Supersonic Collisions between Two Gas Streams

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Abstract
A star around a massive black hole can be disrupted tidally by the gravity of the black hole. Then, its debris may form a precessing stream which may even collide with itself. In order to understand the dynamical effects of the stream-stream collision on the eventual accretion of the stellar debris onto the black hole, we have studied how gas flow behaves when the outgoing stream collides supersonically with the incoming stream. We have investigated the problem analytically with one-dimensional plane-parallel streams and numerically with more realistic three-dimensional streams. A shock formed around the contact surface converts the bulk of the orbital streaming kinetic energy into thermal energy. In three-dimensional simulations, the accumulated hot post-shock gas then expands adiabatically and drives another shock into the low density ambient region. Through this expansion, thermal energy is converted back to the kinetic energy associated with the expanding motion. Thus, in the end, only a small fraction of the orbital kinetic energy is actually converted to the thermal energy, while most of it is transferred to the kinetic energy of the expanding gas. Nevertheless the collision is effective in circularizing the debris orbit, because the shock efficiently transforms the ordered motion of the streams into the expanding motion in directions perpendicular to the streams. The circularization efficiency decreases, if two colliding streams have a large ratio of cross sections and a large density contrast. But even in such cases, the main shock extends beyond the overlapping contact surface and the high pressure region behind the shock keeps the stream of the larger cross section from passing freely. Thus the stream-stream collisions are still expected to circularize the stellar debris rather efficiently, unless the ratio
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