Black hole variability and the star formation-AGN connection: Do all
  star-forming galaxies host an AGN?
  We investigate the effect of active galactic nucleus (AGN) variability on the
observed connection between star formation and black hole accretion in
extragalactic surveys. Recent studies have reported relatively weak
correlations between observed AGN luminosities and the properties of AGN hosts,
which has been interpreted to imply that there is no direct connection between
AGN activity and star formation. However, AGNs may be expected to vary
significantly on a wide range of timescales (from hours to Myr) that are far
shorter than the typical timescale for star formation (>~100 Myr). This
variability can have important consequences for observed correlations. We
present a simple model in which all star-forming galaxies host an AGN when
averaged over ~100 Myr timescales, with long-term average AGN accretion rates
that are perfectly correlated with the star formation rate (SFR). We show that
reasonable prescriptions for AGN variability reproduce the observed weak
correlations between SFR and L_AGN in typical AGN host galaxies, as well as the
general trends in the observed AGN luminosity functions, merger fractions, and
measurements of the average AGN luminosity as a function of SFR. These results
imply there may be a tight connection between AGN activity and SFR over galaxy
evolution timescales, and that the apparent similarities in rest-frame colors,
merger rates, and clustering of AGNs compared to "inactive" galaxies may be due
primarily to AGN variability. The results provide motivation for future deep,
wide extragalactic surveys that can measure the distribution of AGN accretion
rates as a function of SFR.
