The most massive black holes in the universe:: Effects of mergers in massive galaxy clusters

Recent observations support the idea that nuclear black holes grew by gas accretion while shining as luminous quasars at high redshift, and they establish a relation of the black hole mass with the host galaxy's spheroidal stellar system. We develop an analytic model to calculate the expected impact of mergers on the masses of black holes in massive clusters of galaxies. We use the extended Press-Schechter formalism to generate Monte Carlo merger histories of halos with a mass 10(15) h(-1) M-circle dot. We assume that the black hole mass function at z = 2 is similar to that inferred from observations at z = 0 ( since quasar activity declines markedly at z < 2), and we assign black holes to the progenitor halos assuming a monotonic relation between halo mass and black hole mass. We follow the dynamical evolution of subhalos within larger halos, allowing for tidal stripping, the loss of orbital energy by dynamical friction, and random orbital perturbations in gravitational encounters with subhalos, and we assume that most black holes will efficiently merge after their host galaxies ( represented as the nuclei of subhalos in our model) merge. Our analytic model reproduces numerical estimates of the subhalo mass function. We find that mergers can increase the mass of the most massive black holes in massive clusters typically by a factor similar to 2, after gas accretion has stopped. In our 10 realizations of 10(15) h(-1)M(circle dot) clusters, the highest initial ( z = 2) black hole masses are 5-7 x 10(9) M-circle dot, but four of the clusters contain black holes in the range 1 - 1.5 x 10(10) M-circle dot at z = 0. Satellite galaxies may host black holes whose mass is comparable to, or even greater than, that of the central galaxy. Thus, black hole mergers can significantly extend the very high end of the black hole mass function.