AGN evolution from a galaxy evolution viewpoint

We explore the connections between the evolving galaxy and AGN populations. We present a simple phenomenological model that links the evolving galaxy mass function and the evolving quasar luminosity function, which makes specific and testable predictions for the distribution of host galaxy masses for AGN of different luminosities. We show that the $\phi^{*}$ normalisations of the galaxy mass function and of the AGN luminosity function closely track each other over a wide range of redshifts, implying a constant "duty cycle" of AGN activity. The strong redshift evolution in the AGN $L^*$ can be produced by either an evolution in the distribution of Eddington ratios, or in the $m_{bh}/m_{*}$ mass ratio, or both. To try to break this degeneracy we look at the distribution of AGN in the SDSS ($m_{bh},L$) plane, showing that an evolving ratio $m_{bh}/m_{*} \propto (1+z)^2$ reproduces the observed data and also reproduces the local relations which connect the black hole population with the host galaxies for both quenched and star-forming populations. We stress that observational studies that compare the masses of black holes in active galaxies at high redshift with those in quiescent galaxies locally will always see much weaker evolution. Evolution of this form would produce, or could be produced by, a redshift-independent $m_{bh} - \sigma$ relation and could explain why the local $m_{bh} - \sigma$ relation is tighter than $m_{bh} - m_{*}$ even if $\sigma$ is not directly linked to black hole growth. Irrespective of the evolution of $m_{bh}/m_{*}$, the model reproduces both the appearance of "downsizing" and the so-called "sub-Eddington boundary" without any mass-dependence in the evolution of black hole growth rates.