How an improved implementation of H$_2$ self-shielding influences the formation of massive stars and black holes

Tilman Hartwig, Simon C. O. Glover, Ralf S. Klessen, Muhammad A. Latif, Marta Volonteri

Published 2015-05-01Version 1

The highest redshift quasars at z>6 have mass estimates of about a billion M$_\odot$. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star ($\sim 10^5\,\mathrm{M}_\odot$) precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H$_2$) formation is inhibited by a strong external UV flux. Above a certain value of UV flux ($J_{\rm crit}$), the gas in a halo collapses isothermally at $\sim10^4$K and provides the conditions for supermassive star formation. However, H$_2$ can self-shield and the effect of photodissociation is reduced. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of $J_{\rm crit}$. This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H$_2$ against the photodissociating radiation. We estimate $J_{\rm crit}$ for 4 different haloes and find that our method yields a value of $J_{\rm crit}$ that is a factor of two smaller than with the Jeans approach ($\sim\,2000\,J_{21}$ vs. $\sim\,4000\,J_{21}$ with $J_{21}=10^{-21}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{Hz}^{-1}\,\mathrm{sr}^{-1}$). The main reason for this difference is the strong directional dependence of the H$_2$ column density, which cannot be captured with one-dimensional approximations. With this lower value of $J_{\rm crit}$, the number of haloes exposed to a flux $>J_{\rm crit}$ is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.