THE ASSEMBLY OF SUPERMASSIVE BLACK HOLES AT HIGH REDSHIFTS

The supermassive black holes (SMBHs) massive enough (greater than or similar to few x 10(9) M-circle dot)to power the bright redshift z approximate to 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 similar to 10(2) M-circle dot 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 protogalaxies by the large (several x 10(2) 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 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 (1) to map out plausible scenarios for successful assembly of the z approximate to 6 quasar BHs by exploring a wide region of parameter space, and (2) 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) similar to 100 M-circle dot seed BHs can grow into the SDSS quasar BHs without super-Eddington accretion, but only if they form in minihalos at z greater than or similar to 30 and subsequently accrete greater than or similar to 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 x 10(5) M-circle dot less than or similar to M-bh less than or similar to few x 10(7) M-circle dot) BHs by a factor of 10(2)-10(3), unless seeds stop forming, or accrete at a severely diminished rates or duty cycles (e. g., due to feedback), at z less than or similar to 20-30. We also present several successful assembly models and their LISA detection rates, including a maximal model that gives the highest rate (similar to 30 yr(-1) at z = 6) without overproducing the total SMBH density.