Two-component gravitating systems and the red giant-like structure

The present study investigates the equilibria and evolution of gravitating systems composed of two components by approximating their equations of states to polytropes. The structures are explored in hydrostatic equilibrium systematically under the condition that two components interact with each other only through gravity. The systems are found to be characterized by four parameters, the ratio of central densities and the ratio of central thermal energies per unit mass, and the polytropic indices of two components. If the central density is much higher, the structure is little affected by the presence of the other component. If the difference in the central thermal energies is smaller than specified by beta-cri, the system adopts an equilibrium configuration for any mass ratio. Two-component systems necessarily evolve to have the red giantlike structure if one component suffers cooling faster than the other. It is concluded that the red giant structure is a general characteristic of gravitating systems for which there is an appropriate mechanism to decouple the constituent into the hotter and cooler components.