Investigating magnetic activity with asteroseismology

In the Sun, the frequencies of the acoustic modes are observed to vary in phase with the magnetic activity level. Magnetic fields can affect the modes in two ways: directly, by the action of the Lorentz force on the gas, thus providing an additional restoring force, the result being an increase of frequency; or indirectly, by affecting the physical properties in the mode cavities and, as a result, the propagation of the acoustic waves within them, leading to either an increase or decrease of the mode frequencies.

These frequency variations are expected to be common in solar-type stars and contain information on the activity-related changes that take place in their interiors. The unprecedented duration of Kepler photometric time series provides a unique opportunity to detect and characterize stellar magnetic cycles through asteroseismology.

In a previous work (hereafter Paper I), we analyzed a sample of 87 solar-type stars, measuring their temporal frequency shifts over segments of length 90 days (see Fig. 1). The mean frequency shifts were then computed and compared with: i) those obtained from a cross-correlation method; ii) the variation in the mode heights; iii) a photometric activity proxy; and iv) the characteristic timescale of the granulation. Interestingly, more than 60% of the stars in our sample showed evidence of (quasi-)periodic variations in the frequency shifts. In the majority of cases, these variations were accompanied by variations in other activity proxies. Furthermore, about 20% of the stars showed mode frequencies and heights varying approximately in phase, contrary to what is observed for the Sun.

In our most recent work (hereafter Paper II), we have taken one step forward. Its goal was to investigate the dependence of the observed mode frequency variations on the stellar parameters and whether they are consistent with an activity-related origin. We selected the solar-type oscillators in our sample with the highest signal-to-noise ratio, totaling 75 targets. Using the temporal frequency variations determined in Paper I, we studied the relation between those variations and the fundamental properties of such stars (see Fig. 2). We also compared the observed frequency shifts with chromospheric and photometric activity indices, which are only available for a subset of the sample. We found that frequency shifts increase with increasing chromospheric activity, which is consistent with an activity-related origin of the observed frequency shifts. Frequency shifts were also found to increase with effective temperature, which is in agreement with the theoretical predictions for the activity-related frequency shifts by Metcalfe et al. (2007, MNRAS, 379, L16). Frequency shifts are largest for fast rotating and young stars, which is consistent with these stars being more active than slower rotators and older stars. Finally, we found evidence for frequency shifts increasing with stellar metallicity.

A link to Paper I (arXiv) is provided here.

A link to Paper II (arXiv) is provided here.

Figure 1: Results for the solar-type star KIC 8006161. Top panel: Comparison between the measured mean frequency shifts (black) with those obtained from a cross-correlation method (blue). Second panel: Logarithmic mode height obtained from a peak-bagging analysis. Third panel: Photometric magnetic activity proxy. Bottom panel: Characteristic timescale of the granulation. Vertical dotted lines mark the start/end of Kepler quarters.

Figure 2: Maximum frequency-shift variation as a function of: a) chromospheric activity index; b) photometric activity proxy; c) effective temperature; d) age; e) rotation period; and f) metallicity. All panels are color coded by age, except panels b) and d), which are color coded by inclination angle and rotation period (stars with unknown rotation period in gray), respectively. Solid lines in panel c) show the theoretical prediction of activity-related frequency shifts for different ages by Metcalfe et al. (2007). The yellow star marks the maximum frequency-shift variation for the complete solar cycle 23. The yellow-shaded region indicates the range of values from 4-year subseries of solar cycle 23. Its width is set at 10% of the parameter range shown. KIC 8006161 is highlighted by a green square.