Simulations of Shocks with Smoothed Particles Hydrodynamics Method

Abstract

Shock waves in accretion flows onto compact objects are very important to transform the gravitational potential energy into radiation. The possibility that they exist also around black holes has been suggested years ago by Hawley, Smarr and Wilson (1984a, 1984b). Recently it has been shown that there is a wide range of parameters (essentially angular momentum and specific energy [for adiabatic flows] or temperature [for isothermal flows]) for which steady shock configurations are possible (Chakrabarti 1990, Chakrabarti & Molteni, 1993). Recent analytical calculations have shown the stability for isothermal and adiabatic shocks (Lu 1997; Nakayama, 1994). This fact has great astrophysical relevance since, in this way, the emission due to the shock is not a transient episode but can be a permanent mechanism responsible for the radiated energy. Here we review the relevant results obtained in the last few years through numerical simulations by a novel technique named Smoothed Particles Hydrodynamics (SPH). We concentrate on the axisymmetric problems which are done using cylindrical coordinates. The plan of this contribution is the following: in Section 2 we describe the SPH numerical method in cylindrical coordinates for axisymmetric problems, then, in Section 3 and its subsections, we give the basic ingredients, analytical equations, of the physical problem of accretion flows onto Black Holes. In Section 4 we present some results of the simulations and comment on them.