Sounding stellar cycles with Kepler – III. Comparative analysis of chromospheric, photometric, and asteroseismic variability

By combining ground-based spectrographic observations of variability in the chromospheric emission from Sun-like stars with the variability seen in their eigenmode frequencies, it is possible to relate the changes observed at the surfaces of these stars to the changes taking place in the interior. By further comparing this variability to changes in the relative flux from the stars, one can obtain an expression for how these activity indicators relate to the energy output from the stars. Such studies become very pertinent when the variability can be related to stellar cycles as they can then be used to improve our understanding of the solar cycle and its effect on the energy output from the Sun. Here we present observations of chromospheric emission in 20 Sun-like stars obtained over the course of the nominal 4-year Kepler mission. Even though 4 years is too short to detect stellar equivalents of the 11-year solar cycle, observations from the Kepler mission can still be used to analyse the variability of the different activity indicators thereby obtaining information of the physical mechanism generating the variability. The analysis reveals no strong correlation between the different activity indicators, except in very few cases. We suggest that this is due to the sparse sampling of our ground-based observations on the one hand and that we are likely not tracing cyclic variability on the other hand. We also discuss how to improve the situation.