Period Changes in a Rapidly Evolving Pulsating Star

Abstract

In this last chapter, attention is paid to pulsating stars that evolve on their Helmholtz–Kelvin time-scale. Each star is in thermal imbalance, but is regarded to be in instantaneous hydrostatic equilibrium. By means of a two-time-variable expansion procedure, an expression is established for the relative rate of change of the period of a, radial or non-radial, isentropic pulsation. The expression also results from the property that, for an isentropic pulsation in an evolving star, the mean rates of change of the kinetic energy and the potential energy, taken over a period in the fast time variable, remain equal to each other as functions of the slow time variable. The general expression is explicitly developed for the case of a radial isentropic pulsation. The relative rate of period change depends on the relative rates of change of the mass density, the isentropic sound velocity, and the radial distances of the mass elements inside the evolving star. By way of example, the relative rate of period change of a radial pulsation is determined for a star that is subject to a homologous contraction or expansion.