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An Upper Limit to the Degree of Evolution Between Supermassive Black Holes and their Host Galaxies

Philip F. Hopkins·Brant Robertson·Elisabeth Krause·Lars Hernquist·Thomas J. Cox
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Abstract

We describe a model-independent integral constraint which 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 >6 sigma observational and theoretical estimates suggesting that M_BH/M_host was significantly larger at high redshifts than locally, although relatively weak (factor ~2 by z=2) evolution is still allowed. 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.

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Philip F. Hopkins, Brant Robertson, Elisabeth Krause, Lars Hernquist, Thomas J. Cox. 2006-08-03. An Upper Limit to the Degree of Evolution Between Supermassive Black Holes and their Host Galaxies. https://doi.org/10.1086/508055

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