A special case of two-component polytropes with rigid rotation

ECN polytropes are defined as Emden-Chandrasekhar concentric, copolar, axisymmetric, solid-body rotating, N-component polytropes, and the basic theory reported previously for EC1 polytropes is generalized to the case of EC2 polytropes. The physical parameters of equilibrium configurations are determined, and it becomes possible to compute them numerically. Attention is limited to the special case of homogeneity (ni = nj = 0), and an exact solution to equilibrium equations is outlined, according to which the equipotentials lying in the volume filled by both subsystems are spheroidal in shape and similar while the equipotentials lying in the volume filled by only one component are not. As a possible application of the theory, galaxies are modeled as EC2 polytropes with ni = nj = 0, where energy dissipation occurs together with mass transfer from one subsystem to another. Starting from a simple hypothesis and with an initial configuration where both components fill the same volume, the whole sequence of equilibrium configurations is described until the limit of a vanishing gaseous subsystem is reached. An interesting feature of the results is that low-mass inner components may be very efficient in flattening more massive outer components.