Normal Modes of Radial Pulsation of Stars at the End Point of Thermonuclear Evolution

The lowest three normal modes of radial pulsation are studied for stellar configurations at the end point of thermonuclear evolution. Two alternative equations of state are assumed-the Harrison-Wheeler equation of state, and the Skyrme-Cameron-Saakyan equation of state. The adiabatic index is discussed for each equation of state, taking into account the extent to which periodic changes in nuclear composition are produced by stellar pulsation. The periods and e-folding times of the lowest three normal modes of a wide range of configurations are calculated to an accuracy of + 1 per cent. The eigenfunctions of some of the normal modes and the pulsation energy which they can store are also calculated; and a discussion is presented of the damping of neutron-star pulsations and of the consequent heating of the star. An account is given of a few of the implications of our calculations: The damping of neutron-star pulsations by the modified URCA process is so great that only with efficiencies of >30 per cent for energy conversion could pulsations be the energy source for exponentially decaying upernova light-curves (theory of Finzi). An energy-conversion efficiency of >5 per cent would be required to continually replenish from neutron-star pulsations the energy being radiated by high-energy electrons in the Crab Nebula (theories of Hoyle, Narlikar, and Wheeler, and of Cameron). Moreover, the gradual conversion of pulsation energy to heat by the modified URCA process could substantially decrease neutron-star cooling rates and might, therefore, make it easier for astronomers to detect X-rays from neutron stars. Pulsation damping by the emission of gravitational radiation may be even more important than damping by the modified URCA process-gravitational radiation may damp out all pulsations, radial and non-radial, in a time of the order of a day.