Theoretical velocity structure of long-period variable star photospheres

Abstract

Numerical models for shock waves propagating through atmospheres of cool supergiant stars for a grid of masses and surface gravities have been calculated by assuming spherical symmetry, isothermality, and a periodic piston boundary condition. The results of these models can be restated by using parameters derived in Willson and Hill (1976); the reparametrization allows the generalization of these results to arbitrary stellar masses and radii. Application of the theoretical generalization to a variety of observed properties of R Leonis and Omicron Ceti allows the selection of a limited range of probable masses and radii for these stars; a mass of approximately 0.8 to 1.5 solar masses and a radius of about (1.3 to 2) x 10 to the 13th cm for Omicron Cet and a mass of 1.8 to 4.0 solar masses and a radius of (1.7 to 2.5) x 10 to the 13th cm for R Leo. It is concluded that both stars are pulsating in the fundamental mode, with a pulsation constant Q of approximately 0.1 day.