A periodic shock wave model for Mira variable atmospheres

Abstract

A semianalytic model for the time-dependent structure of a stellar atmosphere traversed by periodic shock waves is presented. The shock solution is presented in the plane-parallel limit where fluid elements move distances that are small compared with the stellar radius. Since the plane-parallel assumption is violated for long-period variables, the solution is generalized to allow certain quantities to vary with radius. An approximate semianalytic solution is found by dividing Lagrangian fluid trajectories into 'planar' and 'spherical' parts. The thermodynamic quantities and radius are obtained from fits to the phase-dependent excitation temperatures and velocities. These values and the column densities are used to obtain a complete hydrodynamic description of the region in which the lines form. A model shock luminosity curve is calculated, and it is concluded that at early phases the visual luminosity of Mira variables is dominated by shock emission.