arXiv subjects

Kohei Inayoshi

Publications and source records attributed to Kohei Inayoshi.

At least 145 records · Page 8Linked to original sources

arXiv2017

Probing stellar binary black hole formation in galactic nuclei via the imprint of their center of mass acceleration on their gravitational wave signal

Multi-frequency gravitational wave (GW) observations are useful probes of the formation processes of coalescing stellar-mass binary black holes (BBHs). We discuss the phase drift in the GW inspiral waveform of the merging BBH caused by its center-of-mass acceleration. The acceleration strongly depends on the location where a BBH forms within a galaxy, allowing observations of the early inspiral phase of LIGO-like BBH mergers by the Laser Interferometer Space Antenna (LISA) to test the formation mechanism. In particular, BBHs formed in dense nuclear star clusters or via compact accretion disks around a nuclear supermassive black hole in active galactic nuclei would suffer strong acceleration, and produce large phase drifts measurable by LISA. The host galaxies of the coalescing BBHs in these scenarios can also be uniquely identified in the LISA error volume, without electromagnetic counterparts. A non-detection of phase drifts would rule out or constrain the contribution of the nuclear formation channels to the stellar-mass BBH population.

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arXiv2017

Quenching of supermassive black hole growth around the apparent maximum mass

Recent quasar surveys have revealed that supermassive black holes (SMBHs) rarely exceed a mass of $M_{\rm BH} \sim {\rm a~few}\times10^{10}~M_{\odot}$ during the entire cosmic history. It has been argued that quenching of the BH growth is caused by a transition of a nuclear accretion disk into an advection dominated accretion flow, with which strong outflows and/or jets are likely to be associated. We investigate a relation between the maximum mass of SMBHs and the radio-loudness of quasars with a well-defined sample of $\sim 10^5$ quasars at a redshift range of $0<z<2$, obtained from the Sloan Digital Sky Surveys DR7 catalog. We find that the number fraction of the radio-loud (RL) quasars increases above a threshold of $M_{\rm BH} \simeq 10^{9.5}~M_{\odot}$, independent of their redshifts. Moreover, the number fraction of RL quasars with lower Eddington ratios (out of the whole RL quasars), indicating lower accretion rates, increases above the critical BH mass. These observational trends can be natural consequences of the proposed scenario of suppressing BH growth around the apparent maximum mass of $\sim 10^{10}~M_{\odot}$. The ongoing VLA Sky Survey in radio will allow us to estimate of the exact number fraction of RL quasars more precisely, which gives further insights to understand quenching processes for BH growth.

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arXiv2017

Formation pathway of Population III coalescing binary black holes through stable mass transfer

We study formation of stellar mass binary black holes (BBHs) originating from Population III (PopIII) stars, performing stellar evolution simulations for PopIII binaries with MESA. We find that a significant fraction of PopIII binaries form massive BBHs through stable mass transfer between two stars in a binary, without experiencing common envelope phases. We investigate necessary conditions required for PopIII binaries to form BBHs coalescing within the Hubble time with a semi-analytical model calibrated by the stellar evolution simulations. The formation efficiency of coalescing PopIII BBHs is estimated for two different initial conditions for PopIII binaries with large and small separations, respectively. Consequently, in both models, $\sim 10\%$ of the total PopIII binaries form BBHs only through stable mass transfer and $\sim 10\%$ of these BBHs merge due to gravitational wave emission within the Hubble time. Furthermore, the chirp mass of merging BBHs has a flat distribution over $15\lesssim M_{\rm chirp}/M_\odot \lesssim 35$. This formation pathway of PopIII BBHs is presumably robust because stable mass transfer is less uncertain than common envelope evolution, which is the main formation channel for Population II BBHs. We also test the hypothesis that the BBH mergers detected by LIGO originate from PopIII stars using our result and the total number of PopIII stars formed in the early universe as inferred from the optical depth measured by Planck. We conclude that the PopIII BBH formation scenario can explain the mass-weighted merger rate of the LIGO's O1 events with the maximal PopIII formation efficiency inferred from the Planck measurement, even without BBHs formed by unstable mass transfer or common envelope phases.

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arXiv2016

Hyper-Eddington mass accretion onto a black hole with super-Eddington luminosity

We perform one-dimensional radiation hydrodynamical simulations to solve accretion flows onto massive black holes (BHs) with a very high rate. Assuming that photon trapping limits the luminosity emerging from the central region to $L\lesssim L_{\rm Edd}$, Inayoshi, Haiman & Ostriker (2016) have shown that an accretion flow settles to a "hyper-Eddington" solution, with a steady and isothermal ($T\simeq 8000$ K) Bondi profile reaching $\gtrsim 5000$ times the Eddington accretion rate $\dot{M}_{\rm Edd}\equiv L_{\rm Edd}/c^2$. Here we address the possibility that gas accreting with finite angular momentum forms a bright nuclear accretion disc, with a luminosity exceeding the Eddington limit ($1\lesssim L/L_{\rm Edd}\lesssim 100$). Combining our simulations with an analytic model, we find that a transition to steady hyper-Eddington accretion still occurs, as long as the luminosity remains below $L/L_{\rm Edd}\lesssim 35~(M_{\rm BH}/10^4~M_\odot)^{3/2}(n_\infty/10^5~{\rm cm^{-3}})(T_\infty/10^4~{\rm K})^{-3/2}(r_{\star}/10^{14}~{\rm cm})^{-1/2}$, where $n_\infty$ and $T_\infty$ are the density and temperature of the ambient gas, and $r_\star$ is the radius of the photosphere, at which radiation emerges. If the luminosity exceeds this value, accretion becomes episodic. Our results can be accurately recovered in a toy model of an optically thick spherical shell, driven by radiation force into a collapsing medium. When the central source is dimmer than the above critical value, the expansion of the shell is halted and reversed by ram pressure of the collapsing medium, and by shell's weight. Our results imply that rapid, unimpeded hyper-Eddington accretion is possible even if the luminosity of the central source far exceeds the Eddington limit, and can be either steady or strongly episodic.

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arXiv2016

Stellar Tidal Disruption Events by Direct Collapse Black Holes

We analyze the early growth stage of direct-collapse black holes (DCBHs) with $\sim 10^{5} \ \rm M_\odot$, which are formed by collapse of supermassive stars in atomic-cooling halos at $z \gtrsim 10$. A nuclear accretion disk around a newborn DCBH is gravitationally unstable and fragments into clumps with a few $10 \ \rm M_\odot$ at $\sim 0.01-0.1 \ \rm pc$ from the center. Such clumps evolve into massive population III stars with a few $10-100 \ \rm M_\odot$ via successive gas accretion and a nuclear star cluster is formed. Radiative and mechanical feedback from an inner slim disk and the star cluster will significantly reduce the gas accretion rate onto the DCBH within $\sim 10^6 \ \rm yr$. Some of the nuclear stars can be scattered onto the loss cone orbits also within $\lesssim 10^6 \ \rm yr$ and tidally disrupted by the central DCBH. The jet luminosity powered by such tidal disruption events can be $L_{\rm j} \gtrsim 10^{50} \ \rm erg \ s^{-1}$. The prompt emission will be observed in X-ray bands with a peak duration of $δt_{\rm obs} \sim 10^{5-6} \ (1+z) \ \rm s$ followed by a tail $\propto t_{\rm obs}^{-5/3}$, which can be detectable by Swift BAT and eROSITA even from $z \sim 20$. Follow-up observations of the radio afterglows with, e.g., eVLA and the host halos with JWST could probe the earliest AGN feedback from DCBHs.

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arXiv2016

Gravitational wave background from Population III binary black holes consistent with cosmic reionization

The recent discovery of the gravitational wave source GW150914 has revealed a coalescing binary black hole (BBH) with masses of $\sim 30~M_\odot$. Previous proposals for the origin of such a massive binary include Population III (PopIII) stars. PopIII stars are efficient producers of BBHs and of a gravitational wave background (GWB) in the $10-100$ Hz band, and also of ionizing radiation in the early Universe. We quantify the relation between the amplitude of the GWB ($Ω_{\rm gw}$) and the electron scattering optical depth ($τ_{\rm e}$), produced by PopIII stars, assuming that $f_{\rm esc}\approx 10\%$ of their ionizing radiation escapes into the intergalactic medium. We find that PopIII stars would produce a GWB that is detectable by the future O5 LIGO/Virgo if $τ_{\rm e} \gtrsim 0.07$, consistent with the recent Planck measurement of $τ_e=0.055 \pm 0.09$. Moreover, the spectral index of the background from PopIII BBHs becomes as small as ${\rm d}\ln Ω_{\rm gw}/{\rm d}\ln f\lesssim 0.3$ at $f \gtrsim 30$ Hz, which is significantly flatter than the value $\sim 2/3$ generically produced by lower-redshift and less-massive BBHs. A detection of the unique flattening at such low frequencies by the O5 LIGO/Virgo will indicate the existence of a high-chirp mass, high-redshift BBH population, which is consistent with the PopIII origin. A precise characterization of the spectral shape near $30-50$ Hz by the Einstein Telescope could also constrain the PopIII initial mass function and star formation rate.

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arXiv2016

Is there a maximum mass for black holes in galactic nuclei?

The largest observed supermassive black holes (SMBHs) have a mass of M_BH ~ 10^{10} M_sun, nearly independent of redshift, from the local (z~0) to the early (z>6) Universe. We suggest that the growth of SMBHs above a few 10^{10} M_sun is prevented by small-scale accretion physics, independent of the properties of their host galaxies or of cosmology. Growing more massive BHs requires a gas supply rate from galactic scales onto a nuclear region as high as >10^3 M_sun/yr. At such a high accretion rate, most of the gas converts to stars at large radii (~10-100 pc), well before reaching the BH. We adopt a simple model (Thompson et al. 2005) for a star-forming accretion disk, and find that the accretion rate in the sub-pc nuclear region is reduced to the smaller value of at most a few M_sun/yr. This prevents SMBHs from growing above ~10^{11} M_sun in the age of the Universe. Furthermore, once a SMBH reaches a sufficiently high mass, this rate falls below the critical value at which the accretion flow becomes advection dominated. Once this transition occurs, BH feeding can be suppressed by strong outflows and jets from hot gas near the BH. We find that the maximum SMBH mass, given by this transition, is between M_{BH,max} ~ (1-6) * 10^{10} M_sun, depending primarily on the efficiency of angular momentum transfer inside the galactic disk, and not on other properties of the host galaxy.

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arXiv2016

Hyper-Eddington accretion flows onto massive black holes

We study very-high rate spherically symmetric accretion flows onto a massive black hole (BH; 10^2 < M_BH < 10^6 Msun) embedded in a dense gas cloud with a low abundance of metals, performing one-dimensional hydrodynamical simulations which include multi-frequency radiation transfer and non-equilibrium primordial chemistry. We find that rapid gas supply from the Bondi radius at a hyper-Eddington rate can occur without being impeded by radiation feedback when (n/10^5 cm^-3) > (M_BH/10^4Msun)^{-1}(T/10^4 K)^{3/2}, where n and T are the density and temperature of ambient gas outside of the Bondi radius. The resulting accretion rate in this regime is steady, and larger than 3000 times the Eddington rate. At lower Bondi rates, the accretion is episodic due to radiative feedback and the average rate is limited below the Eddington rate. For the hyper-Eddington case, the steady solution consists of two parts: a radiation-dominated central core, where photon trapping due to electron scattering is important, and an accreting envelope which follows a Bondi profile with T~8000 K. When the emergent luminosity is limited below the Eddington luminosity because of photon trapping, radiation from the central region does not affect the gas dynamics at larger scales. We apply our result to the rapid formation of massive BHs in protogalaxies with a virial temperature of T_vir> 10^4 K. Once a seed BH forms at the center of the galaxy, it can grow up to a maximum ~10^5 (T_vir/10^4 K) Msun via gas accretion independent of the initial BH mass. Finally, we discuss possible observational signatures of rapidly accreting BHs with/without allowance for dust. We suggest that these systems could explain Lya emitters without X-rays and luminous infrared sources with hot dust emission, respectively.

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arXiv2015

Direct collapse black hole formation via high-velocity collisions of protogalaxies

We propose high-velocity collisions of protogalaxies as a new pathway to form supermassive stars (SMSs) with masses of ~ 10^5 Msun at high redshift (z > 10). When protogalaxies hosted by dark matter halos with a virial temperature of ~ 10^4 K collide with a relative velocity > 200 km/s, the gas is shock-heated to ~ 10^6 K and subsequently cools isobarically via free-free emission and He^+, He, and H line emission. Since the gas density (> 10^4 cm^{-3}) is high enough to destroy H_2 molecules by collisional dissociation, the shocked gas never cools below ~ 10^4 K. Once a gas cloud of ~ 10^5 Msun reaches this temperature, it becomes gravitationally unstable and forms a SMS which will rapidly collapse into a super massive black hole (SMBH) via general relativistic instability. We perform a simple analytic estimate of the number density of direct-collapse black holes (DCBHs) formed through this scenario (calibrated with cosmological N-body simulations) and find n_{DCBH} ~ 10^{-9} Mpc^{-3} (comoving) by z = 10. This could potentially explain the abundance of bright high-z quasars.

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arXiv2015

The suppression of direct collapse black hole formation by soft X-ray irradiation

The origin of supermassive black holes (SMBHs) in galactic nuclei is one of the major unsolved problems in astrophysics. One hypothesis is that they grew from >10^5 M_sun black holes that formed in the `direct collapse' of massive gas clouds that have low concentrations of both metals and molecular hydrogen (H_2). Such clouds could form in the early (z>10) Universe if pre-galactic gas is irradiated by H_2-photodissociating, far-ultraviolet (FUV) light from a nearby star-forming galaxy. In this work, we re-examine the critical FUV flux J_crit that is required to keep H_2 photodissociated and lead to direct collapse. We submit that the same galaxies that putatively supply the extraordinary FUV fluxes required for direct collapse should also produce copious amounts of soft X-rays, which work to offset H_2 photodissociation by increasing the ionization fraction and promoting H_2 formation. Accounting for this effect increases the value of J_crit by a factor of at least 3-10, depending on the brightness temperature of FUV radiation. This enhancement of J_crit suppresses the abundance of potential direct collapse sites at z>10 by several orders of magnitude. Recent studies---without accounting for the soft X-rays from the FUV source galaxies---had already arrived at large values of J_crit that implied that direct collapse may occur too rarely to account for the observed abundance of high-redshift quasars. Our results suggest that J_crit should be even higher than previously estimated, and pose an additional challenge for the direct collapse scenario via strong FUV radiation to explain the high-redshift quasar population.

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arXiv2014

Does disk fragmentation prevent the formation of supermassive stars in protogalaxies?

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. The clumps grow via accretion and migrate inward rapidly on a timescale of ~10^4 yr, which is comparable or shorter than the Kelvin-Helmholz time >10^4 yr. Some clumps may evolve to zero-age main sequence stars and halt gas accretion by radiative feedback, but most of the clumps can migrate inward and merge with the central protostar before forming massive stars. Moreover, we found that dust-induced-fragmentation in metal-enriched gas does not modify these conclusions unless Z> 3*10^{-4} Zsun, because clump migration below this metallicity remains as rapid as in the primordial case. Our results suggest that fragmentation of a compact, metal--poor disk can not prevent the formation of a SMS.

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arXiv2014

Formation of an embryonic supermassive star in the first galaxy

We studied the gravitational collapse of a warm (~8000 K) primordial-gas cloud as a candidate progenitor for a supermassive star (SMS; >10^5 Msun) using a three-dimensional hydrodynamical simulation, including all the relevant cooling processes of both H_2 and H, which can potentially induce cloud fragmentation. This is the first simulation of this kind to resolve protostar formation. We find that the cloud undergoes runaway collapse without a major episode of fragmentation. Although the H_2 fraction jumps by a large factor via the three-body reaction at ~10^-13 g/cm^3, its cooling remains inefficient due to the optical thickness, and the temperature remains >3000 K. When the central core of the cloud becomes opaque to continuum radiation at ~10^-8 g/cm^3, a hydrostatic protostar with ~0.2 Msun is formed. The protostar grows to the mass ~1 Msun and the radius ~2 AU within ~1 yr via rapid accretion of dense filamentary flows. With high accretion rate ~2 Msun/yr, the protostar is expected to turn into a SMS within its lifetime, eventually collapsing to a seed for the supermassive black hole observed in the early Universe at z~7.

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arXiv2014

Conditions for HD Cooling in the First Galaxies Revisited: Interplay between Far-Ultraviolet and Cosmic Ray Feedback in Population III Star Formation

HD dominates the cooling of primordial clouds with enhanced ionization, e.g. shock-heated clouds in structure formation or supernova remnants, relic HII regions of Pop III stars, and clouds with cosmic-ray (CR) irradiation. There, the temperature decreases to several 10 K and the characteristic stellar mass decreases to $\sim 10\ {\rm M}_{\odot}$, in contrast with first stars formed from undisturbed pristine clouds ($\sim 100\ {\rm M}_{\odot}$). However, without CR irradiation, even weak far ultra-violet (FUV) irradiation suppresses HD formation/cooling. Here, we examine conditions for HD cooling in primordial clouds including both FUV and CR feedback. At the beginning of collapse, the shock-compressed gas cools with its density increasing, while the relic HII region gas cools at a constant density. Moreover, shocks tend to occur in denser environments than HII regions. Owing to the higher column density and the more effective shielding, the critical FUV intensity for HD cooling in a shock-compressed gas becomes $\sim 10$ times higher than in relic HII regions. Consequently, in the shock-compressed gas, the critical FUV intensity exceeds the background level for most of the redshift we consider ($6 \lesssim z \lesssim 15$), while in relic HII regions, HD cooling becomes effective after the CR intensity increases enough at $z \lesssim 10$. Our result suggests that less massive ($\sim 10\ {\rm M}_{\odot}$) Pop III stars may be more common than previously considered and could be the dominant population of Pop III stars.

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arXiv2014

Possible Indirect Confirmation of the Existence of Pop III Massive Stars by Gravitational Wave

We perform population synthesis simulations for Population III (Pop III) coalescing binary neutron stars (NS-NSs), neutron star - black hole binaries (NS-BHs), and binary black holes (BH-BHs) which merge within the age of the universe. We found that the typical mass of Pop III BH-BHs is $\sim 30\ \rm{M}_{\odot}$ so that the inspiral chirp signal of gravitational waves can be detected up to z=0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH-BHs is $140 (68) \cdot ({\rm SFR}_{\rm p}/10^{-2.5} \rm{M}_{\odot} {\rm yr}^{-1} {\rm Mpc}^{-3}) \cdot {\rm Err}_{\rm sys} ~{\rm events} ~{\rm yr}^{-1}$ for the flat (Salpeter) initial mass function (IMF), respectively, where $\rm SFR_p$ and $\rm Err_{sys}$ are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. $\rm Err_{sys}=1$ correspond to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH-BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH-BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass $\sim 30~\rm M_{\odot}$ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.

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arXiv2013

Formation of Primordial Supermassive Stars by Rapid Mass Accretion

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.

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arXiv2013

Direct diagnostics of forming massive stars: stellar pulsation and periodic variability of maser sources

The 6.7 GHz methanol maser emission, a tracer of forming massive stars, sometimes shows enigmatic periodic flux variations over several 10-100 days. In this Letter, we propose that this periodic variations could be explained by the pulsation of massive protostars growing under rapid mass accretion with rates of Mdot > 10^-3 Msun/yr. Our stellar evolution calculations predict that the massive protostars have very large radius exceeding 100 Rsun at maximum, and we here study the pulsational stability of such the bloated protostars by way of the linear stability analysis. We show that the protostar becomes pulsationally unstable with various periods of several 10-100 days, depending on different accretion rates. With the fact that the stellar luminosity when the star is pulsationally unstable also depends on the accretion rate, we derive the period-luminosity relation log (L/Lsun) = 4.62 + 0.98log(P/100 day), which is testable with future observations. Our models further show that the radius and mass of the pulsating massive protostar should also depend on the period. It would be possible to infer such protostellar properties and the accretion rate with the observed period. Measuring the maser periods enables a direct diagnosis of the structure of accreting massive protostars, which are deeply embedded in dense gas and inaccessible with other observations.

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arXiv2013

Pulsational instability of supergiant protostars: Do they grow supermassive by accretion?

Supermassive stars (SMSs; M>10^5 Msun) and their remnant black holes are promising progenitors for supermassive black holes (SMBHs) observed in the early universe at z>7. It has been postulated that SMSs forms through very rapid mass accretion onto a protostar at a high rate exceeding 0.01 Msun/yr. According to recent studies, such rapidly accreting protostars evolve into "supergiant protostars", i.e. protostars consisting of a bloated envelope and a contracting core, similar to giant star. However, like massive stars as well as giant stars, both of which are known to be pulsationally unstable, supergiant protostars may also be also unstable to launch strong pulsation-driven outflows. If this is the case, the stellar growth via accretion will be hindered by the mass loss. We here study the pulsational stability of the supergiant protostars in the mass range M<10^3 Msun through the method of the linear perturbation analysis. We find that the supergiant protostars with M>600 Msun and very high accretion rate Mdot>1.0 Msun/yr are unstable due to the kappa mechanism. The pulsation is excited in the He^+ ionization layer in the envelope. Even under a conservative assumption that all the pulsation energy is converted into the kinetic energy of the outflows, the mass-loss rate is ~10^-3 Msun/yr, which is lower than the accretion rate by more than two orders of magnitude. We thus conclude that the supergiant protostars should grow stably via rapid accretion at least in the mass range we studied. As long as the rapid accretion is maintained in the later stage, protostars will become SMSs, which eventually produce seeds for the high-z SMBHs.

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arXiv2012

Supermassive black hole formation by the cold accretion shocks in the first galaxies

We propose a new scenario for supermassive star (SMS;>10^5Msun) formation in shocked regions of colliding cold accretion flows near the centers of first galaxies. Recent numerical simulations indicate that assembly of a typical first galaxy with virial temperature (~10^4K) proceeds via cold and dense flows penetrating deep to the center, where the supersonic streams collide each other to develop a hot and dense (~10^4K, ~10^3/cc) shocked gas. The post-shock layer first cools by efficient Ly alpha emission and contracts isobarically until 8000K. Whether the layer continues the isobaric contraction depends on the density at this moment: if the density is high enough for collisionally exciting H2 rovibrational levels (>10^4/cc), enhanced H2 collisional dissociation suppresses the gas to cool further. In this case, the layer fragments into massive (>10^5Msun) clouds, which collapse isothermally (~8000K) by the Ly alpha cooling without subsequent fragmentation. As an outcome, SMSs are expected to form and evolve eventually to seeds of supermassive black holes (SMBH). By calculating thermal evolution of the post-shock gas, we delimit the range of post-shock conditions for the SMS formation, which can be expressed as: T>6000K/(n/10^4/cc) for n<10^4/cc and T>5000-6000K for n>10^4/cc, depending somewhat on initial ionization degree. We found that metal enrichment does not affect the above condition for metallicity below 10^-3Zsun if metals are in the gas phase, while condensation of several percent of metals into dust decreases this critical value of metallicity by an order of magnitude. Unlike the previously proposed scenario for SMS formation, which postulates extremely strong ultraviolet radiation to quench H2 cooling, our scenario naturally explains the SMBH seed formation in the assembly process of the first galaxies, even without such a strong radiation.

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