  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. Recent work has shown that the
behavior of stellar spindown differs significantly from prior expectations for
late-type stars. We study the 4Gyr-old benchmark open cluster M67 to explore
this behavior further. We combined a Gaia DR3 sample with the Kepler K2
superstamp of Campaign 5 around M67 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. 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
M67 and extend it to much later spectral types. We find that the rotation
periods of single stars of age 4Gyr 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 4Gyr. 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.

Solar and Stellar Astrophysics;Astrophysics of Galaxies