Abstract
Acoustic modes of oscillation are affected by stellar activity, however it is unclear how starspots contribute to these changes. Here we investigate the nonmagnetic effects of starspots on global modes with angular degree $\ell \leq 2$ in highly active stars, and characterize the spot seismic signature on synthetic light curves. We perform 3D time-domain simulations of linear acoustic waves to study their interaction with a model starspot. We model the spot as a 3D change in the sound speed stratification with respect to a convectively stable stellar background, built from solar Model S. We perform a parametric study by considering different depths and perturbation amplitudes. Exact numerical simulations allow the investigation of the wavefield-spot interaction beyond first order perturbation theory. The interaction of the axisymmetric modes with the starspot is strongly nonlinear. As mode frequency increases, the frequency shifts for radial modes exceed the value predicted by linear theory, while the shifts for the $\ell=2, m=0$ modes are smaller than predicted by linear theory, with avoided-crossing-like patterns forming between the $m=0$ and $m=1$ mode frequencies. The nonlinear behavior increases with increasing spot amplitude and/or decreasing depth. Linear theory still reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear regime the mode eigenfunctions are not pure spherical harmonics, but rather a mixture of different spherical harmonics. This mode mixing, together with the frequency changes, may lead to misidentification of the modes in the observed acoustic power spectra.
Highlights
For the starspot we model only the indirect changes induced in the sound speed in the stellar interior
In all the tests performed, the extracted eigenfrequencies and eigenfunctions were compared with ADIPLS solutions and showed good agreement: the difference between ADIPLS and GLobal Acoustic Spherical Simulator (GLASS) for the eigenfrequencies was below 0.16 μHz and the maximum difference for the eigenfunctions was ∼0.1%, after the damping was accounted for
We note that because of the initial conditions we set (i.e., the choice made in Eq (10) of using the same phase in exciting all of the modes), the |m| > 0 peaks in these spectra are twice as high as the peaks in a spectrum of acoustic oscillations resulting from stochastic excitation
Summary
Starspots are the main observed features of magnetic activity in stars and play a fundamental role in understanding stellar dynamos They have been detected in many stars through the modulation of light curves (Mosser & Appourchaux 2009) and Doppler imaging (Strassmeier 2009), the latter suggesting polar and high- to mid-latitude concentrations of magnetic fields. In the case of the Sun they found that the frequency changes are too small (by two orders of magnitude) to explain the observed shifts They concluded that the indirect effects of starspots on the stellar stratification cannot be responsible for the observed changes in the acoustic oscillations, at least for a star with a solar-like level of activity
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