Eddington ratios of faint AGN at intermediate redshift: evidence for a population of half-starved black holes*

We use one of the deepest spectroscopic samples of broad-line active galactic nuclei (AGN) currently available, extracted from the VIMOS VLT Deep Survey (VVDS), to compute the $\ion{Mg}{ii}$and $\ion{C}{iv}$virial-mass estimates of 120 super-massive black holes in the redshift range $1.0<z<1.9$and $2.6<z<4.3$. We find that the mass-luminosity relation shows considerably enhanced dispersion towards low AGN luminosities ($\log L_\mathrm{bol} \sim 45$). At these luminosities, there is a substantial fraction of black holes accreting far below their Eddington limit ($L_\mathrm{bol}/L_\mathrm{Edd} < 0.1$), in marked contrast to what is generally found for AGN of higher luminosities. We speculate that these may be AGN on the decaying branch of their lightcurves, well past their peak activity. This would agree with recent theoretical predictions of AGN evolution. In the electronic Appendix of this paper we publish an update of the VVDS type-1 AGN sample, including the first and most of the second-epoch observations. This sample contains 298 objects of which 168 are new.