arXiv subjects

Kazuyuki Omukai

Publications and source records attributed to Kazuyuki Omukai.

At least 37 records · Page 2Linked to original sources

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

Protostellar-disc fragmentation across all metallicities

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 $1$--$10^{-3}$ $Z_{\odot}$.

astro-ph.GA↗

arXiv2022

Impact of the cosmic background radiation on the initial mass function of metal-poor stars

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 $Z/Z_\odot=0.1$.

astro-ph.GA↗

arXiv2022

Merger rate density of binary black holes through isolated Population I, II, III and extremely metal-poor binary star evolution

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.

astro-ph.HE↗

arXiv2021

Formation of the first galaxies in the aftermath of the first supernovae

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$α$- and H$α$-line fluxes from the first galaxies. We show that the James Webb Space Telescope will be able to detect both UV continuum, Ly$α$ and H$α$ line emission from first galaxies with halo mass $\gtrsim 10^{9}~M_\odot$ at $z \gtrsim 10$.

astro-ph.GA↗

arXiv2021

Transition of the initial mass function in the metal-poor environments

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.

astro-ph.GA↗

arXiv2021

Signatures of Hierarchical Mergers in Black Hole Spin and Mass distribution

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 ($χ_\mathrm{eff}$), the precession spin parameter ($χ_\mathrm{p}$), 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 ${\bar χ}_\mathrm{typ}\equiv \overline{(χ_\mathrm{eff}^2+χ_\mathrm{p}^2)^{1/2}}$, up to roughly the maximum $m_\mathrm{chirp}$ among first-generation (1g) BHs, and (ii) a plateau at ${\bar χ}_\mathrm{typ}\sim 0.6$ at higher $m_\mathrm{chirp}$. We suggest that the maximum mass and typical spin magnitudes for 1g BHs can be estimated from ${\bar χ}_\mathrm{typ}$ as a function of $m_\mathrm{chirp}$. The GW data observed in LIGO/Virgo O1--O3a prefers an increase in ${\bar χ}_\mathrm{typ}$ at low $m_\mathrm{chirp}$, which is consistent with the growth of the BH spin magnitude by hierarchical mergers, at $\sim 2 σ$ 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 ${\bar χ}_\mathrm{typ}$ distribution can be confidently recovered once the number of GW events increases to $\gtrsim O(100)$.

astro-ph.HE↗

arXiv2021

Radiation hydrodynamics simulations of line-driven AGN disc winds: metallicity dependence and black hole growth

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.

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

Formation of massive stars under protostellar radiation feedback: Very metal-poor stars

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.

astro-ph.GA↗

arXiv2021

Gravitational Wave Physics and Astronomy in the nascent era

The detections of gravitational waves (GW) by LIGO/Virgo collaborations provide various possibilities to physics and astronomy. We are quite sure that GW observations will develop a lot both in precision and in number owing to the continuous works for the improvement of detectors, including the expectation to the newly joined detector, KAGRA, and the planned detector, LIGO-India. In 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.

gr-qc↗

arXiv2021

Ionization degree and magnetic diffusivity in star-forming clouds with different metallicities

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.

astro-ph.GA↗

arXiv2020

Mass-gap Mergers in Active Galactic Nuclei

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.

astro-ph.HE↗

arXiv2020

Eccentric Black Hole Mergers in Active Galactic Nuclei

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.

astro-ph.HE↗

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↗

arXiv2020

Cosmological DCBH formation sites hostile for their growth

The direct collapse (DC) is a promising mechanism that provides massive seed black holes (BHs) with $\sim 10^{5}~M_{\odot}$ in the early universe. To study a long-term accretion growth of a DCBH thus formed, 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 onto the BH is far below the Eddington value. Such slow mass growth is partly because of the strong radiative feedback from the accreting BH. Moreover, we find that the BH has a large velocity of $\sim 100~{\rm km~s^{-1}}$ relative to the gas after it falls into the first galaxy, which substantially reduces the accretion rate. The latter effect stems from the fact that the DCBHs form in metal-free environments typically at $\sim 1~$kpc from the galaxy. The BH accelerates as it approaches the galactic center due to the gravity. The relative velocity never damps after that, and the BH does not settle down to the galactic center but continues to wander around it. An analytic estimate predicts that the DCBH formation within $\sim 100$~pc around the galactic center is necessary to decelerate the BH with dynamical friction before $z=7$. Since metal enrichment with $Z \sim 10^{-5} - 10^{-3}~Z_\odot$ is expected in such a case, the formation of DCBHs in the metal-poor environments is preferable for the subsequent rapid growth.

astro-ph.GA↗

arXiv2020

Pulsation-driven mass loss from massive stars behind stellar mergers in metal-poor dense clusters

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.

astro-ph.SR↗

arXiv2020

Star cluster formation and cloud dispersal by radiative feedback: dependence on metallicity and compactness

We study star cluster formation in various environments with different metallicities and column densities by performing a suite of three-dimensional radiation hydrodynamics simulations. We find that the photoionization feedback from massive stars controls the star formation efficiency (SFE) in a star-forming cloud, and its impact sensitively depends on the gas metallicity $Z$ and initial cloud surface density $Σ$. At $Z=1~Z_{\odot}$, SFE increases as a power law from 0.03 at $Σ= 10~M_{\odot}{\rm pc^{-2}}$ to 0.3 at $Σ= 300~M_{\odot}{\rm pc^{-2}}$. In low-metallicity cases $10^{-2}- 10^{-1} Z_{\odot}$, star clusters form from atomic warm gases because the molecule formation time is not short enough with respect to the cooling or dynamical time. In addition, the whole cloud is disrupted more easily by expanding H{\sc ii} bubbles which have higher temperature owing to less efficient cooling. With smaller dust attenuation, the ionizing radiation feedback from nearby massive stars is stronger and terminate star formation in dense clumps. These effects result in inefficient star formation in low-metallicity environments: the SFE drops by a factor of $\sim 3$ at $Z=10^{-2}~Z_{\odot}$ compared to the results for $Z=1~Z_{\odot}$, regardless of $Σ$. Newborn star clusters are also gravitationally less bound. We further develop a new semi-analytical model that can reproduce the simulation results well, particularly the observed dependencies of the SFEs on the cloud surface densities and metallicities.

astro-ph.GA↗