Direct collapse to supermassive black hole seeds: the critical conditions for suppression of H2 cooling

Abstract

Observations of high-redshift quasars imply the presence of supermassive black holes (SMBHs) 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 H 2 formation is inhibited by a strong background radiation field, whose intensity exceeds a critical value, J crit . To estimate J crit , idealized spectra have been assumed, with a fixed ratio of H 2 photo-dissociation rate k H 2 to the H − photodetachment rate k 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 show that the critical condition for suppressing the H 2 cooling in the collapsing gas could be described in a more general way by a combination of k H 2 and k H − parameters, without any additional assumptions about the shape of the underlying radiation spectrum. By performing a series of cosmological zoom-in simulations with an encompassing set of k H 2 and k 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 H 2 and/or atomic cooling. We confirm the existence of a critical curve in the k H 2 − k 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 H 2 self-shielding on the critical curve, by adopting three methods for the effective column density approximation in H 2 . We find that the estimate of the characteristic length-scale for shielding can be improved by using λ Jeans25 , which is 0.25 times that of the local Jeans length.

Atomic and molecular gas from the epoch of reionisation down to redshift 2

“…The effects of alternative choices are small in thin media, but become important in dense sites (e.g. when estimating molecular cooling of collapsing gas or critical fluxes of impinging radiation during the formation of massive black-hole seeds; Luo et al 2020;Maio et al 2019). Neglecting HI shielding corrections at high redshift (z > 5) leads to a large degree of H ionisation and H 2 photodissociation, causing underestimation of HI and H 2 cosmological densities and leading to a trend of the atomic and molecular density parameters in tension with data even at z < 5.…”

“…36 of Draine & Bertoldi (1996) unless otherwise stated. In the case of Wolcott-Green et al (2017), the optimal scale at which to estimate the local H 2 column density, N H 2 , and related shielding have been investigated in depth by Luo et al (2020). These latter authors showed that N H 2 can be quantified as N H 2 = n H 2 λ J /4, where n H 2 is the the three-dimensional H 2 number density and λ J the Jeans length.…”

“…Gas self shielding (e.g. Draine & Bertoldi 1996;Rahmati et al 2013;Hartwig et al 2015;Wolcott-Green et al 2017;Ploeckinger & Schaye 2020;Luo et al 2020;Walter et al 2020) limits the ability of UV radiation to penetrate dense material and preserves HI or H 2 fractions in star forming regions. However, the relevance and the relative effects of the two main (HI and H 2 ) shielding processes for chemical abundances in cosmic environments need to be further explored.…”

FOREVER22: galaxy formation in protocluster regions

“…Therefore, unlike Johnson et al (2013), we use the same value to both Pop III and II stars, and it is fLW = 15. The LW radiation can be attenuated locally due to self-shielding gas (e.g., Draine & Bertoldi 1996;Glover & Brand 2001;Wolcott-Green et al 2011Luo et al 2020). To take the self-shielding effect into account, we evaluate the column density over the local Jeans length as follows:…”

Atomic and molecular gas from the epoch of reionization down to redshift 2

“…Gas self-shielding (e.g. Draine & Bertoldi 1996;Rahmati et al 2013;Hartwig et al 2015;Wolcott-Green et al 2017;Ploeckinger & Schaye 2020;Luo et al 2020;Walter et al 2020), limits the ability of UV radiation to penetrate dense material and preserves HI or H 2 fractions in star forming regions. The relevance and the relative role of the two main (HI and H 2 ) shielding processes for chemical abundances in cosmic environments need to be further explored, though.…”