Seismic Investigations of Solar and Stellar Magnetic Activity

Context. Understanding the solar activity cycle - its origin, the mechanisms that drive it, and its relation to stellar activity cycles - is an outstanding open issue in solar and stellar astrophysics. Helio- and asteroseismology have developed into powerful tools to gain insight into the interior conditions of the Sun and the stars. The properties of stellar acoustic oscillation eigenmodes (p modes) change with the level of magnetic activity. However, seismic techniques to infer the location and configuration of the magnetic field inside the Sun or the stars from observations are few and far between.

Aims. With this thesis, I contribute to the development of seismic diagnostics and tools with which solar and stellar magnetic activity can be studied. Additionally, I aim to further the seismic exploration of stellar activity cycles as well as the investigation of the change of the parameters of the Sun's acoustic oscillations over the solar cycle.

Methods and Data. I analyze photometric data of a sample of 24 solar-like stars from the Kepler satellite looking for signatures of stellar magnetic activity in the parameters of their acoustic oscillations: the temporal evolution of mode frequencies, the height of the p-mode envelope, as well as granulation time scales are explored. Furthermore, I use data from the ground-based GONG network to examine the solar cycle dependence of the damping widths, amplitudes, as well as several physical quantities of solar p modes as functions of the level of solar activity. Finally, I employ techniques from quasi-degenerate perturbation theory to derive the analytical expression for the coupling strengths of oscillation eigenmodes under the influence of a superposition of zonal toroidal magnetic fields. These coupling strengths are then used to compute the effect of six magnetic field models on p-mode multiplet frequencies.

Results and Conclusions. I detect significant frequency shifts in time for 23 of the 24 investigated solar-like stars. For six of them, I link these shifts to magnetic activity. I also find that the amplitude of the frequency shifts decreases with stellar age and rotation period. These results show that magnetic activity can be routinely observed in the oscillation parameters for solar-like stars. This opens up the possibility of placing the solar activity cycle in the context of other stars by asteroseismology. From my analysis of 22 years of GONG data, I find that the amplitude of the parameter variation changes with mode frequency and harmonic degree. Damping widths are correlated with the level of solar activity, mode energy and mean square velocity are anti-correlated with it. Generally, I can confirm previous measurements of the variation of mode parameters with the solar cycle. Two main results of this thesis are the general matrix elements for a superposition of zonal toroidal fields: first, the general matrix element for the direct effect - that is the coupling of modes conveyed by the magnetic field - and second, the indirect effect - that is the coupling of modes due to a change in the stellar structural quantities due to the introduced perturbation. From forward calculations with these matrix elements, it can be seen that the magnetic field affects the multiplet frequencies in a way that depends on its location and the geometry inside the Sun. By comparison of my theoretical results and observed shifts, I conclude that strong tachocline fields cannot be responsible for the observed frequency shifts of p modes over the solar cycle. I also find that part of the surface effect in helioseismic oscillation frequencies might be attributed to magnetic fields in the outer layers of the Sun.