Can we measure the accretion efficiency of Active Galactic Nuclei?

The accretion efficiency for individual black holes is very difficult to determine accurately. There are many factors that can influence each step of the calculation, such as the dust and host galaxy contribution to the observed luminosity, the black hole mass and more importantly, the uncertainties on the bolometric luminosity measurement. Ideally, we would measure the AGN emission at every wavelength, remove the host galaxy and dust, reconstruct the AGN spectral energy distribution and integrate to determine the intrinsic emission and the accretion rate. In reality, this is not possible due to observational limitations and our own galaxy line of sight obscuration. We have then to infer the bolometric luminosity from spectral measurements made in discontinuous wavebands and at different epochs. In this paper we tackle this issue by exploring different methods to determine the bolometric luminosity. We first explore the trend of accretion efficiency with black hole mass (efficiency proportional to M^{\sim 0.5}) found in recent work by Davis & Laor and discuss why this is most likely an artefact of the parameter space covered by their PG quasar sample. We then target small samples of AGN at different redshifts, luminosities and black hole masses to investigate the possible methods to calculate the accretion efficiency. For these sources we are able to determine the mass accretion rate and, with some assumptions, the accretion efficiency distributions. Even though we select the sources for which we are able to determine the parameters more accurately, there are still factors affecting the measurements that are hard to constrain. We suggest methods to overcome these problems based on contemporaneous multi-wavelength data measurements and specifically targeted observations for AGN in different black hole mass ranges.