The dynamical state of galaxy groups and their luminosity content

We analyse the dependence of the luminosity function of galaxies in groups (LF) on group dynamical state. We use the Gaussianity of the velocity distribution of galaxy members as a measurement of the dynamical equilibrium of groups identified in the SDSS Data Release 7 by Zandivarez & Martinez. We apply the Anderson-Darling goodness-of-fit test to distinguish between groups according to whether they have Gaussian or Non-Gaussian velocity distributions, i.e., whether they are relaxed or not. For these two subsamples, we compute the $^{0.1}r-$band LF as a function of group virial mass and group total luminosity. For massive groups, ${\mathcal M}>5 \times 10^{13} \ M_{\odot} \ h^{-1}$, we find statistically significant differences between the LF of the two subsamples: the LF of groups that have Gaussian velocity distributions have a brighter characteristic absolute magnitude ($\sim0.3$ mag) and a steeper faint end slope ($\sim0.25$). We detect a similar effect when comparing the LF of bright ($M^{group}_{^{0.1}r}-5\log(h)<-23.5$) Gaussian and Non-Gaussian groups. Our results indicate that, for massive/luminous groups, the dynamical state of the system is directly related with the luminosity of its galaxy members.