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One of the most difficult properties to derive for stars is their age. For cool main-sequence stars, gyrochronology relations can be used to infer stellar ages from measured rotation periods and Hertzsprung Russell diagram positions. These relations have few calibrators with known ages for old, long rotation period stars. There is a significant sample of old Kepler objects of interest, or KOIs, which have both measurable surface rotation periods and precise asteroseismic measurements from which ages can be accurately derived. In this work, we determine the age and the rotation period of solar-like pulsating KOIs to both compare the rotation properties of stars with and without known planets and enlarge the gyrochronology calibration sample for old stars. We use Kepler photometric light curves to derive the stellar surface rotation periods while ages are obtained with asteroseismology using the Asteroseismic Modelling Portal in which individual mode frequencies are combined with high-resolution spectroscopic parameters. We thus determine surface rotation periods and ages for 11 planet-hosting stars, all over 2 Gyr old. We find that the planet-hosting stars exhibit a rotational behaviour that is consistent with the latest age-rotation models and similar to the rotational behaviour of stars without detected planets. We conclude that these old KOIs can be used to test and calibrate gyrochronology along with stars not known to host planets. [ABSTRACT FROM AUTHOR]

The rotation rates in the deep interior and at the surface of 22 main-sequence stars with masses between 1.0 and 1.6M are constrained by combining asteroseismological analysis with spectroscopic measurements. The asteroseismic data of each star are taken by the Kepler or CoRoT space mission. It is found that the difference between the surface rotation rate and the average rotation rate (excluding the convective core) of most of stars is small enough to suggest that an efficient process of angular momentum transport operates during and/or before the main-sequence stage of stars. If each of the surface convective zone and the underlying radiative zone, for individual stars, is assumed to rotate uniformly, the difference in the rotation rate between the two zones turns out to be no more than a factor of 2 in most of the stars independently of their ages. [ABSTRACT FROM AUTHOR]

We present the results of a blind exercise to test the recoverability of stellar rotation and differential rotation in Kepler light curves. The simulated light curves lasted 1000 d and included activity cycles, Sun-like butterfly patterns, differential rotation and spot evolution. The range of rotation periods, activity levels and spot lifetime were chosen to be representative of the Kepler data of solar-like stars. Of the 1000 simulated light curves, 770 were injected into actual quiescent Kepler light curves to simulate Kepler noise. The test also included five 1000-d segments of the Sun's total irradiance variations at different points in the Sun's activity cycle. Five teams took part in the blind exercise, plus two teams who participated after the content of the light curves had been released. The methods used included Lomb-Scargle periodograms and variants thereof, autocorrelation function and wavelet-based analyses, plus spot modelling to search for differential rotation. The results show that the 'overall' period is well recovered for stars exhibiting low and moderate activity levels. Most teams reported values within 10 per cent of the true value in 70 per cent of the cases. There was, however, little correlation between the reported and simulated values of the differential rotation shear, suggesting that differential rotation studies based on full-disc light curves alone need to be treated with caution, at least for solar-type stars. The simulated light curves and associated parameters are available online for the community to test their own methods. [ABSTRACT FROM AUTHOR]

The solar analogues 16 Cyg A and B are excellent asteroseismic targets in the Kepler field of view and together with a red dwarf and a Jovian planet form an interesting system. For these more evolved Sun-like stars we cannot detect surface rotation with the current Kepler data but instead use the technique of asteroseimology to determine rotational properties of both 16 Cyg A and B. We find the rotation periods to be 23.8-1.8+1.5 and 23.2-3.2+11.5d, and the angles of inclination to be 56-5+6° and 36-7+17°, for A and B, respectively. Together with these results we use the published mass and age to suggest that, under the assumption of a solar-like rotation profile, 16 Cyg A could be used when calibrating gyrochronology relations. In addition, we discuss the known 16 Cyg B star-planet eccentricity and measured low obliquity which is consistent with Kozai cycling and tidal theory. [ABSTRACT FROM AUTHOR]