Context. Stellar differential rotation is important for understanding hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors, as well as for a better treatment of tides in close binary and star-planet systems. Aims. We introduce a method of measuring a lower limit to the amplitude of surface differential rotation from high-precision, evenly sampled photometric time series, such as those obtained by space-borne telescopes. It is designed to be applied to main-sequence late-type stars whose optical flux modulation is dominated by starspots.Methods. An autocorrelation of the time series was used to select stars that allow an accurate determination of starspot rotation periods. A simple two-spot model was applied together with a Bayesian information criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty were obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov chain approach. We applied our method to the Sun and eight other stars for which previous spot modelling had been performed to compare our results with previous ones. Results. We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite for successfully measuring differential rotation through spot modelling. For a proper Monte Carlo Markov chain analysis, it is necessary to take the strong correlations among different parameters that exist in spot modelling into account. For the planet-hosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation of ΔP/P = 0.0523± 0.0016. We confirm that the Sun as a star in the optical passband is not suitable for measuring differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison to more sophisticated and time-consuming approaches.

The high quality light curves from the Transiting Exoplanet Survey Satellite (TESS) represent a unique laboratory for the study of stellar rotation, a fundamental observable driving stellar and planetary evolution, including planetary atmospheres and impacting on habitability conditions and the genesis of life around stars. As of April 14th 2020, this mission delivered public light curves for 1000 TESS Objects of Interest (TOIs), observed with 2 minute cadence during the first 20 months of the mission. Here, we present a search for rotation signatures in these TOIs, using Fast Fourier Transform, Lomb-Scargle, and wavelet techniques, accompanied by a rigorous visual inspection.

Context. Signatures of chromospheric activity enhancement have been found for a dozen stars, pointing to a possible star-planet interaction. Nevertheless in the coronal activity regime, there is no conclusive observational evidence of such an interaction. Does star-planet interaction manifest itself only for a few particular cases, without having a major effect on stars with planets in general? Aims. We aim to add additional observational constraints to support or reject the major effects of star-planet interactions in stellar activity, based on Ca II chromospheric emission flux. Methods. We performed a statistical analysis of Ca II emission flux of stars with planets, as well as a comparison between Ca II and X-ray emission fluxes, searching for dependencies on planetary parameters. Results. In the present sample of stars with planets, there are no significant correlations between chromospheric activity indicator log(R HK ) and planetary parameters. Furthermore, the distribution of the chromospheric activity indicator for stars without planets is indistinguishable from the one with planets.

In the present study, we investigate the multifractal nature of a long-cadence time series observed by the Kepler mission for a sample of 34 M dwarf stars and the Sun in its active phase. Using the Multifractal Detrending Moving Average algorithm (MFDMA), which enables the detection of multifractality in nonstationary time series, we define a set of multifractal indices based on the multifractal spectrum profile as a measure of the level of stellar magnetic activity. This set of indices is given by the (A,∆α,C,H)-quartet, where A, ∆α and C are related to geometric features from the multifractal spectrum and the global Hurst exponent H describes the global structure and memorability of time series dynamics. As a test, we measure these indices and compare them with a magnetic index defined as S ph and verify the degree of correlation among them. First, we apply the Poincaré plot method and find a strong correlation between the S ph index and one of the descriptors that emerges from this method. As a result, we find that this index is strongly correlated with long-term features of the signal. From the multifractal perspective, the S ph index is also strongly linked to the geometric properties of the multifractal spectrum except for the H index. Furthermore, our results emphasize that the rotation period of stars is scaled by the H index, which is consistent with Skumanich's relationship. Finally, our approach suggests that the H index may be related to the evolution of stellar angular momentum and a star's magnetic properties.

Rapidly rotating giant stars are relatively rare and may represent important stages of stellar evolution, resulting from stellar coalescence of close binary systems or accretion of sub-stellar companions by their hosting stars. In the present letter we report 17 giant stars observed in the scope of the Kepler space mission exhibiting rapid rotation behavior. For the first time the abnormal rotational behavior for this puzzling family of stars is revealed by direct measurements of rotation, namely from photometric rotation period, exhibiting very short rotation period with values ranging from 13 to 55 days. This finding points for remarkable surface rotation rates, up to 18 times the Sun rotation. These giants are combined with 6 other recently listed in the literature for mid-IR diagnostic based on WISE information, from which a trend for an infrared excess is revealed for at least a half of the stars, but at a level far lower than the dust excess emission shown by planet-bearing main-sequence stars.

The present study reports the discovery of Sun-like stars, namely mainsequence stars with T eff , log g and rotation periods P rot similar to solar values, presenting evidence of surface differential rotation. An autocorrelation of the time series was used to select stars presenting photometric signal stability from a sample of 881 stars with light curves collected by the Kepler space-borne telescope, in which we have identified 17 stars with stable signals. A simple two-spot model together with a Bayesian information criterion were applied to these stars in the search for indications of differential rotation; in addition, for all 17 stars, it was possible to compute the spot rotation period P , the mean values of the individual spot rotation periods and their respective colatitudes, and the relative amplitude of the differential rotation.

In the present study, high-precision time series photometry for the active Kepler stars is described in the language of multifractals. We explore the potential of using the rescaled range analysis (R/S) and multifractal detrended moving average analysis (MFDMA) methods to characterize the multiscale structure of the observed time series from a sample of ∼40 000 active stars. Among these stars, 6486 have surface differential rotation measurement, whereas 1846 have no signature of differential rotation. As a result, the Hurst exponent (H) derived from both methods shows a strong correlation with the period derived from rotational modulation. In addition, the variability range R var reveals how this correlation follows a high activity "line". We also verify that the H-index is an able parameter for distinguishing the different signs of stellar rotation that can exist between the stars with and without differential rotation. In summary, the results indicate that the Hurst exponent is a promising index for estimating photometric magnetic activity.

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