The assembly and merging history of supermassive black holes in hierarchical models of galaxy formation

We assess models for the assembly of supermassive black holes (SMBHs) at the center of galaxies that trace their hierarchical buildup far up in the dark halo "merger tree." Motivated by the recent discovery of luminous quasars around redshift z ≈ 6 - suggesting a very early assembly epoch - and by numerical simulations of the fragmentation of primordial molecular clouds in cold dark matter (CDM) cosmogonies, we assume that the first "seed" black holes (BHs) had intermediate masses and formed in (mini)halos collapsing at z ∼ 20 from high-σ density fluctuations. As these pregalactic holes become incorporated through a series of mergers into larger and larger halos, they sink to the center because of dynamical friction, accrete a fraction of the gas in the merger remnant to become supermassive, form a binary system, and eventually coalesce. The merger history of dark matter halos and associated BHs is followed by cosmological Monte Carlo realizations of the merger hierarchy from early times until the present in a ACDM cosmology. A simple model, where quasar activity is driven by major mergers and SMBHs accrete at the Eddington rate a mass that scales with the fifth power of the circular velocity of the host halo, is shown to reproduce the observed luminosity function of optically selected quasars in the redshift range 1 < z < 5. A scheme for describing the hardening of a BH binary in a stellar background with core formation due to mass ejection is applied, where the stellar cusp proportional to r-2 is promptly regenerated after every major merger event, replenishing the mass displaced by the binary. Triple BH interactions will inevitably take place at early times if the formation route for the assembly of SMBHs goes back to the very first generation of stars, and we follow them in our merger tree. The assumptions underlying our scenario lead to the prediction of a population of massive BHs wandering in galaxy halos and the intergalactic medium at the present epoch and contributing ≲ 10% to the total BH mass density, ρSMBH = 4 × 105 M⊙ Mpc-3 (h = 0.7). The fraction of binary SMBHs in galaxy nuclei is on the order of 10% today, and it increases with redshift so that almost all massive nuclear BHs at early epochs are in binary systems. The fraction of binary quasars (both members brighter than 0.1L*) instead is less than 0.3% at all epochs. The nuclear SMBH occupation fraction is unity (0.6) at the present epoch if the first seed BHs were as numerous as the 3.5 σ (4 σ) density peaks at z = 20.