THE SUBSEISMIC APPROXIMATION FOR LOW-FREQUENCY MODES OF THE EARTH APPLIED TO LOW-DEGREE, LOW-FREQUENCY G-MODES OF NONROTATING STARS

The subseismic approximation proposed by Smylie & Rochester (1981) for low-frequency modes in the Earth is used in an asymptotic treatment of low-frequency g-modes belonging to low-degree spherical harmonics in the case of a non-rotating, spherically symmetric star in which the square of the Brunt-Vaisala frequency is different from zero everywhere inside the star except at the center and keeps the same sign. The approximation neglects the contribution of the Eulerian perturbation of the pressure to the Lagrangian perturbation of that quantity relative to the contribution stemming from the equilibrium pressure gradient. In contrast to the procedure adopted in the standard asymptotic theory, the Eulerian perturbation of the gravitational potential is not neglected. The subseismic approximation leads to an inadequate representation of the radial component of the Lagrangian displacement near the star's surface. This inadequate representation affects the equation determining the asymptotic eigenfrequencies. The eigenvalue equation is applied to second-degree g--modes of the compressible equilibrium configuration with uniform mass density and second-degree g+-modes of the polytropic model with index n = 3. For the latter model, the asymptotic theory based on the subseismic approximation yields better approximations of the eigenfrequencies of second-degree g-modes up to the order 30 than does the standard asymptotic theory.