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Register a new userPositive or Negative? The Impact of X-ray Feedback on the Formation of Direct Collapse Black Hole Seeds
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John A. Regan
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A nearby source of Lyman-Werner (LW) photons is thought to be a central component in dissociating H$_2$ and allowing for the formation of a direct collapse black hole seed. Nearby sources are also expected to produce copious amounts of hydrogen ionising photons and X-ray photons. We study here the feedback effects of the X-ray photons by including a spectrum due to high-mass X-ray binaries on top of a galaxy with a stellar spectrum. We explicitly trace photon packages emerging from the nearby source and track the radiative and chemical effects of the multi-frequency source $(E_{rm photon} = rm{0.76 eV rightarrow 7500 eV}$). We find that X-rays have a strongly negative feedback effect, compared to a stellar only source, when the radiative source is placed at a separation greater than $gtrsim 1 rm kpc$. The X-rays heat the low and medium density gas in the envelope surrounding the collapsing halo suppressing the mass inflow. The result is a smaller enclosed mass compared to the stellar only case. However, for separations of $lesssim 1 rm kpc$, the feedback effects of the X-rays becomes somewhat neutral. The enhanced LW intensity at close separations dissociates more H$_2$ and this gas is heated due to stellar photons alone, the addition of X-rays is then not significant. This distance dependence of X-ray feedback suggests that a Goldilocks zone exists close to a forming galaxy where X-ray photons have a much smaller negative feedback effect and ideal conditions exist for creating massive black hole seeds.
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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.
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 $rm Z/Z_{odot} leq 10^{-5}$.
Supermassive black holes (SMBHs) of $sim 10^9, M_odot$ are generally believed to be the central engines of the luminous quasars observed at $zgtrsim6$, but their astrophysical origin remains elusive. The $zgtrsim$ quasars reside in rare density peaks, which poses several challenges to uniform hydrodynamic simulations. To investigate the formation of these distant quasars, we perform a suite of zoom-in simulations on a favorable halo, with a mass of $sim 10^{13}, M_odot$ at $z = 6$ and a history of multiple major mergers, ideal for BH growth. We test BH seeds of $10 - 10^6, M_odot$, and various accretion and feedback models, including thin-disk and slim-disk accretion. We find, contrary to previous studies, that light seeds of $lesssim 10^3, M_odot$ fail to grow to $10^8, M_odot$ by $zsim 6$ even with super-critical accretion; that the hyper-Eddington mode leads to lower accretion rates than the Eddington-limited case due to stronger feedback, resulting in significantly smaller BHs by two orders of magnitude; and that while the super-critical model boosts the growth of low-spin BHs, for high-spin BHs the mass may be reduced due to increased radiative feedback. Our simulations show that the first $10^8 - 10^9, M_odot$ SMBHs may grow from heavy seeds of $gtrsim 10^4, M_odot$ via Eddington-limited or mild super-critical accretion facilitated by gas-rich mergers and self-regulated by feedback, and they co-evolve with their host galaxies, producing bright quasars such as those at $zsim$6 and ULAS J1342+0928, currently the most distant quasar at z = 7.54.
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.
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