Standing shocks in a two-fluid solar wind
We present a numerical study of the formation of standing shocks in the solar wind using a two-fluid time-dependent model in the presence of Alfven waves. Included in this model is the adiabatic cooling and thermal conduction of both electrons and protons. In this study, standing shocks develop in the flow when additional critical points form as a result of either localized momentum addition or rapid expansion of the flow tube below the existing sonic point. While the flow speed and density exhibit the same characteristics as found in earlier studies of the formation of standing shocks, the inclusion of electron and proton heat conduction produces different signatures in the electron and proton temperature profiles across the shock layer. Owing to the strong heat conduction, the electron temperature is nearly continuous across the shock, but its gradient has a negative jump across it, thus producing a net heat flux out of the shock layer. The proton temperature exhibits the same characteristics for shocks produced by momentum addition but behaves differently when the shock is formed by the rapid divergence of the flow tube. The adiabatic cooling in a rapidly diverging flow tube reduces the proton temperature so substantially that the proton heat conduction becomes negligible in the vicinity of the shock. As a result, protons experience a positive jump in temperature across the shock. While Alfven waves do not affect the formation of standing shocks, they contribute to the change of the mmomentum and energy balance across them. We also find that for this solar wind model the inclusion of thermal conduction and adiabatic cooling for the elctrons and protons increases significantly the range of parameters characterizing the formation of standing shocks over those previously found for isothermal and polytropic models.