Under the assumption that the presence of comet clouds around otherwise normal stars is a common occurrence in the Galaxy, the observational consequences of random penetration encounters between the general Galactic population of degenerate stars and these comet clouds is considered. The only case considered is where the compact stars is a single star. For this scenario, encounters involving neutron stars (NSs) result in impact rates 1000-10,000 times slower than in the model of Tremaine and Zytkow (1986). The rate for white dwarfs (WDs) is larger than the one for NSs by a factor of about 30 times the ratio of the degenerate star number densities. The mean impact rate is significantly increased if the number of comets in a cloud is nearly independent of the mass of the central star. It is concluded that some of the observed gamma-ray bursts may be caused by accretion of comets onto NSs and that this scenario, but with a WD as the accretor, probably contributes to the optical flash background rate. 38 refs.
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