Gravitational wave backgrounds from coalescing black hole binaries at cosmic dawn: an upper bound

The successive discoveries of binary merger events by Advanced LIGO-Virgo have been revealing the statistical properties of binary black hole (BBH) populations. A stochastic gravitational wave background (GWB) is a useful tool to probe the cosmological evolution of those compact mergers. In this paper, we study the upper bound on a GWB produced by BBH mergers, whose stellar progenitors dominate the reionization process at the cosmic dawn. Since early reionization by those progenitors yields a high optical depth of the universe inconsistent with the {it Planck} measurements, the cumulative mass density is limited to $rho_star lesssim 10^7~M_odot~{rm Mpc}^{-3}$. Even with this upper bound, the amplitude of a GWB owing to the high-$z$ BBH mergers is expected to be as high as $Omega_{rm gw}simeq 1.48_{-1.27}^{+1.80}times 10^{-9}$ at $fsimeq 25$ Hz, while their merger rate at the present-day is consistent or lower than the observed GW event rate. This level of GWB is detectable at the design sensitivity of Advanced LIGO-Virgo and would indicate a major contribution of the high-$z$ BBH population to the local GW events. The spectral index is expected to be substantially flatter than the canonical value of $simeq 2/3$ generically produced by lower-redshift and less massive BBHs. Moreover, if their mass function is more top-heavy than in the local universe, the GWB spectrum is even more skewed toward lower frequencies, which would allow us to extract information on the mass function of merging BBHs at high redshifts.

Super-Eddington mass growth of intermediate-mass black holes embedded in dusty circumnuclear disks

We perform the first three-dimensional radiation hydrodynamical simulations that investigate the growth of intermediate-mass BHs (IMBHs) embedded in massive self-gravitating, dusty nuclear accretion disks. We explore the dependence of mass accretion efficiency on the gas metallicity $Z$ and mass injection at super-Eddington accretion rates from the outer galactic disk $dot{M}_{rm in}$, and find that the central BH can be fed at rates exceeding the Eddington rate only when the dusty disk becomes sufficiently optically thick to ionizing radiation. In this case, mass outflows from the disk owing to photoevaporation is suppressed and thus a large fraction ($gtrsim 40%$) of the mass injection rate can feed the central BH. The conditions are expressed as $dot{M}_{rm in} > 2.2times 10^{-1}~M_odot ~{rm yr}^{-1} (1+Z/10^{-2}~Z_odot)^{-1}(c_{rm s}/10~{rm km~s}^{-1})$, where $c_{rm s}$ is the sound speed in the gaseous disk. With increasing numerical resolution, vigorous disk fragmentation reduces the disk surface density and dynamical heating by formed clumps makes the disk thickness higher. As a result, the photoevaorative mass-loss rate rises and thus the critical injection rate increases for fixed metallicity. This process enables super-Eddington growth of BHs until the BH mass reaches $M_{rm BH} sim 10^{7-8}~M_odot$, depending on the properties of the host dark-matter halo and metal-enrichment history. In the assembly of protogalaxies, seed BHs that form in overdense regions with a mass variance of 3-4$sigma$ at $zsim 15-20$ are able to undergo short periods of their rapid growth and transits into the Eddington-limited growth phase afterwards to be supermassive BHs observed at $z>6-7$.

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.

Hunting for wandering massive black holes

We investigate low-density accretion flows onto massive black holes (BHs) with masses of $gtrsim 10^5~M_odot$ orbiting around in the outskirts of their host galaxies, performing three-dimensional hydrodynamical simulations. Those wandering BHs are populated via ejection from the galactic nuclei through multi-body BH interactions and gravitational wave recoils associated with galaxy and BH coalescences. We find that when a wandering BH is fed with hot and diffuse plasma with density fluctuations, the mass accretion rate is limited at $sim 10-20%$ of the canonical Bondi-Hoyle-Littleton rate owing to a wide distribution of inflowing angular momentum. We further calculate radiation spectra from radiatively inefficient accretion flows onto the wandering BH using a semi-analytical two-temperature disk model and find that the predicted spectra have a peak at the millimeter band, where the Atacama Large Millimeter/submillimeter Array (ALMA) has the highest sensitivity and spatial resolution. Millimeter observations with ALMA and future facilities such as the next generation Very Large Array (ngVLA) will enable us to hunt for a population of wandering BHs and push the detectable mass limit down to $M_bullet simeq 2times10^7~M_odot$ for massive nearby ellipticals, e.g., M87, and $M_bullet simeq 10^5~M_odot$ for the Milky Way. This radiation spectral model, combined with numerical simulations, will be applied to give physical interpretations of off-nuclear BHs detected in dwarf galaxies, which may constrain BH seed formation scenarios.

Universal transition diagram from dormant to actively accreting supermassive black holes

The vast majority of supermassive black holes (SMBHs) in the local universe exhibit levels of activity much lower than those expected from gas supplying rates onto the galactic nuclei, and only a small fraction of silent SMBHs can turn into active galactic nuclei. Revisiting observational data of very nearby SMBHs whose gravitational spheres of influence are spatially reached by the Chandra X-ray satellite, we find that the level of BH activity drastically increases from the quiescent phase when the inflow rate outside of the BH influence radius is higher than 0.1% of the Eddington accretion rate. We also show that the relation between the nuclear luminosity and gas accretion rate from the BH influence radius measured from X-ray observations is well described by the universal state transition of accreting SMBHs, as predicted by recent hydrodynamical simulations with radiative cooling and BH feedback. After the state transition, young massive stars should form naturally in the nucleus, as observed in the case of the nearest SMBH, Sagittarius A$^ast$, which is currently quiescent but was recently active.

Transition of BH feeding from the quiescent regime into star-forming cold disk regime

We study the properties of rotating accretion flows onto supermassive black holes (SMBHs) using axisymmetric two-dimensional hydrodynamical simulations with radiative cooling and BH feedback. The simulations resolve the accretion dynamics of gas outside from the BH influence radius through an inner accretion disk. For lower Bondi accretion rates in units of the Eddington rate ($dot{M}_{rm B}ll 10^{-3}~dot{M}_{rm Edd}$), the BH feeding is suppressed due to turbulent motion by several orders of magnitudes from the Bondi rate. Thus, the radiative luminosity results in as low as $sim 10^{-10}-10^{-7}~L_{rm Edd}$, where $L_{rm Edd}$ is the Eddington luminosity. For higher rates of $dot{M}_{rm B}> 10^{-3}~dot{M}_{rm Edd}$, the optically-thin accreting gas cools via free-free emission and forms a geometrically-thin disk, which feeds the BH efficiently and increases the radiative luminosity to $> 10^{-3}~L_{rm Edd}$. The transitional behavior of accreting BHs in galactic nuclei from radiatively inefficient phases to cold disk accretion naturally explains (1) the reason for the offset between the observed luminosities and theoretical predictions for nearby quiescent SMBHs, and (2) the conditions to fuel gas into the nuclear SMBH. In addition, the cold disk formed in galactic nuclei tends to be gravitationally unstable and leads to star formation when the Bondi rate is as high as $ dot{M}_{rm B} > 10^{-2}~M_odot~{rm yr}^{-1}$. This is a plausible explanation of the correlation observed between star formation rates and BH feeding rates in Seyfert galaxies.

Super-Eddington growth of black holes in the early Universe: effects of disk radiation spectra

We investigate the properties of accretion flows onto a black hole (BH) with a mass of $M_{rm BH}$ embedded in an initially uniform gas cloud with a density of $n_{infty}$ in order to study rapid growth of BHs in the early Universe. In previous work, the conditions for super-Eddington accretion from outside the Bondi radius were studied by assuming that radiation produced at the vicinity of the central BH has a single-power-law spectrum $ u^{-alpha}$ at $h u geq 13.6~{rm eV}$ ($alpha sim 1.5$). However, radiation spectra depends on the BH mass and accretion rate. Here, we perform two-dimensional multi-frequency radiation hydrodynamical simulations taking into account more realistic radiation spectra associated with the properties of nuclear accretion disks. We find that the condition for a transition to super-Eddington accretion is alleviated for a wide range of masses ($10lesssim M_{rm BH}/M_{odot} lesssim 10^6$) because photoionization for accretion disk spectra are less efficient than those for single-power-law spectra. For disk spectra, the transition to super-Eddington is more likely to occur for lower BH masses because the radiation spectra become too hard to ionize the gas. Even when accretion flows are exposed to anisotropic radiation, the effect due to radiation spectra shrinks the ionized region and likely leads to the transition to a wholly neutral accretion phase. Finally, by generalizing our simulation results, we construct a new analytical criterion required for super-Eddington accretion; $(M_{rm BH}/10^5~M_{odot}) (n_{infty}/10^4~{rm cm^{-3}}) gtrsim 2.4~ (langleepsilonrangle /100~{rm eV})^{-5/9}$, where $langleepsilonrangle$ is the mean energy of ionizing radiation from the central BH.

Gravitational waves from supermassive black hole binaries in ultra-luminous infrared galaxies

Gravitational waves (GWs) in the nano-hertz band are great tools for understanding the cosmological evolution of supermassive black holes (SMBHs) in galactic nuclei. We consider SMBH binaries in high-$z$ ultra-luminous infrared galaxies (ULIRGs) as sources of a stochastic GW background (GWB). ULIRGs are likely associated with gas-rich galaxy mergers containing SMBHs that possibly occur at most once in the life of galaxies, unlike multiple dry mergers at low redshift. Adopting a well-established sample of ULIRGs, we study the properties of the GWB due to coalescing binary SMBHs in these galaxies. Since the ULIRG population peaks at $z>1.5$, the amplitude of the GWB is not affected even if BH mergers are delayed by as long as $sim $ 10 Gyrs. Despite the rarity of the high-$z$ ULIRGs, we find a tension with the upper limits from Pulsar Timing Array (PTA) experiments. This result suggests that if a fraction $f_{rm m,gal}$ of ULIRGs are associated with SMBH binaries, then no more than $20 f_{rm m,gal}(lambda_{rm Edd}/0.3)^{5/3}(t_{rm life}/30~{rm Myr})~%$ of the binary SMBHs in ULIRGs can merge within a Hubble time, for plausible values of the Eddington ratio of ULIRGs ($lambda_{rm Edd}$) and their lifetime ($t_{rm life}$).

Massive black hole and Population III galaxy formation in over-massive dark matter halos with violent merger histories

We propose the formation of massive pristine dark-matter (DM) halos with masses of $sim 10^8~M_odot$, due to the dynamical effects of frequent mergers in rare regions of the Universe with high baryonic streaming velocity relative to DM. Since the streaming motion prevents gas collapse into DM halos and delays prior star formation episodes, the gas remains metal-free until the halo virial temperatures $gtrsim 2times 10^4~{rm K}$. The minimum cooling mass of DM halos is boosted by a factor of $sim 10-30$ because frequent major mergers of halos further inhibit gas collapse. We use Monte Carlo merger trees to simulate the DM assembly history under a streaming velocity of twice the root-mean-square value, and estimate the number density of massive DM halos containing pristine gas as $simeq 10^{-4}~{rm cMpc}^{-3}$. When the gas infall begins, efficient Ly$alpha$ cooling drives cold streams penetrating inside the halo and feeding a central galactic disk. When one stream collides with the disk, strong shock forms a dense and hot gas cloud, where the gas never forms H$_2$ molecules due to effective collisional dissociation. As a result, a massive gas cloud forms by gravitational instability and collapses directly into a massive black hole (BH) with $M_bullet sim 10^5~M_odot$. Almost simultaneously, a galaxy with $M_{star, rm tot}sim 10^6~M_odot$ composed of Population III stars forms in the nuclear region. If the typical stellar mass is as high as $sim 100~M_odot$, the galaxy could be detected with the James Webb Space Telescope even at $zgtrsim 15$. These massive seed BHs would be fed by continuous gas accretion from the host galaxy, and grow to be bright quasars observed at $zgtrsim 6$.

Low density, radiatively inefficient rotating-accretion flow onto a black hole

We study low-density axisymmetric accretion flows onto black holes (BHs) with two-dimensional hydrodynamical simulations, adopting the $alpha$-viscosity prescription. When the gas angular momentum is low enough to form a rotationally supported disk within the Bondi radius ($R_{rm B}$), we find a global steady accretion solution. The solution consists of a rotational equilibrium distribution at $rsim R_{rm B}$, where the density follows $rho propto (1+R_{rm B}/r)^{3/2}$, surrounding a geometrically thick and optically thin accretion disk at the centrifugal radius, where thermal energy generated by viscosity is transported via strong convection. Physical properties of the inner solution agree with those expected in convection-dominated accretion flows (CDAF; $rho propto r^{-1/2}$). In the inner CDAF solution, the gas inflow rate decreases towards the center due to convection ($dot{M}propto r$), and the net accretion rate (including both inflows and outflows) is strongly suppressed by several orders of magnitude from the Bondi accretion rate $dot{M}_{rm B}$ The net accretion rate depends on the viscous strength, following $dot{M}/dot{M}_{rm B}propto (alpha/0.01)^{0.6}$. This solution holds for low accretion rates of $dot{M}_{rm B}/dot{M}_{rm Edd}< 10^{-3}$ having minimal radiation cooling, where $dot{M}_{rm Edd}$ is the Eddington rate. In a hot plasma at the bottom ($r<10^{-3}~R_{rm B}$), thermal conduction would dominate the convective energy flux. Since suppression of the accretion by convection ceases, the final BH feeding rate is found to be $dot{M}/dot{M}_{rm B} sim 10^{-3}-10^{-2}$. This rate is as low as $dot{M}/dot{M}_{rm Edd} sim 10^{-7}-10^{-6}$ inferred for SgrA$^*$ and the nuclear BHs in M31 and M87, and can explain the low luminosities in these sources, without invoking any feedback mechanism.