Fossil group origins. III. The relation between optical and X-ray luminosities

Aims: This study is part of the Fossil group origins (FOGO) project which aims to carry 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). Methods: Out of a total 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 has not been 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 to be comparable to the estimates of the comparison sample. For each fossil and normal system we homogeneously compute Lopt in the r-band within the characteristic cluster radius, using data from the Sloan Digital Sky Survey Data Release 7. Results: 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 through the 2D Kolmogorov-Smirnov test nor the fit of the LX-Lopt relation. Thus, 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 discuss our results in comparison with previous literature. Conclusions: 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.