Non-adiabatic pulsations of a stellar model

Abstract

Eddington, Schwarzschild, Woltjer and others have discussed the Non-adiabatic Pulsations of a Star in connection with the problem of phase lag and maintenance and destruction of pulsations in the case of cepheid variable stars, but so far no general method for the solution of the non-adiabatic equation has been given. Rosseland, in connection with the problem of secular stability of variable stars, has suggested a systematic method for the solution of the non-adiabatic equation. We have applied this method and obtained the solution of the non-adiabatic pulsation equation in terms of a series of characteristic functions of the corresponding adiabatic equation. We have worked up to higher approximation than the previous workers. In the second part of the paper we have applied the solution obtained to the study of a homogeneous star, and have made a numerical estimate of the period of pulsation in the fundamental mode and the time of relaxation in case of the cepheid variable having mass equal to 5.02 solar masses and radius equal to 16.382 solar radii. These numerical estimates suggest that the departure from the adiabatic conditions must be taken into account more precisely than what has been done in the present paper.