The Dynamics of Variable Stars

Several closely related classes of variable stars--here called Cepheid variables--have long been known, as a result of detailed observation, to be vibrating in a spherically symmetric dilational mode. The purpose of the work described here has been to understand this motion and thereby to be able to apply the extensive data on variable stars in augmenting our knowledge of the stars. The coupled equations of spherical hydrodynamics and radiation diffusion have been solved numerically as an initial value problem for a variety of stellar models. Unstable models show a growing amplitude of pulsation which ultimately levels off at a stable maximum amplitude of periodic motion. This final motion and the associated large amplitude light variation agree closely with observed variables. Check calculations show that the results are reliable. The interior dynamics have been examined in order to find the physical cause of the instability and also in order to understand peculiar secondary features of the pulsation. In addition, overtone pulsation in the first radial overtone has been studied. In a few cases, the instability can lead to stable large amplitude periodic motion in either the fundamental or the first overtone, depending on the initial conditions.