Constraining the Lifetime of Quasars from Their Spatial Clustering

The lifetime of the luminous phase of quasars is constrained by current observations to be 10 ∼< tQ ∼< 10 years, but is otherwise unkown. We model the quasar luminosity function in detail in the optical and X–ray bands using the Press–Schechter formalism, and show that the expected clustering of quasars depends strongly on their assumed lifetime tQ. We quantify this dependence, and find that existing measurements of the correlation length of quasars are consistent with the range 10 ∼< tQ ∼< 10. We then show that future measurements of the power spectrum of quasars out to z ∼ 3, from the 2dF or Sloan Digital Sky Survey, can significantly improve this constraint, and in principle allow a precise determination of tQ. We estimate the systematic errors introduced by uncertainties in the modeling of the quasar-halo relationship, as well as by the possible existence of obscured quasars. Subject headings: cosmology: theory – cosmology: observation – quasars: formation – large scale structure