We investigate different amplitude scaling relations adopted for the asteroseismology of stars that show solar-like oscillations. Amplitudes are among the most challenging asteroseismic quantities to handle because of the large uncertainties that arise in measuring the background level in the star's power spectrum. We present results computed by means of a Bayesian inference on a sample of 1640 stars observed with Kepler, spanning from main sequence to red giant stars, for 12 models used for amplitude predictions and exploiting recently well-calibrated effective temperatures from SDSS photometry. We test the candidate amplitude scaling relations by means of a Bayesian model comparison. We find the model having a separate dependence upon the mass of the stars to be largely the most favored one. The differences among models and the differences seen in their free parameters from early to late phases of stellar evolution are also highlighted.

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 (v sin i, 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.

Aims. We present a spectroscopic and photometric analysis of the rapid rotator KIC 8429280, discovered by ourselves as a very young star and observed by the NASA Kepler mission, designed to determine its activity level, spot distribution, and differential rotation. Methods. We use ground-based data, such as high-resolution spectroscopy and multicolor broad-band photometry, to derive stellar parameters (v sin i, spectral type, T eff , log g, and [Fe/H]), and we adopt a spectral subtraction technique to highlight the strong chromospheric emission in the cores of hydrogen Hα and Ca ii H&K and infrared triplet (IRT) lines. We then fit a robust spot model to the high-precision Kepler photometry spanning 138 days. Model selection and parameter estimation is performed in a Bayesian manner using a Markov chain Monte Carlo method. Results. We find that KIC 8429280 is a cool (K2 V) star with an age of about 50 Myr, based on its lithium content, that has passed its T Tau phase and is spinning up approaching the ZAMS on its radiative track. Its high level of chromospheric activity is clearly indicated by the strong radiative losses in Ca ii H&K and IRT, Hα, and Hβ lines. Furthermore, its Balmer decrement and the flux ratio of Ca ii IRT lines imply that these lines are mainly formed in optically-thick regions similar to solar plages. The analysis of the Kepler data uncovers evidence of at least seven enduring spots. Since the star's inclination is rather high -nearly 70 • -the assignment of the spots to either the northern or southern hemisphere is not unambiguous. We find at least three solutions with nearly the same level of residuals. Even in the case of seven spots, the fit is far from being perfect. Owing to the exceptional precision of the Kepler photometry, it is not possible to reach the noise floor without strongly enhancing the degrees of freedom and, consequently, the non-uniqueness of the solution. The distribution of the active regions is such that the spots are located around three latitude belts, i.e. around the star's equator and around ±(50 • -60 • ), with the high-latitude spots rotating slower than the low-latitude ones. The equator-to-pole differential rotation dΩ 0.27 rad d −1 is at variance with some recent mean-field models of differential rotation in rapidly rotating main-sequence stars, which predict a much smaller latitudinal shear. Our results are consistent with the scenario of a higher differential rotation, which changes along the magnetic cycle, as proposed by other models.

Aims. We compare surface maps of the chemically peculiar star HD 50773 produced with a Bayesian technique and based on high quality CoRoT photometry with those derived from rotation phase resolved spectropolarimetry. The goal is to investigate the correlation of surface brightness with surface chemical abundance distribution and the stellar magnetic surface field. Methods. The rotational period of the star was determined from a nearly 60 days long continuous light curve obtained during the initial run of CoRoT. Using a Bayesian approach to star-spot modelling, which in this work is applied for the first time for the photometric mapping of a CP star, we derived longitudes, latitudes and radii of four different spot areas. Additional parameters like stellar inclination and the spot's intensities were also determined. The CoRoT observations triggered an extensive ground-based spectroscopic and spectropolarimetric observing campaign and enabled us to obtain 19 different high resolution spectra in Stokes parameters I and V with NARVAL, ESPaDOnS, and SemelPol spectropolarimeters. Doppler and Magnetic Doppler imaging techniques allowed us to derive the magnetic field geometry of the star and the surface abundance distributions of Mg, Si, Ca, Ti, Cr, Fe, Ni, Y, and Cu. Results. We find a dominant dipolar structure of the surface magnetic field. The CoRoT light curve variations and abundances of most elements mapped are correlated with the aforementioned geometry: Cr, Fe, and Si are enhanced around the magnetic poles and coincide with the bright regions on the surface of HD 50773 as predicted by our light curve synthesis and confirmed by photometric imaging.

We apply a robust spot model to fit the light curve of CoRoT-2a. The spots are assumed to be long-living and each has its own rotation period. A model with three circular spots reproduces the basic features of the longitude-time spot coverage map. One of the spots exhibits a noticeably lower rotational frequency than the other two. From the rotational frequencies of the three dark features we infer a differential rotation of above 0.11 rad/d, in rough agreement with theoretical models. Mean field models of angular momentum transport by convection and meridional flow lead to an equatorial rotational frequency that exceeds that of the poles by 0.09 rad/d. The spot decay corresponds to a turbulent magnetic diffusivity of (1.2 ± 0.1) × 10 13 cm 2 /s.