Abstract
Aims. We show the existence of two branches of solutions bifurcating from a point with maximal luminosity. Methods. We investigate a Newtonian description of accreting compact bodies with hard surfaces, including luminosity and selfgravitation of polytropic perfect fluids. This nonlinear integro-differential problem is studied numerically. Its reduced version simplifies (under appropriate boundary conditions) to an algebraic relation between luminosity and the gas abundance in stationary, spherically symmetric flows and it can be dealt with analytically. Results. There exist – for a given luminosity, asymptotic mass and asymptotic temperature – two sub-critical solutions that bifurcate from an extremal point. They differ by the fluid content and the mass of the compact centre. Their relevance to Thorne- u Zytkow stars is discussed.
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