A Simple Model for Quasar Demographics

Abstract

We present a simple model for the relationship between quasars, galaxies, and dark matter halos from 0.5<z<6. In the model, black hole (BH) mass is linearly related to galaxy mass, and galaxies are connected to dark matter halos via empirically constrained relations. A simple "scattered" light bulb model for quasars is adopted, wherein BHs shine at a fixed fraction of the Eddington luminosity during accretion episodes, and Eddington ratios are drawn from a lognormal distribution that is redshift-independent. This model has two free, physically meaningful parameters at each redshift: the normalization of the Mbh-Mgal relation and the quasar duty cycle; these parameters are fit to the observed quasar luminosity function (LF) over the interval 0.5<z<6. This simple model provides an excellent fit to the LF at all epochs, and also successfully predicts the observed projected two-point correlation of quasars from 0.5<z<2.5. It is significant that a single quasar duty cycle at each redshift is capable of reproducing the extant observations. The data are therefore consistent with a scenario wherein quasars are equally likely to exist in galaxies, and therefore dark matter halos, over a wide range in masses. The knee in the quasar LF is a reflection of the knee in the stellar mass-halo mass relation. Future constraints on the quasar LF and quasar clustering at high redshift will provide strong constraints on the model. In the model, the autocorrelation function of quasars becomes a strong function of luminosity only at the very highest luminosities, and will be difficult to observe because such quasars are so rare. Cross-correlation techniques may provide useful constraints on the bias of such rare objects.