Although the population of luminous quasars rises and falls over a period of \sim~ { } 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 \times 10 ^ { 7 } years , the e -folding timescale of an Eddington luminosity black hole with accretion efficiency \epsilon = 0.1 , corresponds to a quasar correlation length r _ { 0 } \approx 10 h ^ { -1 } { Mpc } 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 .