This study is part of the FOssil Groups Origin (FOGO) project which aims at carrying out a systematic and multiwavelength study of a large sample of fossil systems. Here we focus on the relation between the optical luminosity (Lopt) and X-ray luminosity (Lx). Out of a sample of 28 candidate fossil systems, we consider a sample of 12 systems whose fossil classification has been confirmed by a companion study. They are compared with the complementary sample of 16 systems whose fossil nature is not confirmed and with a subsample of 102 galaxy systems from the RASS-SDSS galaxy cluster survey. Fossil and normal systems span the same redshift range 0<z<0.5 and have the same Lx distribution. For each fossil system, the Lx in the 0.1-2.4 keV band is computed using data from the ROSAT All Sky Survey. For each fossil and normal system we homogeneously compute Lopt in the r-band within the characteristic cluster radius, using data from the SDSS DR7. We sample the Lx-Lopt relation over two orders of magnitude in Lx. Our analysis shows that fossil systems are not statistically distinguishable from the normal systems both through the 2D KS test and the fit of the Lx-Lopt relation. The optical luminosity of the galaxy system does strongly correlate with the X-ray luminosity of the hot gas component, independently of whether the system is fossil or not. We conclude that our results are consistent with the classical merging scenario of the brightest galaxy formed via merger/cannibalism of other group galaxies, with conservation of the optical light. We find no evidence for a peculiar state of the hot intracluster medium.
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