We present an X-ray follow-up, based on XMM plus Chandra, of six Fossil Group (FG) candidates identified in our previous work using SDSS and RASS data. Four candidates (out of six) exhibit extended X-ray emission, confirming them as true FGs. For the other two groups, the RASS emission has its origin as either an optically dull/X-ray bright AGN, or the blending of distinct X-ray sources. Using SDSS-DR7 data, we confirm, for all groups, the presence of an r-band magnitude gap between the seed elliptical and the second-rank galaxy. However, the gap value depends, up to 0.5mag, on how one estimates the seed galaxy total flux, which is greatly underestimated when using SDSS (relative to Sersic) magnitudes. This implies that many FGs may be actually missed when using SDSS data, a fact that should be carefully taken into account when comparing the observed number densities of FGs to the expectations from cosmological simulations. The similarity in the properties of seed--FG and non-fossil ellipticals, found in our previous study, extends to the sample of X-ray confirmed FGs, indicating that bright ellipticals in FGs do not represent a distinct population of galaxies. For one system, we also find that the velocity distribution of faint galaxies is bimodal, possibly showing that the system formed through the merging of two groups. This undermines the idea that all selected FGs form a population of true fossils.
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