Analytical Study and Structure of a Stationary Radiative Shock

In this paper we study the radiative shock that arises in certain situations in astrophysics (among others, supernovae, accretion flows, and stars formation). However, it is clear that the high-energy lasers (LIL, LMJ, NIF) will produce plasma flows with hydrodynamics dominated by radiation. Usually, only the radiation flux is considered, and the radiation pressure and energy are neglected. In this paper, in addition to the radiation flux, we take into account the total (matter plus radiation) energy density and pressure. We derive the corresponding generalized Rankine-Huguoniot equations, and it turns out that we can get analytically the structure of the radiative shock. It is shown that three distinct regimes arise; when the Mach number increases (but is small enough), the shock evolves from a continuous structure to a discontinuous one (a discontinuity appears between the shocked medium and the fluid at rest). It is seen then, that this discontinuity disappears for very high values of the Mach number. These behaviors are due to the presence of radiation. Moreover, a precursor develops into the unshocked medium, and scaling laws are derived to obtain the width of the shock and the length of the precursor in terms of the Mach number. Finally, the assumption of the LTE approximation is examined.