Luminosity, selfgravitation and nonuniqueness of stationary accretion

¹ M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland e-mail: malec@th.if.uj.edu.pl
² Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, 14-476 Potsdam, Germany

Received: 3 July 2007
Accepted: 24 October 2007

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-Żytkow stars is discussed.