Starspot evolution, differential rotation, and correlation between chromospheric and photospheric activities on Kepler-411.

We present an analysis of the starspot evolution, the surface differential rotation (SDR), the correlation between chromospheric activity indicators and the spatial connection between chromospheric and photospheric activities on the active star Kepler-411, using time-series photometry over four years from Kepler, and spectroscopic data from Keck I 10-m and Lijiang 2.4-m telescopes. We constructed the light curve (LC) by re-performing photometry and reduction from the Target Pixel Files and Cotrending Basis Vectors with a manually redefined aperture using the software pyke 3. An efficient program, gemc_lcm , was developed to apply a two-spots model to chosen LC segments with three spot groups at fixed latitudes (30○, 45○), (30○, 60○) and (45○, 60○). We found a periodic variation of the starspots at the period of about 660 d which independs on spot latitudes, and estimated the lower limit of SDR rate α  = 0.1016(0.0023) and equatoral rotation period P eq = 9.7810(0.0169) d. Simultaneously, the relative variations of chromospheric activity indicators were derived by subtracting the overall mean spectrum from individual spectrum. It is found that Ca  ii H and K emissions are strongly correlated with each other, and there also exists a correlation between H α and Ca  ii H & K emissions, with large dispersion, in accordance with previous results. Furthermore, we find the correlation between Ca  ii H and K emissions is different in 2011 and 2012. The chromospheric emission variation shows a highly spatial anticorrelation with the LC, suggesting a spatial connection between the chromospheric active region and spot region. [ABSTRACT FROM AUTHOR]