Activity Analyses for Solar-Type Stars Observed With Kepler. I. Proxies of Magnetic Activity

Light curves of solar-type stars often show gradual fluctuations due to rotational modulation by magnetic features (starspots and faculae) on stellar surfaces. Two quantitative measures of modulated light curves are employed as the proxies of magnetic activity for solar-type stars observed with Kepler telescope. The first is named autocorrelation index $i_{AC}$, which describes the degree of periodicity of the light curve, the second is the effective fluctuation range of the light curve $R_{eff}$, which reflects the depth of rotational modulation. The two measures are complementary and depict different aspects of magnetic activities on solar-type stars. By using the two proxies $i_{AC}$ and $R_{eff}$, we analyzed activity properties of two carefully selected solar-type stars observed with Kepler (Kepler ID: 9766237 and 10864581), which have distinct rotational periods (14.7 vs. 6.0 days). We also applied the two measures to the Sun for a comparative study. The result shows that both the measures can reveal cyclic activity variations (referred to as $i_{AC}$-cycle and $R_{eff}$-cycle) on the two Kepler stars and the Sun. For the Kepler star with the faster rotation rate, $i_{AC}$-cycle and $R_{eff}$-cycle are in the same phase, while for the Sun (slower rotator), they are in the opposite phase. By comparing the solar light curve with simultaneous photospheric magnetograms, it is identified that the magnetic feature that causes the periodic light curve during solar minima is the faculae of the enhanced network region, which can also be a candidate of magnetic features that dominate the periodic light curves on the two Kepler stars.