Are quasars accreting at super-Eddington rates?

In a previous paper, Collin & Huré ([CITE]), using a sample of Active Galactic Nuclei (AGN) where the mass has been determined by reverberation studies (the Kaspi et al. [CITE] sample), have shown that if the optical luminosity is emitted by a steady accretion disc, it implies that about half of the objects of the sample are accreting close to the Eddington rate or at super-Eddington rates. We discuss here this problem in more detail, evaluating different uncertainties, and we conclude that this result is unavoidable, unless the masses are strongly underestimated by reverberation studies. This can occur if the broad line region is a flat thin rotating structure with the same axis as the accretion disc, close to the line of sight. However the masses deduced from reverberation mapping in AGN follow the same correlation between the black hole mass and the bulge mass as normal galaxies (Laor [CITE]), suggesting that they are correct within a factor of a few. There are then three issues to the problem: 1. accretion proceeds at Eddington or super-Eddington rates in these objects through slim or thick discs; 2. the optical luminosity is not produced directly by the gravitational release of energy, but by another mechanism, so super-Eddington rates are not required; 3. accretion discs are completely “non standard". Presently neither the predictions of models nor the observed spectral distributions are sufficient to help choose between these solutions. In particular, even for the super-Eddington model, the observed optical to bolometric luminosity ratio would be of the order of the observed one. In the super-Eddington solution, there is a strong anti-correlation between the observed velocity widths of the lines and the computed Eddington ratios (i.e. the accretion rate to the Eddington rate ratios), the largest ratios corresponding to the narrowest lines, actually to “Narrow Line Seyfert 1" nuclei. For the considered sample, the Eddington ratio decreases with an increasing black hole mass, while the opposite is found if the accretion rate is assumed to be proportional to the optical-UV luminosity, as is usually done. If these results are extrapolated to all quasars, it implies that the amount of mass locked in massive black holes should be larger than presently thought. If the Eddington ratio is assumed to be smaller than unity, the optical luminosity has to be produced by an additional non-gravitational mechanism. It has to be emitted by a dense and thick medium located at large distances from the center (103 to 104 gravitational radii). It can be due to reprocessing of the X-ray photons from the central source in a geometrically thin warped disc, or in dense “blobs" forming a geometrically thick system, which can be a part of the accretion flow or can constitute the basis of an outflow. The third possibility is not explored here, as it requires completely new models of accretion discs which are still to be developed