  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.
