Simulating the signature of starspots in stellar oscillations

Abstract

It has been known for a few decades that acoustic oscillations are affected by stellar activity. In the case of the Sun global acoustic modes show a variation with the 11-year cycle and a similar phenomenon has been observed in other stars with asteroseismology. In this work I investigate the effects of large starspots on the global low-degree modes of stellar oscillations. I use the GLASS code to simulate the propagation of small amplitude acoustic waves in 3D stellar interiors. Firstly, I consider the problem of convective stabilization, common to every linear oscillation code in the time domain. A general method to build a convectively stable background starting from a given stellar model is presented. Important properties of the original model, such as hydrostatic equilibrium, are preserved by the method. A perturbative approach to approximately recover the acoustic wavefield in the original unstable stellar model is proposed. Tests show that the corrected frequencies are within 1 μHz of the exact values for low-degree modes near 3 mHz. Secondly, using the GLASS code, I study the effects of a localized sound speed perturbation placed at the north pole on radial, dipole, and quadrupole modes of oscillation. The study shows that the axisymmetric modes are the most strongly affected and their frequencies cannot be modeled by linear theory for large starspots. Mode eigenfunctions depart from their shape of pure spherical harmonics and get mixed with spherical harmonics of different angular degrees. This may affect the correct identification of the modes in the power spectrum. Thirdly, we consider the observational signatures of a large starspot on modes of angular degree ℓ. For an active region rotating with the star (and not situated at a pole), the perturbation is not steady in any inertial frame. The combined effects of rotation and the starspot cause each mode to appear as (2ℓ+1)² peaks in the observed power spectrum. The envelope of the power spectrum of a multiplet is thus complex and depends on the latitude of the active region and the inclination angle of the star. Examples are computed using both perturbation theory and the GLASS code. This work ought to be useful in interpreting oscillation power spectra of spotted pulsators.