Rotation Periods of Wide Binaries in the Kepler Field

In a search of proper motion catalogs for common proper motion stars in the field of the Kepler spacecraft I identified 93 likely binary systems. A comparison of their rotation periods is a test of the gyrochronology concept. To find their periods I calculated the autocorrelation function of the Kepler mission photometry for each star. In most systems for which good periods can be found, the cooler star has a longer period than the hotter component in general agreement with models. However, there is a wide range in the gradients of lines connecting binary pairs in a period-color diagram. Furthermore, near the solar color, only a few stars have longer periods than the Sun, suggesting that they, and their cooler companions are not much older than the Sun. In addition, there is an apparent gap at intermediate periods in the period distribution of the late K and early M stars. Either star formation in this direction has been variable, or stars evolve in period at a non-uniform rate, or some stars evolve more rapidly than others at the same mass. Finally, using the autocorrelation function as a measure of the activity level, I found that while the F, G and early K stars become less active as their periods increase, there is no correlation between period and activity for the mid K to early M stars.