Constraining the Lifetime of Quasars from Their Spatial Clustering

Abstract

The lifetime of the luminous phase of quasars is constrained by current observations to be 10⁶ t_Q 10⁸ yr but is otherwise unknown. 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 t_Q. We quantify this dependence and find that existing measurements of the correlation length of quasars are consistent with the range 10⁶ t_Q 10⁸ yr. We then show that future measurements of the power spectrum of quasars out to z ~ 3, from the Anglo-Australian Telescope Two-Degree Field or Sloan Digital Sky Survey, can significantly improve this constraint and in principle allow a precise determination of t_Q. 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.