A simple model for quasar demographics

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 M BH-M gal 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. The simplicity of the model allows for rapid generation of quasar mock catalogs from N-body simulations that match the observed LF and clustering to high redshift. © 2013. The American Astronomical Society. All rights reserved.