Magnetic activity and differential rotation in the young Sun-like stars KIC 7985370 and KIC 7765135

Aims. We present a detailed study of the two Sun-like stars KIC 7985370 and KIC 7765135, to determine their activity level, spot distribution, and differential rotation. Both stars were previously discovered by us to be young stars and were observed by the NASA Kepler mission. Methods. The fundamental stellar parameters (vsini, spectral type, T_eff, log g, and [Fe/H]) were derived from optical spectroscopy by comparison with both standard-star and synthetic spectra. The spectra of the targets allowed us to study the chromospheric activity based on the emission in the core of hydrogen Hα and Ca ii infrared triplet (IRT) lines, which was revealed by the subtraction of inactive templates. The high-precision Kepler photometric data spanning over 229 days were then fitted with a robust spot model. Model selection and parameter estimation were performed in a Bayesian manner, using a Markov chain Monte Carlo method. Results. We find that both stars are Sun-like (of G1.5 V spectral type) and have an age of about 100–200 Myr, based on their lithium content and kinematics. Their youth is confirmed by their high level of chromospheric activity, which is comparable to that displayed by the early G-type stars in the Pleiades cluster. The Balmer decrement and flux ratio of their Ca ii-IRT lines suggest that the formation of the core of these lines occurs mainly in optically thick regions that are analogous to solar plages. The spot model applied to the Kepler photometry requires at least seven persistent spots in the case of KIC 7985370 and nine spots in the case of KIC 7765135 to provide a satisfactory fit to the data. The assumption of the longevity of the star spots, whose area is allowed to evolve with time, is at the heart of our spot-modelling approach. On both stars, the surface differential rotation is Sun-like, with the high-latitude spots rotating slower than the low-latitude ones. We found, for both stars, a rather high value of the equator-to-pole differential rotation (dΩ ≈ 0.18 rad d^-1), which disagrees with the predictions of some mean-field models of differential rotation for rapidly rotating stars. Our results agree instead with previous works on solar-type stars and other models that predict a higher latitudinal shear, increasing with equatorial angular velocity, that can vary during the magnetic cycle.