Rotating Stars from Kepler Observed with Gaia DR2

We have matched the astrometric data from Gaia Data Release 2 to the sample of stars with measured rotation periods from Kepler. Using 30,305 stars with good distance estimates, we select 16,248 as being likely main sequence single stars centered within a 0.5 mag region about a 1 Gyr isochrone, removing many sub-giants and unresolved binary stars from the sample. The rotation period bimodality, originally discovered by McQuillan et al. (2013), is clearly recovered for stars out to 525pc, but is not detectable at further distances. This bimodality correlates with Galactic height as well, dropping strongly for stars above Z>90 pc. We also find a significant width in the stellar main sequence of $\Delta M_G$ ~0.25 mag, as well as a coherent gradient of increasing rotation periods orthogonal to the main sequence. We interpret this as a signature of stellar angular momentum loss over time, implying a corresponding diagonal age gradient across the main sequence. Stellar evolution models predict changes in color and luminosity that are consistent in amplitude, but not in direction, with those required to produce the gradient we have detected. This rotation gradient suggests that main sequence evolution produces offsets in color-magnitude space that are significantly more orthogonal to the zero-age main sequence than models currently predict, and may provide new tests for both stellar evolution and gyrochronology models.