Hopkins, Philip F.Robertson, BrantKrause, ElisabethHernquist, LarsCox, Thomas J.2019-09-202006Hopkins, Philip F., Brant Robertson, Elisabeth Krause, Lars Hernquist, and Thomas J. Cox. 2006. “An Upper Limit to the Degree of Evolution between Supermassive Black Holes and Their Host Galaxies.” The Astrophysical Journal 652 (1): 107–11. https://doi.org/10.1086/508055.0004-637X1538-4357http://nrs.harvard.edu/urn-3:HUL.InstRepos:41381863We describe a model-independent integral constraint that defines an upper limit to the allowed degree of evolution in the ratio of black hole (BH) mass to host galaxy luminosity or mass, as a function of redshift. Essentially, if the BH/host ratio is excessive at redshift z, then it would imply that the total mass density in BHs above some M-BH(min) is larger at that redshift than at z = 0, which is impossible. This argument requires no knowledge of host or BH properties, only a lower limit to the observed luminosity density in the brightest galaxies at some z. We calculate this upper limit from a variety of luminosity and mass functions in different bands from redshifts z = 0-2. We show that it is consistent with passive evolution of spheroid populations (with a fixed M-BH/M-host relation) in all cases, and provides tighter constraints than have generally been obtained previously, ruling out at greater than or similar to 6 sigma observational and theoretical estimates suggesting that M-BH/M-host was significantly larger at high redshifts than locally. We discuss a variety of possible ''loopholes'' or changes in the BH/ host populations and correlations, and show that they typically lower the upper limits and strengthen our conclusions.en-USJournal Article2019-09-2010.1086/508055