Mixture models for studying stellar populations. II - Multivariate finite mixture models

Abstract

Multivariate finite mixture models provide a framework for analyzing and interpreting observational data that arise from the overlapping spatial, kinematical, chemical, and age distributions of stellar populations. In this paper the basic properties of multivariate finite mixture distributions are summarized. Particular emphasis is placed on the interpretation of observed overall gradients, and on the distinction between models in which a gradient exists in at least one component and those in which there are no gradients within individual stellar population components. Central to this discussion are posterior mixing proportions, which describe how the mixing proportions for an observed sample of stars vary as functions of metal abundance, age, etc., and conditional mixture distributions, which describe the relationships that exist among the variables