Journal.Submited to Astronomy & Astrophysics
Abstract.Kepler ultra-high precision photometry of long and continuous observations provide 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. These relations generally lack good calibrators at old ages, a problem that this Kepler sample of stars is uniquely suited to address. We study the surface rotation and the photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured. The rotation period is determined by comparing the results from two different sets of calibrated data and from two complementary analyses. Global photometric levels of magnetic activity in this sample of stars are also extracted by using a photometric activity index, which takes into account the rotation period of the stars. Out of the 540 solar-like pulsating stars in our sample, we successfully measured the rotation period of 310 stars (excluding known binaries and candidate planet host stars). The rotation periods lay between 1 and 100 days. The remaining stars are classified into two categories: those not showing any surface rotation (6 stars), and those in which the four analyses did not converge to a single and robust rotation period (213). The photometric magnetic activity levels were computed and for 61.5% of the dwarfs, its value is comparable to the solar one. We then extract an age-rotation relation only for the dwarfs with very precise asteroseismic age estimations, highlighting the necessity of excluding the hot stars and the subgiants when inferring such relations. We also studied age-activity-rotation relations with a hint of correlation for the subgiants.