| Abstract
| - We present a study of the X-ray to optical properties of a sample of 545 X-ray selected type 1 AGN, from the XMM-COSMOS survey, over a wide range of redshifts (0.04 < z< 4.25) and X-ray luminosities (40.6 ≤ Log $L_{[2-10]~{\rm keV}}$≤ 45.3). About 60% of them are spectroscopically identified type 1 AGN, while the others have a reliable photometric redshift and are classified as type 1 AGN on the basis of their multi-band Spectral Energy Distributions. We discuss the relationship between UV and X-ray luminosity, as parameterized by the $\alpha_{\rm ox}$ spectral slope, and its dependence on redshift and luminosity. We compare our findings with previous investigations of optically selected broad-line AGN (mostly from SDSS). A highly significant correlation between $\alpha_{\rm ox}$ and $L_{2500~{\rm \AA}}$ is found, in agreement with previous investigations of optically selected samples. We calculate bolometric corrections, kbol, for the whole sample using hard X-ray luminosities ( $L_{[2-10]~{\rm keV}}$), and the Eddington ratios for a subsample of 150 objects for which black hole mass estimates are available. We confirm the trend of increasing bolometric correction with increasing Eddington ratio as proposed in previous works. A tight correlation is found between $\alpha_{\rm ox}$ and kbol, which can be used to estimate accurate bolometric corrections using only optical and X-ray data. We find a significant correlation between $\alpha_{\rm ox}$ and Eddington ratio, in which the ratio between X-ray and optical flux decreases with increasing Eddington ratio.
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