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.
