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

TL;DR

This study analyzes a large dataset of supermassive black holes to demonstrate that their Eddington ratio depends on both mass and redshift, impacting estimates of their growth and radiative efficiency.

Contribution

It provides the first large-scale evidence that Eddington ratio varies with SMBH mass and redshift, challenging the assumption of constant radiative efficiency.

Findings

Eddington ratio decreases with decreasing redshift for similar SMBH masses.

Larger SMBHs have lower Eddington ratios at a given redshift.

Radiative efficiency likely varies with SMBH mass and redshift, affecting accretion estimates.

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.