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Abstract

Axisymmetric magnetic activity on the Sun and sun-like stars increases the frequencies of the modes of acoustic oscillation. However, it is unclear how a corotating patch of activity affects the oscillations, since such a perturbation is unsteady in the frame of the observer. In this paper we qualitatively describe the asteroseismic signature of a large active region in the power spectrum of the dipole (ℓ = 1) and quadrupole (ℓ = 2) p modes. First we calculate the frequencies and the relative amplitudes of the azimuthal modes of oscillation in a frame that corotates with the active region, using first-order perturbation theory. For the sake of simplicity, the influence of the active region is approximated by a near-surface increase in sound speed. In the corotating frame the perturbations due to (differential) rotation and the active region completely lift the (2ℓ + 1)-fold azimuthal degeneracy of the frequency spectrum of modes with harmonic degree ℓ. Then we transform to an inertial frame to obtain the observed power spectrum. In the frame of the observer, the unsteady nature of the perturbation leads to the appearance of (2ℓ + 1)2 peaks in the power spectrum of a multiplet. These peaks blend into each other to form asymmetric line profiles. In the limit of a small active region (angular diameter less than 30°), we approximate the power spectrum of a multiplet in terms of 2 × (2ℓ + 1) peaks, whose amplitudes and frequencies depend on the latitude of the active region and the inclination angle of the star's rotation axis. In order to check the results and to explore the non-linear regime, we perform numerical simulations using the 3D time-domain pseudo-spectral linear pulsation code GLASS. For small sound-speed perturbations, we find a good agreement between the simulations and linear theory. Larger perturbation amplitudes will induce mode mixing and lead to additional complex changes in the predicted power spectrum. However linear perturbation theory provides useful guidance to search for the observational signature of large individual active regions in stellar oscillation power spectra.