SELECTION-RULES FOR PERTURBATIONS TO THE EIGENFUNCTIONS OF THE PULSATIONS OF STARS DUE TO THE ROTATION AND MAGNETIC-FIELD

We derive the selection rules for the perturbations to the eigenfuncti ons of stellar oscillations caused by stellar rigid rotation and axisy mmetric poloidal magnetic fields. We introduce vector spherical harmon ics in order to deal with the perturbation equation of motion, and sho w that they are useful to express the eigenfunctions of nonradial osci llations of stars. It is shown that if the magnetic fields axe express ed by the multipole expansion series up to the order k, the eigenfunct ion of the mode with a spherical degree l and an azimuthal order m in the nonrotating, nonmagnetic case has components of the spherical degr ee max (l - 2k, 0), ..., l + 2k and the azimuthal order -l, ..., l. We discuss the oscillation features of rapidly oscillating Ap stars, and interpret them as being a manifestation of a magnetic perturbation of the nonradial modes.