Quasar Clustering and the Lifetime of Quasars

Although the population of luminous quasars rises and falls over a period of 10^9 years, the typical lifetime of individual quasars is uncertain by several orders of magnitude. We show that quasar clustering measurements can substantially narrow the range of possible lifetimes with the assumption that luminous quasars reside in the most massive host halos. If quasars are long-lived, then they are rare phenomena that are highly biased with respect to the underlying dark matter, while if they are short-lived they reside in more typical halos that are less strongly clustered. For a given quasar lifetime, we calculate the minimum host halo mass by matching the observed space density of quasars, using the Press-Schechter approximation. We use the results of Mo & White to calculate the clustering of these halos, and hence of the quasars they contain, as a function of quasar lifetime. A lifetime of t_Q = 4 x 10^7 years, the e-folding timescale of an Eddington luminosity black hole with accretion efficiency eps=0.1, corresponds to a quasar correlation length r_0 ~ 10 Mpc/h in low-density cosmological models at z=2-3; this value is consistent with current clustering measurements, but these have large uncertainties. High-precision clustering measurements from the 2dF and Sloan quasar surveys will test our key assumption of a tight correlation between quasar luminosity and host halo mass, and if this assumption holds then they should determine t_Q to a factor of three or better. An accurate determination of the quasar lifetime will show whether supermassive black holes acquire most of their mass during high-luminosity accretion, and it will show whether the black holes in the nuclei of typical nearby galaxies were once the central engines of high-luminosity quasars.