Impact of gas spin and Lyman-Werner flux on black hole seed formation in cosmological simulations: implications for direct collapse

Direct collapse black holes~(BH) are promising candidates for producing massive $z\gtrsim 6$ quasars, but 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 in order to form BH seeds. We probe the formation of seeds (with initial masses of $M_{\rm seed} \sim 10^4$ - $10^6 M_{\odot}/h)$ in halos with a total mass $> 3000\times M_{\mathrm{seed}}$ and a dense, metal poor gas mass $> 5\times M_{\mathrm{seed}}$. We find that the seed-forming halos have a prior history of star formation and metal enrichment, but contain pockets of dense, metal poor gas. When seeding is further restricted to halos with low gas spins, the number of seeds formed is suppressed by factors of $\sim6$ compared to the baseline model, regardless of the seed mass. Seed formation is much more strongly impacted if the dense, metal poor gas is required to have a critical LW flux ($J_{\mathrm{crit}}$). Even for $J_{\mathrm{crit}}$ values as low as $50J_{21}$, no $8\times10^{5}M_{\odot}/h$ seeds are formed. While lower mass ($1.25\times10^{4},1\times10^{5} M_{\odot}/h$) seeds do form, they are strongly suppressed~(by factors of $\sim10-100$) compared to the baseline model at gas mass resolutions of $\sim10^4~M_{\odot}/h$ (with even stronger suppression at higher resolutions). As a result, BH merger rates are also similarly suppressed. Since early BH growth is dominated by mergers in our models, no seeds are able to grow to the supermassive regime~($\gtrsim10^6 M_{\odot}/h$) by $z=7$. Our results hint that producing the bulk of the $z\gtrsim6$ supermassive BH population may require alternate seeding scenarios that do not depend on the LW flux, early BH growth dominated by rapid or super-Eddington accretion, or a combination of these possibilities.