SIMBAD references

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.