The statistical determination of substructure in clusters of galaxies

Abstract

This paper presents a statistical method, based on the technique of maximum likelihood, for the determination of substructure in clusters of galaxies. A general analysis of the substructure problem is theoretically possible, but computationally unfeasible with present techniques. This paper therefore concentrates on the simpler problem of detecting the presence of two subgroups in a cluster. The method described allocates galaxies to the relevant subgroup and assigns statistical significance to the splitting. This method is shown to be very powerful for the analysis of two-dimensional data. However, the most exciting attribute of the method is its ability to combine spatial and line-of-sight velocity information without the need for arbitrary scaling factors, making a spatial-velocity analysis of substructure possible. Computation requirements are reasonable. The statistic used can therefore be calibrated for various null hypotheses, and this is done for some cases of interest.