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

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We 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 MBHmin 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 MBH/Mhost relation) in all cases, and provides tighter constraints than have generally been obtained previously, ruling out at ≳6 σ observational and theoretical estimates suggesting that MBH/Mhost 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.

Original languageEnglish (US)
Pages (from-to)107-111
Number of pages5
JournalAstrophysical Journal
Issue number1 I
StatePublished - Nov 20 2006


  • Cosmology: theory
  • Galaxies: active
  • Galaxies: evolution
  • Quasars: general

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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