Cumulants and symmetries in a trivariate normal mixture

A qualitative study of the local velocity distribution

Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, 08034 Barcelona, Catalonia, Spain e-mail: rcubarsi@mat.upc.es

Received: 22 April 2004
Accepted: 21 July 2004

Abstract

An alternative parameterization of a trivariate normal mixture for the stellar velocity distribution provides a set of constraint equations between global cumulants that are used to estimate characteristic constants of the mixture and population parameters. Under particular distribution symmetries these relationships become simpler and easy to evaluate, and they are used to test some meaningful mixtures. This method for the analysis of trivariate normal mixtures is applied to local star catalogs with known velocity space in order to find Gaussian components and underlying distribution symmetries. A large local sample (13 678 stars, 300 pc) obtained from HIPPARCOS catalog allows us to identify two mixed velocity ellipsoids with parameters corresponding to thin and thick disk populations, similar to those of samples selected from non-kinematical criteria. In addition to the usual assumptions of distribution symmetry plane and non-significant differential movement in the radial direction, our analysis also detects a slight but clear loss of axial symmetry associated with the vertex deviation of both population ellipsoids.