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. To date, the CoRoT space mission has produced more than 124 471 light curves. Classifying these curves in terms of unambiguous variability behavior is mandatory for obtaining an unbiased statistical view on their controlling root-causes. Aims. The present study provides an overview of semi-sinusoidal light curves observed by the CoRoT exo-field CCDs. Methods. We selected a sample of 4206 light curves presenting well-defined semi-sinusoidal signatures. The variability periods were computed based on Lomb-Scargle periodograms, harmonic fits, and visual inspection. Results. Color-period diagrams for the present sample show the trend of an increase of the variability periods as long as the stars evolve. This evolutionary behavior is also noticed when comparing the period distribution in the Galactic center and anti-center directions. These aspects indicate a compatibility with stellar rotation, although more information is needed to confirm their rootcauses. Considering this possibility, we identified a subset of three Sun-like candidates by their photometric period. Finally, the variability period versus color diagram behavior was found to be highly dependent on the reddening correction.

Magnetic activity on stars manifests itself in the form of dark spots on the stellar surface, that cause modulation of a few percent in the light curve of the star as it rotates. When a planet eclipses its host star, it might cross in front of one of these spots creating a "bump" in the transit light curve. By modelling these spot signatures, it is possible to determine the physical properties of the spots such as size, temperature, and location. In turn, the monitoring of the spots longitude provides estimates of the stellar rotation and differential rotation. This technique was applied to the star Kepler-17, a solar-type star orbited by a hot Jupiter. The model yields the following spot characteristics: average radius of 49 ± 10 Mm, temperatures of 5100 ± 300 K, and surface area coverage of 6 ± 4 %. The rotation period at the transit latitude, −5• , occulted by the planet was found to be 11.92 ± 0.05 d, slightly smaller than the out-of-transit average period of 12.4 ± 0.1 d. Adopting a solar like differential rotation, we estimated the differential rotation of Kepler-17 to be ∆Ω = 0.041 ± 0.005 rd/d, which is close to the solar value of 0.050 rd/d, and a relative differential rotation of ∆Ω/Ω = 8.0 ± 0.9 %. Since Kepler-17 is much more active than our Sun, it appears that for this star larger rotation rate is more effective in the generation of magnetic fields than shear.

Aims. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. Methods. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Results. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern signature in the local wavelet map of pulsating stars over the entire time span was also detected.

We analyzed the host stars of the present sample of confirmed planets detected by Kepler and Kepler Objects of Interest (KOI) to compute new photometric rotation periods and to study the behavior of their angular momentum. Lomb-Scargle periodograms and wavelet maps were computed for 3, 807 stars. For 540 of these stars, we were able to detect rotational modulation of the light curves at a significance level of greater than 99%. For 63 of these 540 stars, no rotation measurements were previously available in the literature. According to the published masses and evolutionary tracks of the stars in this sample, the sample is composed of M-to F-type stars (with masses of 0.48-1.53 M ⊙ ) with rotation periods that span a range of 2 to 89 days. These periods exhibit an excellent agreement with previously reported (for the stars for which such values are available), and the observed rotational period distribution strongly agrees with theoretical predictions. Furthermore, for the 540 sources considered here, the stellar angular momentum provides an important test of Kraft's relation based on the photometric rotation periods. Finally, this study directly contributes in a direct approach to our understanding of how angular momentum is distributed between the host star and its (detected) planetary system; the role of angular momentum exchange in such systems is an unavoidable piece of the stellar rotation puzzle.