The oblique pulsator model revisited

The oblique pulsator model accounts for most of the pulsation properties of the rapidly oscillating Ap (roAp) stars. The model predicts that modes are seen as equidistant multiplets separated by the angular frequency of rotation. The relative amplitudes of the components may be calculated and directly compared with observations. The effects of rotation introduce amplitude asymmetry, that is peaks corresponding to azimuthal numbers m and m are unequal. In this paper we propose improvements to the model that consist of including effects of the centrifugal force and in using a non-perturbative treatment of the magnetic field influence. We show that in roAp stars the centrifugal force is the primary source of the rotational frequency shift. Although the amplitude asymmetry arises from the Coriolis force, its size is strongly affected by the centrifugal force. For dipole modes (l = 1) we develop a simple geometrical picture of pulsation in the presence of rotation and a magnetic field. We provide some numerical results for a representative model of roAp stars which is applied to the case of HR 3831. We find that the mode that agrees with the observed amplitude ratios in this star significantly departs from alignment with the magnetic axis. We discuss problems posed by the observational data of HR 3831, emphasizing difficulties of the standard oblique pulsator model which assumes that the excited mode is nearly aligned with the magnetic field.