$ suggest that they are more luminous and clumpier than predicted by most models, prompting several proposals on the physics of star formation and feedback in the first galaxies. In this paper, we focus on the role of ultraviolet (UV) radiation in regulating star formation by performing a set of cosmological radiation hydrodynamics simulations of one galaxy at sub-pc resolution with different radiative feedback models. We find that the suppression of cooling by far UV (FUV) radiation (i.e., $\mathrm{H_2}$ dissociating radiation) from Pop II stars is the main physical process triggering the formation of compact and massive star clusters and is responsible for the bursty star formation observed in metal-poor galaxies at $z\gtrsim 10$. Indeed, artificially suppressing FUV radiation leads to a less intense continuous mode of star formation distributed into numerous, but low-mass open star clusters. Due to the intense FUV field, low-metallicity clouds remain warm ($\sim 10^4\,\mathrm{K}$) until they reach a relatively high density ($\gtrsim 10^3\,\mathrm{cm^{-3}}$), before becoming self-shielded and transitioning to a colder ($\sim 100\,\mathrm{K}$), partially molecular phase. As a result, star formation is delayed until the clouds accumulate enough mass to become gravitationally unstable. At this point, the clouds undergo rapid star formation converting gas into stars with high efficiency. We, therefore, observe exceptionally bright galaxies (ten times brighter than for continuous star formation) and subsequent quenched "dead" galaxies that did not form stars for tens of Myrs.

astro-ph.GA↗

arXiv2024

Impact of Turbulent Magnetic Fields on Disk Formation and Fragmentation in First Star Formation

Recent cosmological hydrodynamic simulations have suggested that the first stars in the universe often form as binary or multiple systems. However, previous studies typically overlooked the potential influence of magnetic fields during this process, assuming them to be weak and minimally impactful. Emerging theoretical investigations, however, propose an alternative perspective, suggesting that turbulent dynamo effects within first-star forming clouds can generate strong magnetic fields. In this study, we perform three-dimensional ideal magnetohydrodynamics simulations, starting from the gravitational collapse of a turbulent cloud core to the early accretion phase, where disk fragmentation frequently occurs. Our findings reveal that turbulent magnetic fields, if they reach an equipartition level with turbulence energy across all scales during the collapse phase, can significantly affect the properties of the multiple systems. Specifically, both magnetic pressure and torques contribute to disk stabilization, leading to a reduction in the number of fragments, particularly for low-mass stars. Additionally, our observations indicate the launching of protostellar jets driven by magnetic pressure of toroidal fields, although their overall impact on star formation dynamics appears to be minor. Given the case with which seed magnetic fields amplify to the full equipartition level, our results suggest that magnetic fields likely play a significant role in shaping the initial mass function of the first stars, highlighting the importance of magnetic effects on star formation in the early universe.

astro-ph.GA↗

arXiv2024

Gas Dynamical Friction on Accreting Objects

The drag force experienced by astronomical objects moving through gaseous media (gas dynamical friction) plays a crucial role in their orbital evolution. Ostriker (1999) derived a formula for gas dynamical friction by linear analysis, and its validity has been confirmed through subsequent numerical simulations. However, the effect of gas accretion onto the objects on the dynamical friction is yet to be understood. In this study, we investigate the Mach number dependence of dynamical friction considering gas accretion through three-dimensional nested-grid simulations. We find that the net frictional force, determined by the sum of the gravitational force exerted by surrounding gas and momentum flux transferred by accreting gas, is independent of the resolution of simulations. Only the gas outside the Bondi-Hoyle-Lyttleton radius contributes to dynamical friction, because the gas inside this radius is eventually absorbed by the central object and returns the momentum obtained through the gravitational interaction with it. In the subsonic case, the front-back asymmetry induced by gas accretion leads to larger dynamical friction than predicted by the linear theory. Conversely, in the slightly supersonic case with the Mach number between 1 and 1.5, the nonlinear effect leads to a modification of the density distribution in a way reducing the dynamical friction compared with the linear theory. At a higher Mach number, the modification becomes insignificant and the dynamical friction can be estimated with the linear theory. We also provide a fitting formula for dynamical friction based on our simulations, which can be used in a variety of applications.

astro-ph.GA↗

arXiv2024

On the origin of outward migration of Population III stars

Outward migration of massive binary stars or black holes in their circumbinary disc is often observed in simulations and it is key to the formation of wide black hole binaries. Using numerical simulations of Population III (Pop III) star formation, we study the angular momentum of Pop III binaries and the torques between stars and gas discs to understand the origin of outward migration and high ellipticity. The outward migration of protostars is produced by gravitational torques exerted on them by their circumstellar minidiscs. The minidiscs, on the other hand, migrate outward mainly by gaining angular momentum by accreting gas from the circumbinary disc. The angular momentum transfer is most efficient for rapidly accreting equal-mass binaries, and weaker when the secondary mass is small or the massive companion evaporates the gas disc via radiative feedback. We conclude that outward migration and the formation of wide equal-mass massive binaries is common in metal-free/metal-poor star formation, mainly driven by their large accretion rates. We expect that the lower gas temperature and accretion rates in metal-enriched circumstellar discs would lead more often to inward migration and closer binary separations. We also observe inward migration for smaller mass Pop III protostars/fragments, leading to the rapid merging of sink particles and likely the formation of close binary black holes that, however, reach separations below the resolution of our simulations. We discuss the implications that Pop III separations and ellipticity may have on the interpretation that gravitational wave signals from merging intermediate-mass black holes come from Pop III remnants.

astro-ph.GA↗

arXiv2024

Formation of Massive and Wide First-star Binaries in Radiation Hydrodynamics Simulations

We study the formation of Pop III stars by performing radiation hydrodynamics simulations for three different initial clouds extracted from cosmological hydrodynamics simulations. Starting from the cloud collapse stage, we follow the growth of protostars by accretion for $\sim 10^5$ yr until the radiative feedback from the protostars suppresses the accretion and the stellar properties are nearly fixed. We find that the Pop III stars form in massive and wide binaries/small-multiple stellar systems, with masses $>30\,M_\odot$ and separations $>2000$ au. We also find that the properties of the final stellar system correlate with those of the initial clouds: the total mass increases with the cloud-scale accretion rate, and the angular momentum of the binary orbit matches that of the initial cloud. While the total mass of the system in our simulations is consistent with our previous single-star formation simulations, individual masses are lower due to mass sharing, suggesting potential modification in the extent of feedback from Pop III stars in the subsequent evolution of the Universe. We also identify such systems as mini-binaries embedded in a wider outer multiple-star system, which could evolve into progenitors for observed gravitational wave events.

astro-ph.CO↗

arXiv2023

3D Radiation-Hydrodynamic Simulations Resolving Interior of Rapidly Accreting Primordial Protostar

Direct collapse of supermassive stars is a possible pathway to form supermassive black hole seeds at high redshifts. Whereas previous three-dimensional (3D) simulations demonstrate that supermassive stars form via rapid mass accretion, those resolving the stellar interior have been limited. We here report 3D radiation-hydrodynamic (RHD) simulations following the evolution of rapidly accreting protostars resolving the stellar interior. We use an adaptive mesh refinement code with our newly developed RHD solver employing an explicit M1 closure method. We follow the early evolution until the stellar mass reaches $\sim 10~M_\odot$ from two different initial configurations of spherical and turbulent clouds. We demonstrate that, in both the cases, a swollen protostar whose radius is $100\mathrm{-}1000~R_\odot$ appears, as predicted by the stellar evolution calculations. Its effective temperature remains a few thousand Kelvin, and the radiative feedback by ionizing photons is too weak to disturb the accretion flow up to the epoch examined in this work. In the turbulent case, the protostar rotates rapidly at more than 0.4 times the Keplerian velocity owing to the angular momentum provided by the initial turbulence. The protostar approximates an oblate spheroid, and its equatorial radius is more than twice the polar radius. Our results suggest that we need to consider the rapid stellar rotation to elucidate the realistic 3D protostellar evolution in the supermassive star formation.

astro-ph.GA↗

arXiv2022

Star Cluster Formation and Survival in the First Galaxies

Using radiation-hydrodynamic cosmological simulations, we present a detailed ($0.1$ pc resolution), physically motivated portrait of a typical-mass dwarf galaxy before the epoch of reionization, resolving the formation and evolution of star clusters into individual $10\:\mathrm{M_{\odot}}$ star particles. In the rest-frame UV, the galaxy has an irregular morphology with no bulge or galactic disk, dominated by light emitted from numerous, compact, and gravitationally-bound star clusters. This is especially interesting in light of recent HST and JWST observations that -- aided by the magnifying power of gravitational lenses -- have imaged, at parsec-scale resolution, individual young star clusters in the process of forming in similar galaxies at $z>6$. Because of their low metallicities and high temperatures, star-forming gas clouds in this galaxy have densities $\sim 100$ times higher than typical giant molecular clouds; hence, their star formation efficiencies are high enough ($f_*\sim10-70$ per cent) to produce a sizeable population of potential globular cluster progenitors but typically smaller (between a few $100\:-\: 2\times10^4\:\mathrm{M_{\odot}}$, sizes of $0.1-3$ pc) and of lower metallicities ($10^{-3.5}-10^{-2.5}\:\mathrm{Z_{\odot}}$). The initial mass function of the star-forming clouds is log-normal while the bound star cluster mass function is a power-law with a slope that depends mainly on $f_*$ but also on the temporal proximity to a major starburst. We find slopes between $-0.5$ and $-2.5$ depending on the assumed sub-grid $f_*$. Star formation is self-regulated on galactic scales; however, the multi-modal metallicity distribution of the star clusters and the fraction of stars locked into surviving bound star clusters depends on $f_*$.

astro-ph.GA↗

arXiv2022

Non-ideal magnetohydrodynamic simulations of the first star formation: the effect of ambipolar diffusion

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.

astro-ph.GA↗

arXiv2022

Population III star formation in an X-ray background: III. Periodic radiative feedback and luminosity induced by elliptical orbits

We model Pop III star formation in different FUV and X-ray backgrounds, including radiation feedback from protostars. We confirm previous results that a moderate X-ray background increases the number of Pop III systems per unit cosmological volume, but masses and multiplicities of the system are reduced. The stellar mass function also agrees with previous results, and we confirm the outward migration of the stars within the protostellar discs. We find that nearly all Pop III star systems are hierarchical, i.e., binaries of binaries. Typically, two equal-mass stars form near the centre of the protostellar disc and migrate outward. Around these stars, mini-discs fragment forming binaries that also migrate outward. Stars may also form at Lagrange points L4/L5 of the system. Afterward, star formation becomes more stochastic due to the large multiplicity, and zero-metallicity low-mass stars can form when rapidly ejected from the disc. Stars in the disc often have eccentric orbits, leading to a periodic modulation of their accretion rates and luminosities. At the pericenter, due to strong accretion, the star can enter a red-supergiant phase reaching nearly Eddington luminosity in the optical bands ($m_{\rm AB} \sim 34$ for a $100~M_{odot}$ star at $z=6$). During this phase, the star, rather than its nebular lines, can be observed directly by JWST, if sufficiently magnified by a gravitational lens. The $\sim 10,000$ AU separations and high eccentricities of many Pop III star binaries in our simulations are favorable parameters for IMBH mergers - and gravitational waves emission - through orbital excitation by field stars.

astro-ph.GA↗

arXiv2021

Population III Star Formation in an X-ray background: I. Critical Halo Mass of Formation and Total Mass in Stars

The first luminous objects forming in the universe produce radiation backgrounds in the FUV and X-ray bands that affect the formation of Population III stars. Using a grid of cosmological hydrodynamics zoom-in simulations, we explore the impact of the Lyman-Warner (LW) and X-ray radiation backgrounds on the critical dark matter halo mass for Population III star formation and the total mass in stars per halo. We find that the LW radiation background lowers the H$_2$ fraction and delays the formation of the Population III stars. On the other hand, X-ray irradiation anticipates the redshift of collapse and reduces the critical halo mass, unless the X-ray background is too strong and gas heating shuts down gas collapse into the halos and prevents star formation. Therefore, an X-ray background can increase the number of dark matter halos forming Population III stars by about a factor of ten, but the total mass in stars forming in each halo is reduced. This is because X-ray radiation increases the molecular fraction and lowers the minimum temperature of the collapsing gas (or equivalently the mass of the quasi-hydrostatic core) and therefore slows down the accretion of the gas onto the central protostar.

astro-ph.GA↗

arXiv2021

Population III Star Formation in an X-ray background: II. Protostellar Discs, Multiplicity and Mass Function of the Stars

Disc fragmentation plays an important role in determining the number of primordial stars (Pop III stars), their masses, and hence the initial mass function. In this second paper of a series, we explore the effect of uniform FUV H$_2$-photodissociating and X-ray radiation backgrounds on the formation of Pop~III stars using a grid of high-resolution zoom-in simulations. We find that, in an X-ray background, protostellar discs have lower surface density and higher Toomre $Q$ parameter, so they are more stable. For this reason, X-ray irradiated discs undergo fewer fragmentations and typically produce either binary systems or low-multiplicity systems. In contrast, the cases with weak or no X-ray irradiation produce systems with a typical multiplicity of $6 \pm 3$. In addition, the most massive protostar in each system is smaller by roughly a factor of two when the disc is irradiated by X-rays, due to lower accretion rate. With these two effects combined, the initial mass function of fragments becomes more top-heavy in a strong X-ray background and is well described by a power-law with slope $1.53$ and high-mass cutoff of $61$ M$_\odot$. Without X-rays, we find a slope $0.49$ and cutoff mass of $229$ M$_\odot$. Finally, protostars migrate outward after their formation due to the accretion of high-angular momentum gas from outside and the migration is more frequent and significant in absence of X-ray irradiation.

astro-ph.GA↗

arXiv2021

Magnetohydrodynamic effect on first star formation: prestellar core collapse and protostar formation

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.

astro-ph.GA↗

arXiv2021

Growth of Massive Disk and Early Disk Fragmentation in the Primordial Star Formation

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.

astro-ph.GA↗

arXiv2020

Disk fragmentation and intermittent accretion onto supermassive stars

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.

astro-ph.GA↗