On equilibrium rotation of the central object of an accretion disc

The hydrodynamic interaction of an accretion disc with its central object i s reanalysed within the framework of the slim-disc approximation. Arguments are presented against an interpretation of the total angular momentum flux as an eigenvalue of the system. A simple intuitive consideration is provid ed, which shows that the central object may be in a state of stationary rot ation even if the disc imposes the constraint of a finite angular momentum flux into it. It is argued that equilibrium rotation is characterized by va nishing viscous torque rather than by zero total angular momentum flux. As a consequence, the central object can be in a state of stationary rotation below the break-up limit, although its angular momentum increases. Despite accretion, even for positive total angular momentum flux and subcritical ro tation, central objects are spun down within a considerable range of their parameters. The results are illustrated by application to FU Orionis system s.