Implicit 2D-Radiation Hydrodynamics

Abstract

It is a well known fact that explicit numerical methods do not apply to evolutionary models of protostars. As was already pointed out by McNally (1964) and by Bodenheimer and Sweigart (1968), due to the conspicuous non-homology of the gravitational collapse of a (non-rotating, non-magnetic) interstellar cloud on the verge of being Jeans-unstable, both time and length scales vary by several orders of magnitude during the evolution of the cloud. To arrive at a reasonable spatial resolution and accuracy the famous Courant-Friedrichs-Lewy (CFL-) condition would demand a billion (!) time steps or so. This is why purely explicit methods are completely ruled out for tackling stellar formation models. The main difficulty to overcome is to physically and consistently describe the flow pattern which basically consists of a highly supersonic part (the freely falling envelope) and a quasihydrostatic part (the stellar embryo) separated by a strong shock front (the accretion shock). The accretion shock is of fundamental importance for the structure of a protostar, since there, within a very narrow zone, the kinetic energy of the matter in the envelope is almost entirely transformed into outgoing radiation, i.e. luminosity; it also determines the entropy distribution in the postshock layers, i.e. the structure of the outer layers of the stellar core. Needless to say, the problem becomes even more difficult, if the stringent condition of spherical symmetry is abandoned.