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. 
Gregory S. Novak, Patrik Jonsson, Joel R. Primack, Thomas J. Cox, and   Avishai Dekel
astro-ph.GA