The pressure mode oscillation spectrum of a rotating gaseous sphere: Application to Jupiter

Abstract

This paper explores the influence of rotation of the pattern of pressure mode oscillations of a gaseous sphere in rotation. The method presented here deals with the removal of degeneracy due to rotation in the case of Jupiter, but all results are transposable to a rotating star. With the help of the asymptotic methods developed for the solar oscillations, high radial order or high degree p-odes eigenperiods can be easily calculated for a nonrotating Jupiter. However, Jovian seismology differs from helioseismology because of rapid planetary rotation. It is shown that a major effect of the Jovian rotation on the oscillation pattern is produced by oblateness (the external oblateness of Jupiter is about 6.5%); it consists in the removal of degeneracy of the eigenperiods. A perturbation theory is developed to treat this effect. The current modal description (radial order n, degree l and azimuthal order m) remains valid, but with some first-order modifications of oblateness. This work points out to the possibility of measuring the variations of oblateness in the planet's interior, but also to the difficulty of identifying the rotating oscillation pattern.