Two-component, concentric, and co-polar homogeneous spheroids in virial equilibrium: A review with additional results

The theory of two-component, concentric, and co-polar homogeneous spheroids in virial equilibrium is reviewed and extended, with explicit expressions of some physical parameters and a detailed analysis of a number of limiting situations. First, a fixed configuration with given physical parameters is taken into consideration, then further investigation is devoted to configurations moving along a specified sequence. As a possible application of the theory, galaxies are modeled as two-component spheroids of the kind considered and further analysis is performed, which allows a description of galactic evolution characterized by contraction (via energy dissipation) of one component and mass transfer (via star formation) from the contracting component to the other. The results of the current paper are to be intended as an organic and complete reference, that might help additional work involving any generalization of the method and/or application of the theory.