Calibrating the galaxy halo-black hole relation based on the clustering of quasars

The observed number counts of quasars can be explained either by long-lived activity within rare massive hosts or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes can therefore be inferred from their clustering length, which determines the typical mass of the quasar host. Here we point out that the relationship between the mass of the black hole and the circular velocity of its host dark matter halo is more fundamental to the determination of the clustering length. In particular, the clustering length observed in the Two-Degree Field (2dF) quasar redshift survey is consistent with the galactic halo-black hole relation observed in local galaxies, provided that quasars shine at similar to10%-100% of their Eddington luminosity. The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black hole mass whose redshift-independent scaling is with halo circular velocity rather than halo mass. These results are independent from observations of the number counts of bright quasars, which can be used to determine the quasar lifetime and its dependence on redshift. We show that if quasar activity results from galaxy mergers, then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time. Our results imply that as the redshift increases, the central black holes comprise a larger fraction of their host galaxy mass, and the quasar lifetime gets shorter.