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Appendix A: Projected number density profiles for different classes of CGs: ranking vs. luminosity

We investigated what is the most important parameter in the determination of the centre around which the clustering of faint galaxies occurs in CGs, i.e. if faint galaxies are preferentially distributed around the most luminous galaxy (in which case the most important is the ranking of the galaxy) or around any luminous galaxy (most important parameter is the luminosity). Therefore, we studied the density profiles of faint galaxies around different subsamples of CGs classified according to different group properties. The criteria used to split the subsamples are:

• Faint vs bright first ranked galaxy: we split the sample of CGs according to the absolute magnitude of the brightest galaxy of the system. Those having a brightest galaxy brighter than the 30th percentile of the distribution of absolute magnitudes of the first ranked galaxies of all the CGs are classified as , while CGs whose first ranked galaxy is fainter than the 70th percentile of the distribution of absolute magnitudes of the first ranked galaxies in the complete sample of CGs are .

• Dominated vs non-dominated groups: we split the sample of CGs according to the difference in absolute magnitude between the first and second ranked galaxies. CGs dominated by a very bright galaxy (Dom) will exhibit a larger difference between their two brightest members. We used the 30th and 70th percentiles of the distribution to split the sample into Dom and non-Dom CGs, respectively.

Faint galaxies are selected from a volume limited sample having −17 ≤ M_r − 5 log (h) ≤ −13.8 and z_cm ≤ 0.03 (see Fig. 2). Figure A.1 shows the projected number density profiles of faint galaxies around different classes of CGs. It can be seen that

• groups having the brighter first ranked galaxies are denser around the first and the second ranked galaxies (top panels);

• the projected number density profiles around the first and second ranked galaxies of CGs non-dominated by a single galaxy are remarkably similar.

These two results lead us to conclude that faint galaxies are more frequent around bright galaxies, regardless of the ranking in the CG.

Fig. A.1 Projected number density profiles of faint galaxies around the 1st ranked (black) and 2nd ranked galaxy (grey) for different subsamples of CGs. Faint galaxies are defined within a volume limited sample with −17 ≤ Mr − 5log (h) ≤ −13.8 and zcm< 0.03. Top panels: CGs with bright/faint 1st ranked galaxies. Bottom panels: CGs dominated/non-dominated by a single bright galaxy. Error bars are the standard deviations computed with 100 bootstraps.

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© ESO, 2014