The Assembly of Supermassive Black Holes at High Redshifts

The supermassive black holes (SMBHs) massive enough (& few×10M⊙) to power the bright redshift z ≈ 6 quasars observed in the Sloan Digital Sky Survey (SDSS) are thought to have assembled by mergers and/or gas accretion from less massive “seed” BHs. If the seeds are the ∼ 10M⊙ remnant BHs from the first generation of stars, they must be in place well before redshift z = 6, and must avoid being ejected from their parent proto–galaxies by the large (several×102 km s−1) kicks they suffer from gravitational–radiation induced recoil during mergers with other BHs. We simulate the SMBH mass function at redshift z > 6 using dark matter (DM) halo merger trees, coupled with a prescription for the halo occupation fraction, accretion histories, and radial recoil trajectories of the growing BHs. Our purpose is (i) to map out plausible scenarios for successful assembly of the z ≈ 6 quasar BHs by exploring a wide region of parameter space, and (ii) to predict the rate of low–frequency gravitational wave events detectable by the Laser Interferometer Space Antenna (LISA) for each such scenario. Our main findings are as follows: (1) ∼ 100M⊙ seed BHs can grow into the SDSS quasar BHs without super–Eddington accretion, but only if they form in minihalos at z & 30 and subsequently accrete & 60% of the time; (2) the scenarios with optimistic assumptions required to explain the SDSS quasar BHs overproduce the mass density in lower–mass (few×10M⊙ ∼ < Mbh ∼ < few×10M⊙) BHs by a factor of 102−103, unless seeds stop forming, or accrete at a severely diminished rates or duty cycles (e.g. due to feedback), at z ∼< 20− 30. We also present several successful assembly models and their LISA detection rates, including a “maximal” model that gives the highest rate (∼ 30 yr−1 at z = 6) without overproducing the total SMBH density. Subject headings: cosmology: theory – galaxies: formation – quasars: general – black hole physics – accretion