The virial theorem for subsystems: application to a globular cluster within a galaxy

A self-similar evolution of a globular cluster within a galaxy, which implies a one-component formulation of the virial theorem (Mouri & Taniguchi 2003), is extended to a two-component formulation (Caimmi & Secco 2003). To this aim, the general case of an embedded sphere within an embedding sphere, both represented as truncated, singular isothermal spheres, is applied to the situation of interest. It is shown that, in the case under consideration, a two-component formulation of the virial theorem reproduces the analytical results of a one-component formulation. The process of energy change due to mass loss through the surface is analysed in detail, in connection with both a one-component and a two-component formulation of the virial theorem.