Assessing inflow rates in atomic cooling halos: implications for direct collapse black holes

Supermassive black holes are not only common in the present-day galaxies, but billion solar masses black holes also powered $z\geq 6$ quasars. One efficient way to form such black holes is the collapse of a massive primordial gas cloud into a so-called direct collapse black hole. The main requirement for this scenario is the presence of large accretion rates of $\rm \geq 0.1~M_{\odot}/yr$ to form a supermassive star. It is not yet clear how and under what conditions such accretion rates can be obtained. The prime aim of this work is to determine the mass accretion rates under non-isothermal collapse conditions. We perform high resolution cosmological simulations for three primordial halos of a few times $\rm 10^7~M_{\odot}$ illuminated by an external UV flux, $\rm J_{21}=100-1000$. We find that a rotationally supported structure of about parsec size is assembled, with an aspect ratio between $\rm 0.25 - 1$ depending upon the thermodynamical properties. Rotational support, however, does not halt collapse, and mass inflow rates of $\rm \sim 0.1~M_{\odot}/yr$ can be obtained in the presence of even a moderate UV background flux of strength $\rm J_{21} \geq 100$. To assess whether such large accretion rates can be maintained over longer time scales, we employed sink particles, confirming the persistence of accretion rates of $\rm \sim 0.1~M_{\odot}/yr$. We propose that complete isothermal collapse and molecular hydrogen suppression may not always be necessary to form supermassive stars, precursors of black hole seeds. Sufficiently high inflow rates can be obtained for UV flux $\rm J_{21}=500-1000$, at least for some cases. This value brings the estimate of the abundance of direct collapse black hole seeds closer to that high redshift quasars.