The breakdown of current gyrochronology as evidenced by old coeval stars

Gyrochronology can yield useful ages for field main-sequence stars, a regime where other techniques are problematic. Typically, gyrochronology relations are calibrated using young ($\lesssim$ 2 Gyr) clusters, but the constraints at older ages are scarce, making them potentially inaccurate and imprecise. In order to test the performance of current gyrochronology relations, we construct samples of stellar pairs with coeval components, for a range of ages and with available rotation periods. These include both randomly paired stars in clusters, and wide binaries in the Kepler field. We design a parameter, $\Delta P_{rot, gyro}$, that quantifies the level of agreement between the components of coeval stellar pairs and the gyrochronology calibrations under scrutiny. Our results show that wide binaries and cluster members are in better concordance with gyrochronology than samples of randomly paired field stars (which we use as a control group), confirming that the relations do have predicting power in identifying coeval stars. However, the agreement with the examined relations decreases for older stars, suggesting a degradation of the current gyrochronology with age, in agreement with recent literature results. We argue for the need of novel gyrochronology constraints at older ages that may allow revised calibrations. Ultimately, using coeval stars to test gyrochronology poses the advantage of circumventing the need for age determinations while simultaneously exploiting larger samples at older ages. In addition, taking gyrochronology at face value, we note that our results provide new empirical evidence that the components of field wide binaries are indeed coeval.