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Kepler ultra-high precision photometry of long and continuous observations provides a unique dataset in which surface rotation and variability can be studied for thousands of stars. Because many of these old field stars also have independently measured asteroseismic ages, measurements of rotation and activity are particularly interesting in the context of age-rotation-activity relations. In particular, age-rotation relations generally lack good calibrators at old ages, a problem that this Kepler sample of old-field stars is uniquely suited to address. We study the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the mainsequence and the subgiant branch for which stellar pulsations have been measured. The rotation period was determined by comparing the results from two different analysis methods: i) the projection onto the frequency domain of the time-period analysis, and ii) the autocorrelation function of the light curves. Reliable surface rotation rates were then extracted by comparing the results from two different sets of calibrated data and from the two complementary analyses. General photometric levels of magnetic activity in this sample of stars were also extracted by using a photometric activity index, which takes into account the rotation period of the stars. We report rotation periods for 310 out of 540 targets (excluding known binaries and candidate planet-host stars); our measurements span a range of 1 to 100 days. The photometric magnetic activity levels of these stars were computed, and for 61.5% of the dwarfs, this level is similar to the range, from minimum to maximum, of the solar magnetic activity. We demonstrate that hot dwarfs, cool dwarfs, and subgiants have very different rotation-age relationships, highlighting the importance of separating out distinct populations when interpreting stellar rotation periods. Our sample of cool dwarf stars with age and metallicity data of the highest quality is consistent with gyrochronology relations reported in the literature.

Aims. We aim to measure the starspot rotation periods of active stars in the Kepler field as a function of spectral type and to extend reliable rotation measurements from F-, G-, and K-type to M-type stars. Methods. Using the Lomb-Scargle periodogram we searched more than 150 000 stellar light curves for periodic brightness variations. We analyzed periods between 1 and 30 days in eight consecutive Kepler quarters, where 30 days is an estimated maximum for the validity of the PDC_MAP data correction pipeline. We selected stable rotation periods, i.e., periods that do not vary from the median by more than one day in at least six of the eight quarters. We averaged the periods for each stellar spectral class according to B-V color and compared the results to archival v sin i data, using stellar radii estimates from the Kepler Input Catalog. Results. We report on the stable starspot rotation periods of 12 151 Kepler stars. We find good agreement between starspot velocities and v sin i data for all F-, G-and early K-type stars. The 795 M-type stars in our sample have a median rotation period of 15.4 days. We find an excess of M-type stars with periods less than 7.5 days that are potentially fast-rotating and fully convective. Measuring photometric variability in multiple Kepler quarters appears to be a straightforward and reliable way to determine the rotation periods of a large sample of active stars, including late-type stars.

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 days 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-day 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, auto-correlation function, and waveletbased 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% of the true value in 70% 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-disk 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.active stars. The exquisite photometric quality and baseline of space-based telescopes such as Kepler, CoRoT and MOST have made it possible to do this for tens of thousands of moderately active field stars, many of which display sub-millimagnitude variations that would have been undetectable from the ground. The resulting, extensive rotation period catalogs represent an exciting opportunity to test and refine our understanding of stellar angular momentum evolution, and to develop efficient methods for estimating c 2014 RAS

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement using asteroseismology of latitudinal differential rotation in the convection zones of 40 Sun-like stars. For the most significant detections, the stars’ equators rotate approximately twice as fast as their midlatitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.

Context. The measurement of obliquities -the angle between the orbital and stellar rotation -in star-planet systems is of great importance for understanding planet system formation and evolution. The bright and well-studied HAT-P-7 (Kepler-2) system is intriguing because several Rossiter-McLaughlin (RM) measurements found a high projected obliquity in this system, but it was not possible so far to determine whether the orbit is polar and/or retrograde. Aims. The goal of this study is to measure the stellar inclination and hereby the full 3D obliquity of the HAT-P-7 system instead of only the 2D projection as measured by the RM effect. In addition, we provide an updated set of stellar parameters for the star. Methods. We used the full set of available observations from Kepler spanning Q0-Q17 to produce the power spectrum of HAT-P-7. We extracted oscillation-mode frequencies via an Markov chain Monte Carlo peak-bagging routine and used the results from this to estimate the stellar inclination angle. Combining this with the projected obliquity from RM and the inclination of the orbital plane allowed us to determine the stellar obliquity. Furthermore, we used asteroseismology to model the star from the extracted frequencies using two different approaches to the modelling, for which either the stellar evolution codes MESA or GARSTEC were adopted. Results. Our updated asteroseismic modelling shows, i.a., the following stellar parameters for HAT-P-7: M = 1.51+0.01 −0.02 R , and age = 2.07 +0.28 −0.23 Gyr. The modelling offers a high precision on the stellar parameters, the uncertainty on age, for instance, is of the order ∼11%. For the stellar inclination we estimate i < 36.5• , which translates into an obliquity of 83 • < ψ < 111• . The planet HAT-P-7b is likely retrograde in its orbit, and the orbit is close to being polar. The new parameters for the star give an updated planetary density of ρ p = 0.65 ± 0.03 g cm −3 , which is lower than previous estimates.

The most powerful tests of stellar models come from the brightest stars in the sky, for which complementary techniques, such as astrometry, asteroseismology, spectroscopy, and interferometry can be combined. The K2 Mission is providing a unique opportunity to obtain high-precision photometric time series for bright stars along the ecliptic. However, bright targets require a large number of pixels to capture the entirety of the stellar flux, and bandwidth restrictions limit the number and brightness of stars that can be observed. To overcome this, we have developed a new photometric technique, that we call halo photometry, to observe very bright stars using a limited number of pixels. Halo photometry is simple, fast and does not require extensive pixel allocation, and will allow us to use K2 and other photometric missions, such as TESS, to observe very bright stars for asteroseismology and to search for transiting exoplanets. We apply this method to the seven brightest stars in the Pleiades open cluster. Each star exhibits variability; six of the stars show what are most-likely slowly pulsating Bstar (SPB) pulsations, with amplitudes ranging from 20 to 2000 ppm. For the star Maia, we demonstrate the utility of combining K2 photometry with spectroscopy and interferometry to show that it is not a 'Maia variable', and to establish that its variability is caused by rotational modulation of a large chemical spot on a 10 d time scale.

We present ultraviolet, optical and infrared photometry and optical spectroscopy of the type Ic superluminous supernova (SLSN) Gaia16apd (= SN 2016eay), covering its evolution from 26 d before the g-band peak to 234.1 d after the peak. Gaia16apd was followed as a part of the NOT Unbiased Transient Survey (NUTS). It is one of the closest SLSNe known (z = 0.102 ± 0.001), with detailed optical and ultraviolet (UV) observations covering the peak. Gaia16apd is a spectroscopically typical type Ic SLSN, exhibiting the characteristic blue early spectra with O ii absorption, and reaches a peak M g = −21.8±0.1 mag. However, photometrically it exhibits an evolution intermediate between the fast-and slowly-declining type Ic SLSNe, with an early evolution closer to the fast-declining events. Together with LSQ12dlf, another SLSN with similar properties, it demonstrates a possible continuum between fast-and slowlydeclining events. It is unusually UV-bright even for a SLSN, reaching a non-K-corrected M uvm2 −23.3 mag, the only other type Ic SLSN with similar UV brightness being SN 2010gx. Assuming that Gaia16apd was powered by magnetar spin-down, we derive a period of P = 1.9 ± 0.2 ms and a magnetic field of B = 1.9 ± 0.2 × 10 14 G for the magnetar. The estimated ejecta mass is between 8 and 16 M and the kinetic energy between 1.3 and 2.5 × 10 52 erg, depending on opacity and assuming that the entire ejecta is swept up into a thin shell. Despite the early photometric differences, the spectra at late times are similar to slowly-declining type Ic SLSNe, implying that the two subclasses originate from similar progenitors.