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Kepler-13b (KOI-13.01) is a most intriguing exoplanet system due to the rapidprecession rate, exhibiting several exotic phenomena. We analyzed $Kepler$Short Cadence data up to Quarter 14, with a total time-span of 928 days, toreveal changes in transit duration, depth, asymmetry, and identify the possiblesignals of stellar rotation and low-level activity. We investigated long-termvariations of transit light curves, testing for duration, peak depth andasymmetry. We also performed cluster analysis on $Kepler$ quarters. We computedthe autocorrelation function of the out-of-transit light variations. Transitduration, peak depth, and asymmetry evolve slowly, due to the slowly driftingtransit path through the stellar disk. The detected transit shapes will map thestellar surface on the time scale of decades. We found a very significantclustering pattern with 3-orbit period. Its source is very probably therotating stellar surface, in the 5:3 spin-orbit resonance reported in aprevious study. The autocorrelation function of the out-of-transit lightvariations, filtered to 25.4 hours and harmonics, shows slow variations and apeak around 300--360 day period, which could be related to the activity cycleof the host star.

Mapping a star with transits: orbit precession effects in the Kepler-13 system