A new solution to the accretion problem.

The Bondi-Hoyle theory of line-accretion is briefly reviewed, and it is shown that there are an infinity of steady-state solutions satisfying the requirements originally imposed as boundary conditions. Questions are raised as to the applicability of these solutions to physical reality. The existence of an entirely different type of steady-state solution that implies slow velocity in the accretion stream beyond the neutral point is demonstrated. Accurate numerical values of this solution are obtained for a number of cases. The braking action given by this solution, for any selected cut-off distance, is far stronger than in the Bondi-Hoyle solution. Consideration of the physical state in the accretion stream shows that for this slow solution the appropriate cutoff range would be only of the order of 100 AU rather than of interstellar-distance order.