2016MNRAS.462..298O

We present a general method to identify infalling substructure in discrete data sets with position and line-of-sight velocity data. We exploit the fact that galaxies falling on to a brightest cluster galaxy (BCG) in a virialized cluster, or dwarf satellites falling on to a central galaxy like the Milky Way, follow nearly radial orbits. If the orbits are exactly radial, we show how to find the probability distribution for a satellite's energy, given a tracer density for the satellite population, by solving an Abel integral equation. This is an extension of Eddington's classical formula for the isotropic distribution function. When applied to a system of galaxies, clustering in energy space can then be quantified using the Kullback-Leibler divergence, and groups of objects can be identified which, though separated in the sky, may be falling in on the same orbit. This method is tested using mock data and applied to the satellite galaxy population around M87, the BCG in Virgo, and a number of associations that are found, which may represent infalling galaxy groups.