Numerical simulations of axisymmetric accretion flows

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Abstract
We study properties of axisymmetric accretion flow on to a gravitating compact object from a uniform flow by performing pure hydrodynamic calculations. At first a comparison is made between a numerical solution and an analytic solution based on a ballistic orbit theory, and it is found that the analytic solution is an extremely good approximation even for Mach numbers as low as 1.4. Next, results are presented for Mach numbers of 0.6, 1.4, 2.4, 5, and 10, and for a ratio of specific heats of 5/3. The accretion rate, the stand-off distance of the bow shock, and the stagnation point on the rear axis are computed based on various boundary conditions. An empirical formula for the accretion rate is proposed. It is found that the flow is not completely in steady state but a dome-like shock is formed quasi-periodically in front of the compact object for higher Mach number cases. It is argued that this shock perturbs the flow, leading to the destruction of axisymmetry of the flow eventually.

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