Zero-energy rotating accretion flows near a black hole

We characterize the nature of thin, axisymmetric, inviscid accretion flows of cold adiabatic gas with zero specific energy in the vicinity of a black hold by the specific angular momentum. Using two-dimensional hydrodynamic simulations in cylindrical geometry, we present various regimes in which the accretion flows behave distinctly differently. When the flow has a small angular momentum (lambda less than or similar to lambda(b)), most of the material is accreted into the black hold, forming a quasi-spherical flow or a simple disklike structure around it. When the flow has a large angular momentum (typically, larger than the marginally bound, value, lambda greater than or similar to(mb)), almost no accretion into the black hole occurs. Instead, the flow produces a stable shock with one or more vortices behind it and is deflected away at the shock as a conical, outgoing wind of higher entropy. If the flow has an angular momentum somewhat smaller than lambda(mb) (lambda less than or similar to lambda less than or similar to lambda(mb)), a fraction (typically 5%-10%) of the incoming material is accreted into the black hole, but the flow structure formed is similar to that for lambda greater than or similar to lambda(mb). Some of the deflected material is accreted back into the black hole while the rest is blown away as an outgoing wind. These two cases with lambda greater than or similar to lambda(u) correspond those studied in the previous works by Molteni, Lanzafame, & Chakrabarti, and Ryu et al. However, the flow with angular momentum close to the marginally stable value (lambda(ms)) is found to be unstable. More specifically, if lambda(b) less than or similar to lambda similar to lambda(ms) less than or similar to lambda(u), the flow displays a distinct periodicity in the sense that the inner part of the disk is built and destroyed regularly. The period is roughly equal to (4-6) x 10(3) R(g)/c, depending on the angular momentum of the flow. In this case, the internal energy of the flow around the black hold becomes maximum when the structure with the accretion shock and vortices is fully developed. But the mass accretion rate into the black hole reaches a maximum value when the structure collapses. Averaged over periods, more than half the incoming material is accreted into the black hole. We suggest the physical origin of these separate regimes from a global perspective. Then we discuss the possible relevance of the instability work to quasi-periodic oscillations.