Quasar Clustering and the Lifetime of Quasars

Although the population of luminous quasars rises and falls over a period of10^9 years, the typical lifetime of individual quasars is uncertain by severalorders of magnitude. We show that quasar clustering measurements cansubstantially narrow the range of possible lifetimes with the assumption thatluminous quasars reside in the most massive host halos. If quasars arelong-lived, then they are rare phenomena that are highly biased with respect tothe underlying dark matter, while if they are short-lived they reside in moretypical halos that are less strongly clustered. For a given quasar lifetime, wecalculate the minimum host halo mass by matching the observed space density ofquasars, using the Press-Schechter approximation. We use the results of Mo &White to calculate the clustering of these halos, and hence of the quasars theycontain, 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 accretionefficiency eps=0.1, corresponds to a quasar correlation length r_0 ~ 10 Mpc/hin low-density cosmological models at z=2-3; this value is consistent withcurrent clustering measurements, but these have large uncertainties.High-precision clustering measurements from the 2dF and Sloan quasar surveyswill test our key assumption of a tight correlation between quasar luminosityand host halo mass, and if this assumption holds then they should determine t_Qto a factor of three or better. An accurate determination of the quasarlifetime will show whether supermassive black holes acquire most of their massduring high-luminosity accretion, and it will show whether the black holes inthe nuclei of typical nearby galaxies were once the central engines ofhigh-luminosity quasars.