The structure of shocks in the atmospheres of pulsating stars

Abstract

The structure of shocks propagating through partially ionized hydrogen gas with characteristics typical of the atmospheres of RR Lyr, W Vir, and RV Tau type variables is analyzed in terms of a self-consistent solution of the equations of gas dynamics, atomic kinetics, and radiation transfer. The solutions were obtained for shock waves with velocities 20 km/s≤U ₁≤90 km/s and unperturbed hydrogen gas with temperatures 3000 K≤T ₁≤9000 K and density ρ₁=10⁻¹⁰ g/cm³. The fraction of the energy of the gas-dynamic flux converted into radiation increases with the shock amplitude, and the ratio of the radiation flux emitted by the shock to the gas kinetic energy flux is 0.4≲ℜ≲0.8 for the velocities U ₁ considered. This ratio also increases slightly with the ambient gas temperature T ₁ due to an increase in hydrogen ionization in the radiative precursor. The flux emitted by the leading edge of the shock opposite to the gas flow is several percent higher than the flux emitted in the opposite direction by the trailing edge of the shock. Radiation is mostly concentrated in the Balmer continuum, and the region of efficient Lyman radiation transfer includes gas layers located near the viscous jump (δX=±10⁴ cm). The final gas-compression ratio in units of the limiting compression corresponding to an isothermal approximation is virtually independent of the shock amplitude, and increases with the unperturbed gas temperature from r≈0.5 at T ₁=3000 K to r≈0.9 at T ₁=9000 K.