Fossil groups origins. I. RX J105453.3+552102 a very massive and relaxed system at z~0.5

Context: The most accepted scenario for the origin of fossil groups is that they are galaxy associations in which the merging rate was fast and efficient. These systems have assembled half of their mass at early epoch of the Universe, subsequently growing by minor mergers, and therefore could contain a fossil record of the galaxy structure formation. Aims: We have started an observational project in order to characterize a large sample of fossil groups. In this paper we present the analysis of the fossil system RX J105453.3+552102. Methods: Optical deep images were used for studying the properties of the brightest group galaxy and for computing the photometric luminosity function of the group. We have also performed a detail dynamical analysis of the system based on redshift data for 116 galaxies. Combining galaxy velocities and positions we selected 78 group members. Results: RX J105453.3+552102 is located at ⟨z⟩ = 0.47, and shows a quite large line-of-sight velocity dispersion σv 1000 km/s. Assuming the dynamical equilibrium, we estimated a virial mass of M(