The goal of this work is to understand whether the extreme environment of compact groups can affect the distribution and abundance of faint galaxies around them. We performed an analysis of the faint galaxy population in the vicinity of compact groups and normal groups. We built a light-cone mock galaxy catalogue constructed from the Millennium Run Simulation II plus a semi-analytical model of galaxy formation. We identified a sample of compact groups in the mock catalogue as well as a control sample of normal galaxy groups and computed the projected number density profiles of faint galaxies around the first- and the second-ranked galaxies. We also compared the profiles obtained from the semi-analytical galaxies in compact groups with those obtained from observational data. In addition, we investigated whether the ranking or the luminosity of a galaxy is the most important parameter in the determination of the centre around which the clustering of faint galaxies occurs. There is no particular influence of the extreme compact group environment on the number of faint galaxies in such groups compared to control groups. When selecting normal groups with separations between the 1st and 2nd ranked galaxies similar to what is observed in compact groups, the faint galaxy projected number density profiles in compact groups and normal groups are similar in shape and height. We observed a similar behaviour of the population of faint galaxies in observations and simulations in the regions closer to the 1st and 2nd ranked galaxies. Finally, we find that the projected density of faint galaxies is higher around luminous galaxies,regardless of the ranking in the compact group. The semi-analytical approach shows that compact groups and their surroundings do not represent a hostile enough environment to make faint galaxies to behave differently than in normal groups.
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