Hydrodynamical Limit — Classical Problems of Accretion and Ejection

Abstract

There are several reasons why it is useful to start from the pure hydrodynamical case. First of all, the hydrodynamical version of the Grad–Shafranov equation is not as popular as the full MHD one. On the other hand, it has all the features of the full MHD version in the simplest form. In particular, within the hydrodynamical approach one can introduce the 3+1-splitting language—the most convenient one for the description of the ideal flows in the vicinity of a rotating black hole. Starting from the well-known set of equations describing the nonrelativistic ideal flow, we will go step by step to more complicated cases up to the most general one corresponding to the axisymmetric stationary flows in the Kerr metric. Finally, several examples will be considered which demonstrate how the approach under study can be used to obtain the quantitative information of the real transonic flows in the vicinity of rotating black holes. The necessity of taking into account the effects of General Relativity is not so obvious for most compact sources. For instance, one cannot exclude that the black hole plays only a passive role in the jet formation process, and the effects of General Relativity in this case may be unimportant for flow description in the region of jet formation. At the same time, gravitational effects make, apparently, an appreciable contribution to the determination of physical conditions in compact objects. First, this is indicated by the hard spectra and the e ⁺ e ^- annihilation line observed in galactic X-ray sources, which are believed to be solar mass black holes. Such characteristics are never observed in the X-ray sources which are firmly established to show accretion not onto a black hole but onto a neutron star. Another indication comes from superluminal motion in quasars which may be due to the relativistic plasma flow ejected along with a weakly relativistic jet. All these testify in favor of the existence of an additional mechanism for particle creation and acceleration for which the effects of General Relativity may be of principal importance. So, it is undoubtedly interesting to consider the flow structure in the most general conditions, i.e., in the presence of a rotating black hole.