ACTIVITY ANALYSES FOR SOLAR-TYPE STARS OBSERVED WITH KEPLER . I. PROXIES OF MAGNETIC ACTIVITY

Abstract

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.

Magnetic Activity Analysis for a Sample of G-Type Main Sequence Kepler Targets

“…In contrast, for a random time series without any periodic feature, the derived ACF has tiny fluctuations without any regular patterns. To find more details regarding the ACFs for a perfect periodic time series and a random one, see He et al (2015). Moreover, as mentioned above, the ACF for a periodic time series fluctuates with the same period as the original time series.…”

“…In fact, McQuillan et al (2013McQuillan et al ( , 2014 used the autocorrelation method to measure the rotation periods for a large sample of Kepler stars. As proposed by He et al (2015), one can measure the degree of periodicity of a light curve by computing the average value of | ( )| r h over the interval < < h N 0 2 :…”

“…In fact the factor 2 2 in Equation (4) is included to give a corrected value of the fluctuation range of a light curve (for an illustrative example, see He et al 2015).…”

“…Time evolution of the magnetic features leads to the complexity of shapes of the solar light curve (Lanza et al 2003;He et al 2015). It has been found that the lifetimes of most sunspot regions are shorter than the rotation period of the Sun, while facula regions have relatively longer lifetimes owing to their larger spatial scale (Zirin 1985;Solanki et al 2000).…”

“…In the paper by He et al (2015), they applied the two magnetic proxies to the Sun (rotation period: 25.38 days) and two solar-type stars observed with Kepler. One Kepler star (KIC 9766237) has a moderate rotation period (14.7 days) and another Kepler star (KIC 10864581) has a smaller period (6 days).…”