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Register a new userDirect collapse to supermassive black hole seeds: the critical conditions for suppression of $rm H_2$ cooling
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Yang Luo
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Observations of high-redshift quasars imply the presence of supermassive black holes already at z~ 7.5. An appealing and promising pathway to their formation is the direct collapse scenario of a primordial gas in atomic-cooling haloes at z ~ 10 - 20, when the $rm H_2$ formation is inhibited by a strong background radiation field, whose intensity exceeds a critical value, $J_{rm crit}$. To estimate $J_{rm crit}$, typically, studies have assumed idealized spectra, with a fixed ratio of $rm H_{2}$ photo-dissociation rate $k_{rm H_2}$ to the $rm H^-$ photo-detachment rate $k_{rm H^-}$. This assumption, however, could be too narrow in scope as the nature of the background radiation field is not known precisely. In this work we argue that the critical condition for suppressing the $rm H_2$ cooling in the collapsing gas could be described in a more general way by a combination of $k_{rm H_2}$ and $k_{rm H^-}$ parameters. By performing a series of cosmological zoom-in simulations with an encompassing set of $k_{rm H_2}$ and $k_{rm H^-}$, we examine the gas flow by following evolution of basic parameters of the accretion flow. We test under what conditions the gas evolution is dominated by $rm H_{2}$ and/or atomic cooling. We confirm the existence of a critical curve in the $k_{rm H_2}-k_{rm H^-}$ plane, and provide an analytical fit to it. This curve depends on the conditions in the direct collapse, and reveals domains where the atomic cooling dominates over the molecular cooling. Furthermore, we have considered the effect of $rm H_{2}$ self-shielding on the critical curve, by adopting three methods for the effective column density approximation in $rm H_{2}$. We find that the estimate of the characteristic length-scale for shielding can be improved by using $lambda_{rm Jeans25}$, which is 0.25 times that of the local Jeans length.
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Direct collapse within dark matter (DM) halos is a promising path to form supermassive black hole (SMBH) seeds at high redshifts. The outer part of this collapse remains optically thin, and has been studied intensively using numerical simulations. However, the innermost region of the collapse is expected to become optically thick and requires us to follow the radiation field in order to understand its subsequent evolution. So far, the adiabatic approximation has been used exclusively for this purpose. We apply radiative transfer in the flux-limited diffusion (FLD) approximation to solve the evolution of coupled gas and radiation, for isolated halos. For direct collapse within isolated DM halos, we find that (1) the photosphere forms at ~10^{-6} pc and rapidly expands outward. (2) A central core forms, with a mass of ~1 Mo, supported by thermal gas pressure gradients and rotation. (3) Growing thermal gas and radiation pressure gradients dissolve it. (4) This process is associated with a strong anisotropic outflow, and another core forms nearby and grows rapidly. (5) Typical radiation luminosity emerging from the photosphere encompassing these cores is ~5 x 10^{37}-5 x 10^{38} erg/s, of order the Eddington luminosity. (6) Two variability timescales are associated with this process: a long one, which is related to the accretion flow within the central ~10^{-4}-10^{-3} pc, and ~0.1 yr, which is related to radiation diffusion. (7) Adiabatic models have been run for comparison and their evolution differs profoundly from that of the FLD models, by forming a central geometrically-thick disk. Overall, an adiabatic equation of state is not a good approximation to the advanced stage of direct collapse, mainly because the radiation in the FLD is capable of escaping due to anisotropy in the optical depth and associated gradients.
We have modeled direct collapse of a primordial gas within dark matter halos in the presence of radiative transfer, in high-resolution zoom-in simulations in a cosmological framework, down to the formation of the photosphere and the central object. Radiative transfer has been implemented in the flux-limited diffusion (FLD) approximation. Adiabatic models were run for comparison. We find that (a) the FLD flow forms an irregular central structure and does not exhibit fragmentation, contrary to adiabatic flow which forms a thick disk, driving a pair of spiral shocks, subject to Kelvin-Helmholtz shear instability forming fragments; (b) the growing central core in the FLD flow quickly reaches ~10 Mo and a highly variable luminosity of 10^{38}-10^{39} erg/s, comparable to the Eddington luminosity. It experiences massive recurrent outflows driven by radiation force and thermal pressure gradients, which mix with the accretion flow and transfer the angular momentum outwards; and (c) the interplay between these processes and a massive accretion, results in photosphere at ~10 AU. We conclude that in the FLD model (1) the central object exhibits dynamically insignificant rotation and slower than adiabatic temperature rise with density; (2) does not experience fragmentation leading to star formation, thus promoting the fast track formation of a supermassive black hole (SMBH) seed; (3) inclusion of radiation force leads to outflows, resulting in the mass accumulation within the central 10^{-3} pc, which is ~100 times larger than characteristic scale of star formation. The inclusion of radiative transfer reveals complex early stages of formation and growth of the central structure in the direct collapse scenario of SMBH seed formation.
Super-massive black holes weighing up to $sim 10^9 , mathrm{M_{odot}}$ are in place by $z sim 7$, when the age of the Universe is $lesssim 1 , mathrm{Gyr}$. This implies a time crunch for their growth, since such high masses cannot be easily reached in standard accretion scenarios. Here, we explore the physical conditions that would lead to optimal growth wherein stable super-Eddington accretion would be permitted. Our analysis suggests that the preponderance of optimal conditions depends on two key parameters: the black hole mass and the host galaxy central gas density. In the high-efficiency region of this parameter space, a continuous stream of gas can accrete onto the black hole from large to small spatial scales, assuming a global isothermal profile for the host galaxy. Using analytical initial mass functions for black hole seeds, we find an enhanced probability of high-efficiency growth for seeds with initial masses $gtrsim 10^4 , mathrm{M_{odot}}$. Our picture suggests that a large population of high-$z$ lower-mass black holes that formed in the low-efficiency region, with low duty cycles and accretion rates, might remain undetectable as quasars, since we predict their bolometric luminosities to be $lesssim 10^{41} , mathrm{erg , s^{-1}}$. The presence of these sources might be revealed only via gravitational wave detections of their mergers.
Observations of quasars at $ z > 6$ suggest the presence of black holes with a few times $rm 10^9 ~M_{odot}$. Numerous models have been proposed to explain their existence including the direct collapse which provides massive seeds of $rm 10^5~M_{odot}$. The isothermal direct collapse requires a strong Lyman-Werner flux to quench $rm H_2$ formation in massive primordial halos. In this study, we explore the impact of trace amounts of metals and dust enrichment. We perform three dimensional cosmological simulations for two halos of $rm > 10^7~M_{odot}$ with $rm Z/Z_{odot}= 10^{-4}-10^{-6}$ illuminated by an intense Lyman Werner flux of $rm J_{21}=10^5$. Our results show that initially the collapse proceeds isothermally with $rm T sim 8000$ K but dust cooling becomes effective at densities of $rm 10^{8}-10^{12} ~cm^{-3}$ and brings the gas temperature down to a few 100-1000 K for $rm Z/Z_{odot} geq 10^{-6}$. No gravitationally bound clumps are found in $rm Z/Z_{odot} leq 10^{-5}$ cases by the end of our simulations in contrast to the case with $rm Z/Z_{odot} = 10^{-4}$. Large inflow rates of $rm geq 0.1~M_{odot}/yr$ are observed for $rm Z/Z_{odot} leq 10^{-5}$ similar to a zero-metallicity case while for $rm Z/Z_{odot} = 10^{-4}$ the inflow rate starts to decline earlier due to the dust cooling and fragmentation. For given large inflow rates a central star of $rm sim 10^4~M_{odot}$ may form for $rm Z/Z_{odot} leq 10^{-5}$.
Direct collapse models for black hole (BH) formation predict massive ($sim 10^5 M_{odot}$) seeds, which hold great appeal as a means to rapidly grow the observed $sim 10^9 M_{odot}$ quasars by $zgtrsim 7$; however, their formation requires fine-tuned conditions. In this work, we use cosmological zoom simulations to study systematically the impact of requiring: 1) low gas angular momentum, and 2) a minimum incident Lyman Werner (LW) flux radiation in order to form direct-collapse BH seeds. We start with a baseline model (introduced in Bhowmick et. al. 2021) that restricts black hole seed formation (with seed masses of $M_{mathrm{seed}}=1.25times10^{4},1times10^{5} & 8times10^{5}M_{odot}/h$) to occur only in haloes with a minimum total mass ($3000times M_{mathrm{seed}}$) and star forming, metal poor gas mass ($5times M_{mathrm{seed}}$). When seeding is further restricted to halos with low gas spins (i.e. smaller than the minimum value required for the gas disc to be gravitationally stable), the seeding frequency is suppressed by factors of $sim6$ compared to the baseline model regardless of the mass threshold used. In contrast, imposing a minimum LW flux ($>10J_{21}$) disproportionately suppresses seed formation in $lesssim10^9M_{odot}/h$ halos, by factors of $sim100$ compared to the baseline model. Very few BH merger events occur in the models with a LW flux criterion, and because early BH growth is dominated by mergers in our models, this results in only the most massive ($8times10^{5}M_{odot}/h$) seeds being able to grow to the supermassive regime ($gtrsim10^6M_{odot}/h$) by $z=7$. Our results therefore suggest that producing the bulk of the $zgtrsim7$ BH population requires alternate seeding channels, early BH growth dominated by rapid or super-eddington accretion, massive seeding scenarios that do not depend on LW flux, or a combination of these possibilities.
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