Theoretical Pulsation Constants and Cepheid Masses

Abstract

Simple fitting formulae, based on extensive numerical calculations, are presented for the linear, nonadiabatic pulsation constants for the fundamental mode and first two harmonics of stellar models having radiative envelopes and He mass fraction Y 0.3. The formulae are accurate to within a few percent over very wide ranges of stellar parameters. These ranges include classical Cepheids and other familiar types of pulsating stars. The formulae are applied to a sample of classical Cepheids to estimate their masses on the basis of radii reported in the literature, under various assumptions regarding the pulsation mode. It is concluded, in part from stability considerations, that the most likely mode for most of these stars is the fundamental. The resulting masses show considerable scatter about the based on evolution theory without mass loss, but average some 15 percent smaller than these masses. However, the uncertainties in both sets of masses are so large that it is questionable whether this difference can be considered significant.