A possible bias on the estimate of Lbol/Ledd in AGN as a function of   luminosity and redshift
  The BH mass (and the related Eddington ratio) in broad line AGN is usually evaluated by combining estimates (often indirect) of the BLR radius and of the FWHM of the broad lines, under the assumption that the BLR clouds are in Keplerian motion around the BH. Such an evaluation depends on the geometry of the BLR. There are two major options for the BLR configuration: spherically symmetric or ``flattened''. In the latter case the inclination to the line of sight becomes a relevant parameter. This paper is devoted to evaluate the bias on the estimate of the Eddington ratio when a spherical geometry is assumed (more generally when inclination effects are ignored), while the actual configuration is ``flattened'', as some evidence suggests. This is done as a function of luminosity and redshift, on the basis of recent results which show the existence of a correlation between the fraction of obscured AGN and these two parameters up to at least z=2.5. The assumed BLR velocity field is akin to the ``generalized thick disk'' proposed by Collin et al. (2006). Assuming an isotropic orientation in the sky, the mean value of the bias is calculated as a function of luminosity and redshift. It is demonstrated that, on average, the Eddington ratio obtained assuming a spherical geometry is underestimated for high luminosities, and overestimated for low luminosities. This bias converges for all luminosities at z about 2.7, while nothing can be said on this bias at larger redshifts due to the lack of data. The effects of the bias, averaged over the luminosity function of broad line AGN, have been calculated. The results imply that the bias associated with the a-sphericity of the BLR make even worse the discrepancy between the observations and the predictions of evolutionary models. 
Alessandra Lamastra, Giorgio Matt and G. Cesare Perola