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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 $49 pm 10$ Mm, temperatures of $5100 pm 300$ K, and surface area coverage of $6 pm 4$ %. The rotation period at the transit latitude, $-5^circ$, occulted by the planet was found to be $11.92 pm 0.05$ d, slightly smaller than the out--of--transit average period of $12.4 pm 0.1$ d. Adopting a solar like differential rotation, we estimated the differential rotation of Kepler-17 to be $DeltaOmega = 0.041 pm 0.005$ rd/d, which is close to the solar value of 0.050 rd/d, and a relative differential rotation of $DeltaOmega/Omega=8.0 pm 0.9$ %. 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.
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The study of young Sun-like stars is of fundamental importance to understand the magnetic activity and rotational evolution of the Sun. Space-borne photometry by the Kepler telescope provides unprecedented datasets to investigate these phenomena in Sun-like stars. We present a new analysis of the entire Kepler photometric time series of the moderately young Sun-like star Kepler-17 that is accompanied by a transiting hot Jupiter. We applied a maximum-entropy spot model to the long-cadence out-of-transit photometry of the target to derive maps of the starspot filling factor versus the longitude and the time. These maps are compared to the spots occulted during transits to validate our reconstruction and derive information on the latitudes of the starspots. We find two main active longitudes on the photosphere of Kepler-17, one of which has a lifetime of at least $sim 1400$ days, although with a varying level of activity. The latitudinal differential rotation is of solar type, that is, with the equator rotating faster than the poles. We estimate a minimum relative amplitude $Delta Omega/ Omega$ between $sim 0.08 pm 0.05$ and $0.14 pm 0.05$, our determination being affected by the finite lifetime of individual starspots and depending on the adopted spot model parameters. We find marginal evidence of a short-term intermittent activity cycle of $sim 48$ days and an indication of a longer cycle of $400-600$ days characterized by an equatorward migration of the mean latitude of the spots as in the Sun. The rotation of Kepler-17 is likely to be significantly affected by the tides raised by its massive close-by planet. We confirm the reliability of maximum-entropy spot models to map starspots in young active stars and characterize the activity and differential rotation of this young Sun-like planetary host.
Kepler-30 is a unique target to study stellar activity and rotation in a young solar-like star accompanied by a compact planetary system. We use about 4 years of high-precision photometry collected by the Kepler mission to investigate the fluctuations caused by photospheric convection, stellar rotation, and starspot evolution as a function of the timescale. Our main goal is to apply methods for the analysis of timeseries to find the timescales of the phenomena that affect the light variations. We correlate those timescales with periodicities in the star as well as in the planetary system. We model the flux rotational modulation induced by active regions using spot modelling and apply the MFDMA in standard and multisca
The stellar magnetic field plays a crucial role in the star internal mechanisms, as in the interactions with its environment. The study of starspots provides information about the stellar magnetic field, and can characterise the cycle. Moreover, the analysis of solar-type stars is also useful to shed light onto the origin of the solar magnetic field. The objective of this work is to characterise the magnetic activity of stars. Here, we studied two solar-type stars Kepler-17 and Kepler-63 using two methods to estimate the magnetic cycle length. The first one characterises the spots (radius, intensity, and location) by fitting the small variations in the light curve of a star caused by the occultation of a spot during a planetary transit. This approach yields the number of spots present in the stellar surface and the flux deficit subtracted from the star by their presence during each transit. The second method estimates the activity from the excess in the residuals of the transit lightcurves. This excess is obtained by subtracting a spotless model transit from the lightcurve, and then integrating all the residuals during the transit. The presence of long term periodicity is estimated in both time series. With the first method, we obtained $P_{rm cycle}$ = 1.12 $pm$ 0.16 yr (Kepler-17) and $P_{rm cycle}$ = 1.27 $pm$ 0.16 yr (Kepler-63), and for the second approach the values are 1.35 $pm$ 0.27 yr and 1.27 $pm$ 0.12 yr, respectively. The results of both methods agree with each other and confirm their robustness.
A major obstacle to interpreting the rotation period distribution for main-sequence stars from Kepler mission data has been the lack of precise evolutionary status for these objects. We address this by investigating the evolutionary status based on Gaia Data Release 2 parallaxes and photometry for more than 30,000 Kepler stars with rotation period measurements. Many of these are subgiants, and should be excluded in future work on dwarfs. We particularly investigate a 193-star sample of solar analogs, and report newly-determined rotation periods for 125 of these. These include 54 stars from a prior sample, of which can confirm the periods for 50. The remainder are new, and 10 of them longer than solar rotation period, suggesting that sun-like stars continue to spin down on the main sequence past solar age. Our sample of solar analogs could potentially serve as a benchmark for future missions such as PLATO, and emphasizes the need for additional astrometric, photometric, and spectroscopic information before interpreting the stellar populations and results from time-series surveys.
An exoplanet transiting in front of the disk of its parent star may hide a dark starspot causing a detectable change in the light curve, that allows to infer physical characteristics of the spot such as size and intensity. We have analysed the Kepler Space Telescope observations of the star Kepler-71 in order to search for variabilities in 28 transit light curves. Kepler-71 is a star with 0.923Ms and 0.816Rs orbited by the hot Jupiter planet Kepler-71b with radius of 1.0452RJ. The physical parameters of the starspots are determined by fitting the data with a model that simulates planetary transits and enables the inclusion of spots on the stellar surface with different sizes, intensities, and positions. The results show that Kepler-71 is a very active star, with several spot detections, with a mean value of 6 spots per transit with size 0.6Rp and 0.5 Ic, as a function of stellar intensity at disk center (maximum value).
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