Simulating acoustic waves in spotted stars

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 ≤ 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 = 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.

Asteroseismic Signature of a Large Active Region

“…Figure 3 also displays the different contributions to the frequency splittings due to rotation and to the active region perturbation in the corotating frame R β . For both multiplets, the M = 0 peaks are shifted by the largest amount, they are the most affected by the AR perturbation and in the frame R β (see also Papini et al, 2015). This feature, which arises from geometrical considerations only, is preserved in the spectrum as seen in the observer's frame, where the M = 0 peaks are clearly visible.…”

“…Instead, we parametrize the active region perturbation as an increase in sound speed near the surface. Following Papini et al (2015), we write…”

“…The function f = exp(−|r − r c | 2 /2σ 2 )[1/2 + cos(|r − r c |/σ)/2] is a Gaussian function centered at radius r c = 0.9985 R with dispersion σ = 0.004 R , multiplied by a raised cosine. This functional form is the same as the one described by Papini et al (2015). The perturbation is thus placed along the polar axis at a depth of 4 Mm, with a surface coverage of 12%.…”

“…As in Sect. 2.3, we assume that the intensity fluctuations are proportional to the Eulerian pressure perturbation measured at r 0 = R + 200 km above the surface (see Papini et al, 2015). To calculate the expectation value of the observed power spectrum, we performed a first set of simulations for which all the modes were excited with the same phase at the initial time.…”

Localizing flares to understand stellar magnetic fields and space weather in exo-systems

“…Activity-driven perturbations in asteroseismic observations can in theory reveal the latitudes of active regions (Gizon, 2002;Papini, Birch, Gizon, & Hanasoge, 2015;Papini & Gizon, 2019). The method poses that strong magnetic field clusters disturb asteroseismic oscillations that then become visible as characteristic shifts in the power spectrum that trace the location of the clusters.…”