Theoretical light curves of dipole oscillations in roAp stars

Context. The dipole modes are the most common geometry of oscillations in roAp stars inferred from photometric measurements and are therefore of special interest for asteroseismic purposes. Aims. We present a theoretical and analytical study of the light curves associated with dipole (l = 1) pulsations of roAp stars in the framework of the revisited oblique pulsator model. Methods. We describe the light curves in terms of the inclination and polarization of the elliptical displacement vector of the dipole modes. We study the influence of the magnetic field and rotation on the shape of these light curves for both amplitudes and phases. Results. Despite the inclination of dipole mode with respect to the magnetic axis, we find that the dipole mode can have maxima that are in phase with the magnetic maxima. We apply our formalism to the well-known roAp star HR 3831 (HD 83368) to derive its mode properties. Our results are similar to those obtained by time-series spectroscopy. We also consider the cases of three other roAp stars, HD 6532, HD 99563, and HD 128898 ({\alpha} Cir). Conclusions. We demonstrate that the formalism of the revisited oblique pulsator model is adequate to explain the properties of the photometric light curves associated with dipole modes in roAp stars. In addition, we show that the coincidence of pulsation and magnetic extrema can also occur for inclined modes with respect to the magnetic axis. With the stars considered in this paper, we conclude that the polarization of the modes present in roAp stars are quasi linearly polarized.