The maximum number density of Active Galactic Nuclei (AGNs), as deduced from X-ray studies, occurs at z<~1, with lower luminosity objects peaking at smaller redshifts. Optical studies lead to a different evolutionary behaviour, with a number density peaking at z~2 independently of the intrinsic luminosity, but this result is limited to active nuclei brighter than the host galaxy. A selection based on optical variability can detect low luminosity AGNs (LLAGNs), where the host galaxy light prevents the identification by non-stellar colours. We want to collect X-ray data in a field where it exists an optically-selected sample of variable galaxies, i.e. variable objects with diffuse appearance, to investigate the X-ray and optical properties of the population of AGNs, particularly of low luminosity ones, where the host galaxy is visible. We observed a field of 0.2 deg^2 in the Selected Area 57, for 67ks with XMM-Newton. We detected X-ray sources, and we correlated the list with a photographic survey of SA 57, complete to B_J~23 and with available spectroscopic data. We obtained a catalogue of 140 X-ray sources to limiting fluxes 5x10^-16, 2x10^-15 erg/cm^2/s in the 0.5-2 keV and 2-10 keV respectively, 98 of which are identified in the optical bands. The X-ray detection of part of the variability-selected candidates confirms their AGN nature. Diffuse variable objects populate the low luminosity side of the sample. Only 25/44 optically-selected QSOs are detected in X-rays. 15% of all QSOs in the field have X/O<0.1.
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