2003/04/09 by J. Stuart B. Wyithe, Stuart Wyithe, Abraham Loeb · 443 citations
Physics and Astronomy · #Active galactic nucleus #Astronomy #Astronomy and Astrophysical Research #Astrophysics #Black hole (networking) #Cosmology #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Galaxy #Galaxy formation and evolution #Halo #Intermediate-mass black hole #Luminosity #Physics #Quasar #Redshift #Supermassive black hole #Velocity dispersion #astro-ph
paper · pdf · doi:10.1086/377475
published in The Astrophysical Journal 595(2), 614-623 (IOP Publishing) · 10 pages, 5 figures, submitted to ApJ
arxiv created 2003/04/09 · openalex publication_date 2003/09/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08
We postulate that supermassive black holes grow in the centers of galaxies until they unbind the galactic gas that feeds them. We show that the corresponding self-regulation condition yields a correlation between black hole mass ( M bh ) and galaxy velocity dispersion (σ) as inferred in the local universe and recovers the observed optical and X-ray luminosity functions of quasars at redshifts up to z ~ 6 based on the hierarchical evolution of galaxy halos in a Λ-dominated cold dark matter cosmology. With only one free parameter and a simple algorithm, our model yields the observed evolution in the number density of optically bright or X-ray-faint quasars with 2 ≲ z ≲ 6 across 3 orders of magnitude in bolometric luminosity and 3 orders of magnitude in comoving density per logarithm of luminosity. The self-regulation condition identifies the dynamical time of galactic disks during the epoch of peak quasar activity ( z ~ 2.5) as the origin of the inferred characteristic quasar lifetime of ~10 7 yr. Since the lifetime becomes comparable to the Salpeter e -folding time at this epoch, the model also implies that the M bh -σ relation is a product of feedback-regulated accretion during the peak of quasar activity. The mass density in black holes accreted by that time is consistent with the local black hole mass density ρ bh ~ (2.3 ) × 10 5 M ☉ Mpc -3 , which we have computed by combining the M bh -σ relation with the measured velocity dispersion function of Sloan Digital Sky Survey galaxies. Comparison of the local black hole mass function with that inferred from combining the feedback relation with the halo mass function suggests that most massive (>10 9 M ☉ ) black holes may have already been in place by z ~ 6. Applying a similar self-regulation principle to supernova-driven winds from starbursts, we find that the local ratio between the black hole mass and the stellar mass of galactic spheroids should be ~0.001, independent of mass and in agreement with observations. This ratio increases with redshift, although the M bh -σ relation is redshift-independent.