New insights into the rotational evolution of near-solar age stars from the open cluster M 67

Context. Gyrochronology allows the derivation of ages for cool main sequence stars from their observed rotation periods and masses, or a suitable proxy of the latter. It is increasingly well explored for FGK stars, but requires further measurements for older ages and K-M-type stars.Aims. Recent work has shown that the behavior of stellar spindown differs significantly from prior expectations for late-type stars. We study the 4 Gyr-old benchmark open cluster M 67 to explore this behavior further.Methods. We combined a Gaia DR3 sample with the Kepler K2 superstamp of Campaign 5 around M 67 and created new light curves from aperture photometry. The light curves are subjected to an extensive correction process to remove instrumental systematics and trending, followed by period analysis to measure stellar rotation.Results. We identify periodic signals in 136 light curves, 47 of which are from the rotation of effectively single main-sequence stars that span from early-G to mid-M type. These results connect well to prior work on M 67 and extend it to much later spectral types.Conclusions. We find that the rotation periods of single stars of age 4 Gyr define a tight relationship with color, ranging from spectral types F through M. The corresponding surface of rotation period against age and mass is therefore well-defined to an older age than was previously known. However, the deviations from prior expectations of the stellar spindown behavior are even more pronounced at 4 Gyr. The binary cluster members do not follow the single star relationship. The majority are widely scattered below the single star sequence. Consequently, they do not seem to be suitable for gyrochronology at present.