Stable and Unstable Accretion Flows with Angular Momentum near a Point Mass

The properties of axisymmetric accretion flows of cold adiabatic gas withzero total energy in the vicinity of a Newtonian point mass are characterizedby a single dimensionless parameter, the thickness of incoming flow. In thelimit of thin accretion flows with vanishing thickness, we show that thegoverning equations become self-similar, involving no free parameters. We studynumerically thin accretion flows with finite thickness as well as those withvanishing thickness. Mass elements of the incoming flow enter the computationalregime as thin rings. In the case with finite thickness, after a transientperiod of initial adjustment, an almost steady-state accretion shock with asmall oscillation amplitude forms, confirming the previous work by Molteni,Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity betweenthe funnel wall and the accretion shock follows closed streamlines, forming atorus. This torus, in turn, behaves as an effective barrier to the incomingflow and supports the accretion shock which reflects the incoming gas away fromthe equatorial plane. The postshock flow, which is further accelerated by thepressure gradient behind the shock, goes through a second shock which thenreflects the flow away from the symmetry axis to form a conical outgoing wind.As the thickness of the inflowing layer decreases (or if the ratio of the halfthickness to the distance to the funnel wall along the equatorial plan issmaller than $\sim0.1$), the flow becomes unstable. In the case with vanishingthickness, the accretion shock formed to stop the incoming flow behind thefunnel wall oscillates quasi-periodically with an amplitude comparable to thethickness. The structure between the funnel wall and the accretion shock isdestroyed as the shock moves inwards toward the central mass and re-generatedComment: ApJ accepted, 23 pages, uuencoded, compressed postscript file, 11 figures available upon request from ryu@sirius.chungnam.ac.k