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The Merger History of Supermassive Black Holes in Galaxies

The ubiquity of supermassive black holes (SMBHs) at the centers of nearby luminous galaxies can arise from the multiple mergers experienced by dark matter halos in hierarchical structure formation models, even if only a small fraction of these galaxies harbor SMBHs at high redshifts. We illustrate this possibility using cosmological Monte Carlo simulations of the merger history of dark matter halos and their associated SMBHs. In our most extreme models, in order to populate nearly every bright galaxy with an SMBH at z = 0, only a few percent of the halos with virial temperatures above 104 K are required to harbor an SMBH at high redshift. This possibility must be included in studies of the luminosity function and the clustering properties of quasars. We predict the number of SMBH merger events that are detectable by the gravitational wave experiment Laser Interferometer Space Antenna (LISA), as a function of redshift, out to z = 5. Although the event rates can be significantly reduced in scenarios with rare SMBHs, a minimum of ~10 detectable merger events per year is predicted if SMBH binaries coalesce efficiently. The observed distribution of events with redshift could yield valuable information on the SMBH formation process. If SMBH binaries do not coalesce, we find that at least several SMBH slingshot ejections probably occurred from z = 5 to the present in each galaxy more massive than ~1011 M☉ at z = 0. Although our results are sensitive to the minimum cooling mass assumed for the formation of SMBHs, we expect the qualitative predictions of our models to be robust.