Radiative efficiency of disc accretion in individual SDSS QSOs

Abstract

We estimate the radiative efficiency εof individual type 1 SDSSQSOs by using their bolometric luminosities (Lbol) and accretion rate ( Ṁ•acc), which may be related to the assembly histories and spins of the central massive black holes (MBHs). We estimate Lbol by using the empirical spectral energy distributions of QSOs and Ṁ•acc by fitting the observed optical luminosity (luminosities) with the thin accretion disc model, assuming the MBH masses given by the virial mass estimator(s) (M•vir). We find an apparent correlation between ε and M•vir, which is strong at redshift z ≲ 1.8, weak at z ≳ 2 and consistent with that found by Davis and Laor for 80 Palomar Green (PG) QSOs at z≤ 0.5. To investigate whether this correlation is intrinsic or not, we construct a mock sample of QSOs according to the true MBH mass and Eddington ratio distributions given in Kelly and Shen. By comparing the results obtained from the mock sample with that from the SDSS sample, we demonstrate that the apparent ε-M•vir correlation can be produced by and mainly due to the selection effects of the SDSS sample and the bias induced by the usage of MM•vir as the true MBH mass. The mean value of of those SDSS QSOs are consistent with being a constant 0.11-0.16 over the redshift range of 0.3 ≲ z ≲ 4. We conclude that the current SDSS QSO data are consistent with no strong intrinsic correlation between radiative efficiency and true MBH mass and no significant redshift evolution of radiative efficiencies. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.