Hydrodynamics of an electron-positron plasma near a black hole; applications to jet formation

We investigate some features of the hydrodynamics and neutrino physics in the (predominantly) electron-positron plasma above a hyperaccreting disk (or torus) around a black hole, a conjectured engine for a short gamma ray burst. We suggest a possible scenario in which plasma in the region very near the black hole, energetically driven by neutrino annihilation, emerges as a subsonic wind, which in a spherically symmetrical case would decelerate as it moves out. In this case we argue that the plasma heating will be primarily through neutrino-electron and neutrino-positron scattering, and that this process will be important throughout a region considerably larger than that of the neutrino annihilation process. In simple solutions a relatively gentle anisotropy in the heating through this process can create an approximately conical sonic surface, aligned with the system's axis. Inside this cone the fluid accelerates upwards as in standard jet models.