On Galaxies and Homology
  The definition of homology for single-component galaxies is clear, but for
multi-component (luminous and dark matter) galaxies there is some ambiguity. We
attempt to clarify the situation by carefully separating the different concepts
of homology that have been used to date. We argue that the most useful
definition is that a set of galaxies is homologous if they are the same in all
respects up to a set of three dimensional scaling constants which may differ
from one galaxy to the next. Noting that we are free to choose the dimensional
constants, we find that a set of hydrodynamic simulated galaxy merger remnants
is significantly closer to homologous when the dimensional length constant is
taken to be the radius containing equal amounts of dark and baryonic matter
rather than the usual observationally motivated choice of the baryonic
half-mass radius. Once the correct dimensional scaling constants are used, the
stellar velocity dispersion anisotropy is essentially the sole source of the
variation in the kinematic structure of these simulated merger remnants. In
order to facilitate the use of these scaling constants to analyse observed
galaxies, we calculated the relationship between our preferred dimensional
scaling constants and the typical observationally accessible quantities.
