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.

The light curves of solar-type stars present both periodic fluctuation and flare spikes. The gradual periodic fluctuation is interpreted as the rotational modulation of magnetic features on the stellar surface and is used to deduce magnetic feature activity properties. The flare spikes in light curves are used to derive flare activity properties. In this paper, we analyze the light curve data of three solartype stars (KIC 6034120, KIC 3118883, and KIC 10528093) observed with Kepler space telescope and investigate the relationship between their magnetic feature activities and flare activities. The analysis shows that: (1) both the magnetic feature activity and the flare activity exhibit long-term variations as the Sun does; (2) unlike the Sun, the long-term variations of magnetic feature activity and flare activity are not in phase with each other; (3) the analysis of star KIC 6034120 suggests that the long-term variations of magnetic feature activity and flare activity have a similar cycle length. Our analysis and results indicate that the magnetic features that dominate rotational modulation and the flares possibly have different source regions, although they may be influenced by the magnetic field generated through a same dynamo process.

Magnetic activity information is concealed in the shape of stellar light curves owing to the process of rotational modulation. We developed approaches to extract magnetic activity characteristics from stellar light curves, and applied the method to a solar-type star observed with Kepler space telescope and also to the Sun for comparison. The result reveals distinct magnetic activity discrepancies between the solar-type star and the Sun. (1) The light-curve periodicity of the solar-type star is generally stronger than that of the Sun. (2) For the solar-type star, when the range of light-curve fluctuation is larger, the periodicity is also higher; while for the Sun, only during the solar minima with minimal range of fluctuation, the light curves show some periodicity. We propose that on the solar-type star, it is the large-scale magnetic field that leads to the light curves with both high periodicity and large range of fluctuation.