The 3D Topology of the Clausius Virial for Two Component Dynamical Models of Elliptical Galaxies

Introduction: as found in Secco (2000, 2001), the presence of the dark halo in a two component astrophysical object, can induce a scale length on the visible component trough the appearance of a maximum in the Clausius Virial potential energy (CV), which we expect, in general, to be monotonic. In this investigation the author used two power law density profiles, but we will find that the same occurs for more complex and realistic models. Method: we present a set of three two component dynamical models of elliptical galaxies to investigate the topology of the CV of a stellar spherical component completely embedded in a dark spherical halo. We have chosen Hernquist and Plummer mass density profiles for the two components in three different combinations: Plummer-Plummer, Hernquist-Hernquist, Hernquist-Plummer, where the first term refers to the stellar component, while the second to the dark component. In this way we can evaluate different combinations of cuspy and cored profiles and see their influence on the general behavior of CV. The fact that Plummer profiles are not perfectly describing real elliptical galaxies, and maybe also dark halos, is not so important for our present study, as the aim is to investigate the general trend of the CV. Results: it will be shown that the presence or not of stationary points in the CV are strongly depending on the ratio R between dark halo and stellar component masses, as expected, but are not much depending on the particular choice of the mass density profiles. Indeed all three models present the maximum of CV, with some restrictions on R. In general, cuspy profiles tend to restrain the presence of the CV, which appears for greater R, while cored profiles tend to enhance it. Discussion: with this preliminary study of the CV trend for two component models of elliptical galaxies we have found that the maximums in the CV are present for certain values of R also for more complex models. This can indicate that the stationary points in the CV could have a physical interesting meaning in the dynamics of elliptical galaxies.