2024MNRAS.530.1512A

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 M_BH. We attempt to resolve this issue using published data for 132 000 SMBHs with M_BH ≥ 10⁷ M_sun (solar masses) at ∼0.1 < z < 2.4 covering ∼10 billion years of cosmic time, with M_BH determined using Mg II lines and bolometric luminosities L_bol based on a weighted mean of L_bol from two or more monochromatic luminosities and a single uniformly applied correction factor. The SMBHs are sorted into seven M_BH 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 M_BH and, in the context of the Bondi accretion model, imply that radiative efficiency is an inverse function of z and M_BH. 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.