Calibrating the Galaxy Halo–Black Hole Relation Based on the Clustering of Quasars

The observed number counts of quasars may be explained either by long-livedactivity within rare massive hosts, or by short-lived activity within smaller,more common hosts. It has been argued that quasar lifetimes may therefore beinferred from their clustering length, which determines the typical mass of thequasar host. Here we point out that the relationship between the mass of theblack-hole and the circular velocity of its host dark-matter halo is morefundamental to the determination of the clustering length. In particular, theclustering length observed in the 2dF quasar redshift survey is consistent withthe galactic halo - black-hole relation observed in local galaxies, providedthat quasars shine at ~10-100% of their Eddington luminosity. The slowevolution of the clustering length with redshift inferred in the 2dF quasarsurvey favors a black-hole mass whose redshift-independent scaling is with halocircular velocity, rather than halo mass. These results are independent fromobservations of the number counts of bright quasars which may be used todetermine the quasar lifetime and its dependence on redshift. We show that ifquasar activity results from galaxy mergers, then the number counts of quasarsimply an episodic quasar lifetime that is set by the dynamical time of the hostgalaxy rather than by the Salpeter time. Our results imply that as the redshiftincreases, the central black-holes comprise a larger fraction of their hostgalaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap