Evidence that Eddington ratio depends upon a supermassive black hole's mass and redshift: implications for radiative efficiency

Abstract

Presently, it is unclear whether the Eddington ratio (λ) and radiative efficiency (ϵ) depend on a supermassive black hole's (SMBH's) redshift z and mass MBH. We attempt to resolve this issue using published data for 132 000 SMBHs with MBH ≥ 107 Msun (solar masses) at ∼0.1 < z < 2.4 covering ∼10 billion years of cosmic time, with MBH determined using Mg ii lines and bolometric luminosities Lbol based on a weighted mean of Lbol from two or more monochromatic luminosities and a single uniformly applied correction factor. The SMBHs are sorted into seven MBH bins separated from each other by half an order of magnitude. The λ and z data in each bin are subjected to spline regression analysis. The results unambiguously show that for similar-size SMBHs, λ decreases as z decreases, and that for a given redshift, larger SMBHs have a lower λ. These findings require that either an SMBH's accretion rate and/or its radiative efficiency be a function of z and MBH and, in the context of the Bondi accretion model, imply that radiative efficiency is an inverse function of z and MBH. These findings suggest that SMBHs become less efficient (higher ϵ) in accreting gases as the ambient gas density decreases with z and that larger SMBHs are more efficient (lower ϵ) than smaller ones. The results leave little doubt that the current widespread practice of assigning ϵ a standard value is untenable and gives erroneous estimates of accretion rates and growth times of SMBHs.