The Variation of the Galaxy Luminosity Function with Group Properties
  We explore the shape of the galaxy luminosity function (LF) in groups of
different mass by creating composite LFs over large numbers of groups.
Following previous work using total group luminosity as the mass indicator,
here we split our groups by multiplicity and by estimated virial (group halo)
mass, and consider red (passive) and blue (star forming) galaxies separately.
In addition we utilise two different group catalogues (2PIGG and Yang et al.)
in order to ascertain the impact of the specific grouping algorithm and further
investigate the environmental effects via variations in the LF with position in
groups. Our main results are that LFs show a steepening faint end for early
type galaxies as a function of group mass/ multiplicity, with a much suppressed
trend (evident only in high mass groups) for late type galaxies. Variations
between LFs as a function of group mass are robust irrespective of which
grouping catalogue is used, and broadly speaking what method for determining
group `mass' is used. We find in particular that there is a significant deficit
of low-mass passive galaxies in low multiplicity groups, as seen in high
redshift clusters. Further to this, the variation in the LF appears to only
occur in the central regions of systems, and in fact seems to be most strongly
dependent on the position in the group relative to the virial radius. Finally,
distance-rank magnitude relations were considered. Only the Yang groups
demonstrated any evidence of a correlation between a galaxy's position relative
to the brightest group member and its luminosity. 2PIGG possessed no such
gradient, the conclusion being the FOF algorithm suppresses the signal for weak
luminosity--position trends and the Yang grouping algorithm naturally enhances
it.
