The Mass Function of Supermassive Black Holes in the Direct Collapse Scenario

Abstract

Abstract One of the ideas to explain the existence of supermassive black holes (SMBH) in place by z ∼ 7 is a phase of rapid accretion onto direct collapse black holes (DCBH) that started their lives with masses ∼104–5 M ⊙ . Considering the DCBH scenario, we show that the SMBH mass function has two characteristic features: 1. a power-law at intermediate masses whose index is the dimensionless ratio α ≡ λ/γ, where λ is the growth rate of the number of DCBH and γ is the growth rate of DCBH masses, both during the DCBH growth era; 2. a break in the power law profile set by β ≡ γ T, where T is the duration of the DCBH growth era. The observed quasar luminosity function can be described with this tapered power-law function.