2001ApJ...552..459H

The recent discoveries of luminous quasars at high redshifts imply that black holes more massive than a few billion solar masses were already assembled when the universe was less than a billion years old. We show that the existence of these black holes is not surprising in popular hierarchical models of structure formation. For example, the black hole needed to power the quasar SDSS 1044-0125 at z=5.8 could arise naturally from the growth of stellar-mass seeds forming at z>10, when typical values are assumed for the radiative accretion efficiency (∼0.1) and the bolometric accretion luminosity in Eddington units (∼1). Nevertheless, SDSS 1044-0125 yields a nontrivial constraint on a combination of these parameters. Extrapolating our model to future surveys, we derive the highest plausible redshift for quasars that are not lensed or beamed, as a function of their apparent magnitude. We find that at a limiting magnitude of K∼20, quasar surveys can yield strong constraints on the growth of supermassive black holes out to z∼10.