Luminosity, selfgravitation and nonuniqueness of stationary accretion

We investigate newtonian description of accreting compact bodies with hard surfaces, including luminosity and selfgravitation of polytropic perfect fluids. This nonlinear integro-differential problem reduces, under appropriate boundary conditions, to an algebraic relation between luminosity and the gas abundance in stationary spherically symmetric flows. There exist, for a given luminosity, asymptotic mass and the asymptotic temperature, two sub-critical solutions that bifurcate from a critical point. They differ by the fluid content and the mass of the compact centre.