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 and radiative efficiency depend upon 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 >1E+7 Msun (solar masses) at ~0.1<z<2.4 covering ~10 billion years of cosmic time, with MBH determined using MgII 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 7 MBH bins separated from each other by half an order of magnitude. The Eddington ratio and z data in each bin are subjected to spline regression analysis. The results unambiguously show that for similar-size SMBHs, the Eddington ratio decreases as z decreases and that for a given redshift larger SMBHs have a lower Eddington ratio. These findings require that either a 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 a SMBH's redshift z and mass MBH. These findings suggest that SMBHs become less efficient (higher radiative efficiency) in accreting gases as the ambient gas density decreases with z and that larger SMBHs are more efficient (lower radiative efficiency) than smaller ones. The results leave little doubt that the current widespread practice of assigning radiative efficiency a standard value is untenable and gives erroneous estimates of accretion rates and growth times of SMBHs.