The radiative efficiency of accretion flows in individual active galactic nuclei

The radiative efficiency of active galactic nucleus (AGN) is commonly estimated based on the total mass accreted and the total AGN light emitted per unit volume in the universe integrated over time (the Soltan argument). In individual AGNs, thin accretion disk model spectral fits can be used to deduce the absolute accretion rate Ṁ, if the black hole mass M is known. The radiative efficiency η is then set by the ratio of the bolometric luminosity L_bol to Ṁ c². We apply this method to determine η in a sample of 80 Palomar-Green quasars with well-determined L _bol, where Ṁ is set by thin accretion disk model fits to the optical luminosity density, and the M determination based on the bulge stellar velocity dispersion (13 objects) or the broad line region. We derive a mean log η = -1.05 ± 0.52 consistent with the Soltan-argument-based estimates. We find a strong correlation of η with M, rising from η ∼ 0.03 at M = 10⁷ M_⊙ and L/L_Edd ∼ 1 to η ∼ 0.4 at M = 10⁹ M_⊙ and L/L_Edd ∼ 0.3. This trend is related to the overall uniformity of L_opt/L _bol in our sample, particularly the lack of the expected increase in L_opt/L_bol with increasing M (and decreasing L/L _Edd), which is a generic property of thermal disk emission at fixed η. The significant uncertainty in the M determination is not large enough to remove the correlation. The rising η with M may imply a rise in the black hole spin with M, as proposed based on other indirect arguments.