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We present a spectroscopic/photometric analysis of the rapid rotatorKIC8429280, discovered by ourselves as a very young star and observed by theKepler mission. We use spectroscopic/photometric ground-based data to derivestellar parameters, and we adopt a spectral subtraction technique to highlightthe chromospheric emission in the cores of Halpha, CaII H&K and IRT lines. Wefit a robust spot model to the high-precision Kepler photometry spanning 138days. Model selection and parameter estimation is performed in a Bayesianmanner using a Markov chain Monte Carlo method. We find that KIC8429280 is acool (K2V) star with an age of ~50 Myr, based on its Li content, that haspassed its T Tau phase and is spinning up approaching the ZAMS. Its high levelof chromospheric activity is indicated by the radiative losses in CaII H&K andIRT, Halpha, and Hbeta lines. Furthermore, its Balmer decrement and the fluxratio of CaII IRT lines imply that these lines are mainly formed inoptically-thick sources analogue to solar plages. The analysis of the Keplerdata uncovers evidence of at least 7 enduring spots. Since the star'sinclination is rather high, ~70{\deg}, the assignment of the spots to thenorthern/southern hemisphere is not unambiguous. We find at least 3 solutionswith nearly the same level of residuals. The distribution of the active regionsis such that the spots are located around 3 latitude belts, i.e. the equatorand +-(50{\deg}-60{\deg}), with the high-latitude spots rotating slower thanthe low-latitude ones. The equator-to-pole differential rotation ~0.27 rad/d isat variance with some recent mean-field models of differential rotation inrapidly rotating MS stars, which predict a much smaller latitudinal shear. Ourresults are consistent with the scenario of a higher differential rotation,which changes along the magnetic cycle.

Magnetic activity and differential rotation in the very young star KIC 8429280