We assess models for the assembly of supermassive black holes ( SMBHs ) at the center of galaxies that trace their hierarchical build-up far up in the dark halo ‘ merger tree ’ .
Motivated by the recent discovery of luminous quasars around redshift z \approx 6 – suggesting a very early assembly epoch – and by numerical simulations of the fragmentation of primordial molecular clouds in cold dark matter cosmogonies , we assume that the first ‘ seed ’ black holes ( BHs ) had intermediate masses and formed in ( mini ) halos collapsing at z \sim 20 from high- \sigma density fluctuations .
As these pregalactic holes become incorporated through a series of mergers into larger and larger halos , they sink to the center owing to 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 \Lambda CDM 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 \propto 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 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } 10 \% to the total BH mass density , \rho _ { SMBH } = 4 \times 10 ^ { 5 } { M _ { \odot } Mpc ^ { -3 } } ( h = 0.7 ) .
The fraction of binary SMBHs in galaxy nuclei is of order 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 0.1 L _ { * } ) 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- \sigma ( 4- \sigma ) density peaks at z = 20 .