Measuring Subclusters in Galaxy Clusters

We assume that there are K c subclusters and K f fields (foreground or background) in a cluster region. Then, the distribution of all galaxies in this region can be described as follow: where, n c and n f are normalized numbers of subcluster members and field galaxies. φ c , φ f , are their normalized distributions in radial velocity space. Both of them can be assumed as Gaussian. μ c and μ f are normalized distributions in the projected surface of the celestial sphere. For field galaxies, it's uniform, and for subcluster members, usually we use the King's approximate formulae. Distribution parameters and their uncertainties can be found by using the standard maximum likelihood method. And membership probabilities of the ith galaxy belonging to the cth subcluster can be calculated as P c ( i ) = φ c ( i )/ φ p( i ).