Excitation of non-radial stellar oscillations by gravitational waves: a first model

TL;DR

This paper develops a formalism to model how gravitational waves excite non-radial oscillations in stars, showing that quadrupolar modes are primarily affected and that larger stars are more susceptible to this excitation mechanism.

Contribution

It introduces a new formalism for calculating stellar oscillation amplitudes caused by gravitational waves, focusing on quadrupolar modes and their dependence on stellar size.

Findings

Gravitational waves excite only quadrupolar spheroidal modes.

Surface velocities depend on the eighth power of stellar radius.

Larger stars are more affected by gravitational wave excitation.

Abstract

The excitation of solar and solar-like g modes in non-relativistic stars by arbitrary external gravitational wave fields is studied starting from the full field equations of general relativity. We develop a formalism that yields the mean-square amplitudes and surface velocities of global normal modes excited in such a way. The isotropic elastic sphere model of a star is adopted to demonstrate this formalism and for calculative simplicity. It is shown that gravitational waves solely couple to quadrupolar spheroidal eigenmodes and that normal modes are only sensitive to the spherical component of the gravitational waves having the same azimuthal order. The mean-square amplitudes in case of stationary external gravitational waves are given by a simple expression, a product of a factor depending on the resonant properties of the star and the power spectral density of the gravitational waves' spherical accelerations. Both mean-square amplitudes and surface velocities show a characteristic R^8-dependence (effective R^2-dependence) on the radius of the star. This finding increases the relevance of this excitation mechanism in case of stars larger than the Sun.