A no-go theorem for direct collapse black holes without a strong ultraviolet background.

Explaining the existence of supermassive black holes larger than ∼10⁹ M_⊙ at redshifts z ≳ 6 remains an open theoretical question. One possibility is that gas collapsing rapidly in pristine atomic cooling haloes (T_vir ≳ 10⁴ K) produces 10⁴-10⁶ M_⊙ black holes. Previous studies have shown that the formation of such a black hole requires a strong UV background to prevent molecular hydrogen cooling and gas fragmentation. Recently, it has been proposed that a high UV background may not be required for haloes that accrete material extremely rapidly or for haloes where gas cooling is delayed due to a high baryon-dark matter streaming velocity. In this work, we point out that building up a halo with T_vir ≳ 10⁴ K before molecular cooling becomes efficient is not sufficient for forming a direct collapse black hole (DCBH). Though molecular hydrogen formation may be delayed, it will eventually form at high densities leading to efficient cooling and fragmentation. The only obvious way that molecular cooling could be avoided in the absence of strong UV radiation, is for gas to reach high enough density to cause collisional dissociation of molecular hydrogen (∼10⁴ cm^-3) before cooling occurs. However, we argue that the minimum core entropy, set by the entropy of the intergalactic medium when it decouples from the cosmic microwave background, prevents this from occurring for realistic halo masses. This is confirmed by hydrodynamical cosmological simulations without radiative cooling. We explain the maximum density versus halo mass in these simulations with simple entropy arguments. The low densities found suggest that DCBH formation indeed requires a strong UV background.