Comparing PyMorph and SDSS photometry. II. The differences are more than
  semantics and are not dominated by intracluster light
  The Sloan Digital Sky Survey pipeline photometry underestimates the
brightnesses of the most luminous galaxies. This is mainly because (i) the SDSS
overestimates the sky background and (ii) single or two-component Sersic-based
models better fit the surface brightness profile of galaxies, especially at
high luminosities, than does the de Vaucouleurs model used by the SDSS
pipeline. We use the PyMorph photometric reductions to isolate effect (ii) and
show that it is the same in the full sample as in small group environments, and
for satellites in the most massive clusters as well. None of these are expected
to be significantly affected by intracluster light (ICL). We only see an
additional effect for centrals in the most massive halos, but we argue that
even this is not dominated by ICL. Hence, for the vast majority of galaxies,
the differences between PyMorph and SDSS pipeline photometry cannot be ascribed
to the semantics of whether or not one includes the ICL when describing the
stellar mass of massive galaxies. Rather, they likely reflect differences in
star formation or assembly histories. Failure to account for the SDSS
underestimate has significantly biased most previous estimates of the SDSS
luminosity and stellar mass functions, and therefore Halo Model estimates of
the z ~ 0.1 relation between the mass of a halo and that of the galaxy at its
center. We also show that when one studies correlations, at fixed group mass,
with a quantity which was not used to define the groups, then selection effects
appear. We show why such effects arise, and should not be mistaken for physical
effects.
