The Black Hole Mass Function across Cosmic Time. II. Heavy Seeds and (Super)Massive Black Holes

This is the second paper in a series aimed at modeling the black hole (BH) mass function from the stellar to the (super)massive regime. In the present work, we focus on (super)massive BHs and provide an ab initio computation of their mass function across cosmic time. We consider two main mechanisms to grow the central BH that are expected to cooperate in the high-redshift star-forming progenitors of local massive galaxies. The first is the gaseous dynamical friction process, which can cause the migration toward the nuclear regions of stellar mass BHs originated during the intense bursts of star formation in the gas-rich host progenitor galaxy and the buildup of a central heavy BH seed, M • ~ 103-5 M ⊙, within short timescales of ≲some 107 yr. The second mechanism is the standard Eddington-type gas disk accretion onto the heavy BH seed through which the central BH can become (super)massive, M • ~ 106-10 M ⊙, within the typical star formation duration, ≲1 Gyr, of the host. We validate our semiempirical approach by reproducing the observed redshift-dependent bolometric AGN luminosity functions and Eddington ratio distributions and the relationship between the star formation and the bolometric luminosity of the accreting central BH. We then derive the relic (super)massive BH mass function at different redshifts via a generalized continuity equation approach and compare it with present observational estimates. Finally, we reconstruct the overall BH mass function from the stellar to the (super)massive regime over more than 10 orders of magnitudes in BH mass.