Abstract
Similarity solutions relevant to axisymmetric gas flows about compact objects are developed on the assumptions that the gravitating object is a point mass and the flow region of interest is much smaller than the accretion radius. Gasdynamic equations are given for steady adiabatic flow with azimuthal symmetry in a point gravitational field, conditions are placed on physically appropriate solutions, and asymptotic solutions near the accretion axis are considered. The equations are integrated numerically to determine the value of the shock cone angle and the variation of flow parameters within the entire shock cone. The significance of the specific heat ratio is examined, and the origin of the shock front is discussed. It is found that axisymmetric accreting solutions occur only for a specific heat ratio less than 5/3 in all but one case and that the shock angle depends on that ratio, with shock detachment indicated when the ratio equals 5/3. The results also confirm a tendency to form a high-density region around the accretion axis.
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