ASYMPTOTIC REPRESENTATION OF LINEAR, ISENTROPIC G-MODES OF STARS

An asymptotic representation of low-frequency, linear, isentropic g-mo des of a star has been developed without the usual neglect of the Eule rian perturbation of the gravitational potential; As governing equatio ns, a fourth-order system of differential equations in the divergence and the radial component of the Lagrangian displacement is adopted. Th e asymptotic representation is based on the use of asymptotic expansio ns adequate for solutions of singular perturbation problems. At the lo west-order asymptotic approximation, a star can be considered as a lin ear oscillator at distances sufficiently large from the centre and the surface, when the divergence of the Lagrangian displacement is used a s the dependent variable. The asymptotic treatment yields lowest-order asymptotic approximations of the various physical quantities involved in an oscillation mode g of a star. The Cowling approximation adopted in previous investigations proves to be justified at the lowest-order asymptotic approximation.