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.

The granulation pattern that we observe on the surface of the Sun is due to hot plasma from the interior rising to the photosphere where it cools down, and descends back into the interior at the edges of granules. This is the visible manifestation of convection taking place in the outer part of the solar convection zone. Because red giants have deeper convection zones and more extended atmospheres than the Sun, we cannot a priori assume that granulation in red giants is a scaled version of solar granulation. Until now, neither observations nor 1D analytical convection models could put constraints on granulation in red giants.However, thanks to asteroseismology, this study can now be performed. The resulting parameters yield physical information about the granulation. We analyze ∼ 1000 red giants that have been observed by Kepler during 13 months. We fit the power spectra with Harvey-like profiles to retrieve the characteristics of the granulation (time scale τ gran and power P gran ). We also introduce a new time scale, τ eff , which takes into account that different slopes are used in the Harvey functions. We search for a correlation between these parameters and the global acoustic-mode parameter (the position of maximum power, ν max ) as well as with stellar parameters (mass, radius, surface gravity (log g) and effective temperature (T eff )). We show that τ eff ∝ ν −0.89 max and P gran ∝ ν −1.90 max , which is consistent with the theoretical predictions. We find that the granulation time scales of stars that belong to the red clump have similar values while the time scales of stars in the red-giant branch are spread in a wider range. Finally, we show that realistic 3D simulations of the surface convection in stars, spanning the (T eff , log g)-range of our sample of red giants, match the Kepler observations well in terms of trends.

Measurements of 500 Sun-like stars show that their properties differ from those predicted by stellar population models.