A New Solution to the Accretion Problem

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Abstract
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 is demonstrated of an entirely different type of steady-state solution that implies slow velocity in the accretion-stream beyond the neutral point. Accurate numerical values are obtained of this solution for a number of cases. The braking-action given by this solution, for any selected cut-off distance, is far stronger than on the Bondi–Hoyle solution. Consideration of the physical state in the accretion-stream shows that for this slow-solution the appropriate cut-off range would be only of the order of 10 2 a.u. rather than of interstellar-distance order. With stronger braking-action, the velocity of stars relative to interstellar material will be reduced in correspondingly shorter times, and more rapid accretion than on the Bondi–Hoyle theory will thereby come about. This result combined with recent measures of gas-densities at various regions of the galaxy suggests that the problem posed by the brightest stars may well be resolvable on the basis of the accretion-process.

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