Context. Using Chandra observations we identified a sample of seven off-nuclear X-ray sources in the redshift range z = 0.072-0.283, located within optically bright galaxies in the COSMOS Survey. All of them, if associated with their closest bright galaxy, would have L[0.5-7 keV] > 1039 erg s-1 and therefore can be classified as ultraluminous X-ray sources (ULXs). Aims. Using the multi-wavelength coverage available in the COSMOS field, we studied the properties of the host galaxies of these ULXs. In detail, we derived their star formation rate from Hα measurements and their stellar masses using SED fitting techniques with the aim to compute the probability to have an off-nuclear source based on the host galaxy properties. We divided the host galaxies in different morphological classes with the available ACS/HST imaging. Methods. We selected off-nuclear candidates with the following criteria: 1) the distance between the X-ray and the optical centroid has to be larger than 0.9, larger than 1.8 times the radius of the Chandra positional error circle and smaller than the Petrosian radius of the host galaxy; 2) the optical counterpart is a bright galaxy (RAB<22); 3) the redshift of the counterpart is lower than z = 0.3; 4) the source has been observed in at least one Chandra pointing at an off-axis angle smaller than 5; 5) the X-ray positional error is smaller than 0.8. We verified each candidate super-imposing the X-ray contours on the optical/IR images. We expect less than one misidentified AGN due to astrometric errors and on average 1.3 serendipitous background source matches. Results. We find that our ULXs candidates are located in regions of the SFR versus M* plane where one or more off-nuclear detectable sources are expected. From a morphological analysis of the ACS imaging and the use of rest-frame colours, we find that our ULXs are hosted both in late and early type galaxies. Finally, we find that the fraction of galaxies hosting a ULX ranges from ≈ 0.5% to ≈ 0.2% going from L 0.5-2keV = 3 × 1039 erg s-1 to L 0.5-2KeV = 2 × 1040 erg s-1.
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