An Upper Limit to the Degree of Evolution between Supermassive Black Holes and Their Host Galaxies

We describe a model-independent integral constraint which defines an upperlimit to the allowed degree of evolution in the ratio of black hole (BH) massto host galaxy luminosity or mass, as a function of redshift. Essentially, ifthe BH/host ratio is excessive at redshift z, then it would imply that thetotal mass density in BHs above some M_BH(min) is larger at that redshift thanat z=0, which is impossible. This argument requires no knowledge of host or BHproperties, only a lower limit to the observed luminosity density in thebrightest galaxies at some z. We calculate this upper limit from a variety ofluminosity and mass functions in different bands from redshifts z=0-2. We showthat it is consistent with passive evolution of spheroid populations (with afixed M_BH/M_host relation) in all cases, and provides tighter constraints thanhave generally been obtained previously, ruling out at >6 sigma observationaland theoretical estimates suggesting that M_BH/M_host was significantly largerat high redshifts than locally, although relatively weak (factor ~2 by z=2)evolution is still allowed. We discuss a variety of possible 'loopholes' orchanges in the BH/host populations and correlations, and show that theytypically lower the upper limits and strengthen our conclusions.Comment: 6 pages, 2 figures. Accepted for publication in Ap