Empirical constraints on the evolution of the relationship between black hole and galaxy mass: Scatter matters

Rachel S. Somerville

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21 Scopus citations


I investigate whether useful constraints on the evolution of the relationship between galaxy mass (mgal) and black hole (BH) mass (mBH) can be obtained from recent measurements of galaxy stellar mass functions and quasi-stellar object (QSO) bolometric luminosity functions at high redshift. I assume a simple power-law relationship between mgal and mBH, as implied by BH mass measurements at low redshift, and consider only evolution in the zero-point of the relation. I argue that one can obtain a lower limit on the zero-point evolution by assuming that every galaxy hosts a BH, shining at its Eddington rate. One can obtain an upper limit by requiring that the number of massive BH at high redshift does not exceed that observed locally. I find that, under these assumptions, and neglecting scatter in the mgal-mBH relation, BH must have been a factor of ∼2 larger at z ∼ 1 and five to six times more massive relative to their host galaxies at z ∼ 2. However, accounting for intrinsic scatter in m gal-mBH considerably relaxes these constraints. With a logarithmic scatter of 0.3-0.5 dex in mBH at fixed mgal, similar to estimates of the intrinsic scatter in the observed relation today, there are enough massive BH to produce the observed population of luminous QSOs at z ∼ 2 even in the absence of any zero-point evolution. Adopting more realistic estimates for the fraction of galaxies that host active BH and the Eddington ratios of the associated quasars, I find that the zero-point of the mgal-mBH relation at z ∼ 2 cannot be much more than a factor of 2 times larger than the present-day value, as the number of luminous quasars predicted would exceed the observed population.

Original languageEnglish (US)
Pages (from-to)1988-1994
Number of pages7
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
StatePublished - Nov 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Black hole physics
  • Cosmology: theory
  • Galaxies: active
  • Galaxies: evolution
  • Galaxies: formation
  • Quasars: general


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