Wide binaries demonstrate the consistency of rotational evolution between open cluster and field stars

Gyrochronology enables the derivation of ages of late-type main sequence stars based on their rotation periods and a mass proxy, such as color. It has been explored in open clusters, but a connection to field stars has yet to be successfully established. We explore the rotation rates of wide binaries, representing enlightening intermediaries between clusters and field stars, and their overlap with those of open cluster stars. We investigated a recently created catalog of wide binaries, matched the cataloged binaries to observations by the Kepler mission (and its K2 extension), validated or re-derived their rotation periods, identified 283 systems where both stars are on the main sequence and have vetted rotation periods, and compared the systems with open cluster data. We find that the vast majority of these wide binaries (236) line up directly along the curvilinear ribs defined by open clusters in color-period diagrams or along the equivalent interstitial gaps between successive open clusters. The parallelism in shape is remarkable. Twelve additional systems are clearly rotationally older. The deviant systems, a minority, are mostly demonstrably hierarchical. Furthermore, the position of the evolved component in the color-magnitude diagram for the additional wide binary systems that contain one is consistent with the main sequence component's rotational age. We conclude that wide binaries, despite their diversity, follow the same spindown relationship as observed in open clusters, and we find that rotation-based age estimates yield the same ages for both components in a wide binary. This suggests that cluster and field stars spin down in the same way and that gyrochronology can be applied to field stars to determine their ages, provided that they are sufficiently distant from any companions to be considered effectively single.