The Mass Function of Supermassive Black Holes in the Direct-collapse Scenario
Abstract
One of the ideas that explains the existence of supermassive black holes (SMBHs) that are in place by z ∼ 7 is that there was an earlier phase of very rapid accretion onto direct-collapse black holes (DCBHs) that started their lives with masses ∼104-5 {M}⊙ . Working in this scenario, we show that the mass function of SMBHs after such a limited time period, with growing formation rate paired with super-Eddington accretion, can be described as a broken power law with two characteristic features. There is 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 DCBHs during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era. A second feature is a break in the power-law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number β = γ T, where T is the duration of the period of DCBH growth. If the SMBHs continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law function derived in this Letter.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- July 2019
- DOI:
- 10.3847/2041-8213/ab2646
- arXiv:
- arXiv:1906.05138
- Bibcode:
- 2019ApJ...879L...3B
- Keywords:
-
- accretion;
- accretion disks;
- black hole physics;
- galaxies: high-redshift;
- quasars: general;
- quasars: supermassive black holes;
- Astrophysics - Astrophysics of Galaxies
- E-Print:
- 6 pages, 3 figures, accepted to ApJ