A quadratic programming technique for modeling gravitating systems

This paper presents a general method that produces analytic distribution functions for gravitating systems. A typical model fits photometric and kinematical data and is a superposition of components. The coefficients of the linear combination are determined by a quadratic programming technique. We give an explicit example for systems with spherical symmetry, and subsequently we apply the method to the Coma Cluster of galaxies. Statistically significant fits are obtained using only a small number of components. This technique is also a dynamical mass estimator. We obtain masses between 1.7 x 10^15^h^-1^_50_ M_sun_ and 5 x 10^15^h^-1^_50_ M_sun_ within 5h^-1^_50_ Mpc, and find some evidence for luminosity segregation in the orbital structure.