Further Evidence of Modified Spin-down in Sun-like Stars: Pileups in the Temperature-Period Distribution

We combine stellar surface rotation periods determined from NASA's Kepler mission with spectroscopic temperatures to demonstrate the existence of pileups at the long-period and short-period edges of the temperature-period distribution for main-sequence stars with temperatures exceeding $\sim 5500$K. The long-period pileup is well-described by a curve of constant Rossby number, with a critical value of $\mathrm{Ro_{crit}} \lesssim 2$. The long-period pileup was predicted by van Saders et al. (2019) as a consequence of weakened magnetic braking, in which wind-driven angular momentum losses cease once stars reach a critical Rossby number. Stars in the long-period pileup are found to have a wide range of ages ($\sim 2-6$Gyr), meaning that, along the pileup, rotation period is strongly predictive of a star's surface temperature but weakly predictive of its age. The short-period pileup, which is also well-described by a curve of constant Rossby number, is not a prediction of the weakened magnetic braking hypothesis but may instead be related to a phase of slowed surface spin-down due to core-envelope coupling. The same mechanism was proposed by Curtis et al. (2020) to explain the overlapping rotation sequences of low-mass members of differently aged open clusters. The relative dearth of stars with intermediate rotation periods between the short- and long-period pileups is also well-described by a curve of constant Rossby number, which aligns with the period gap initially discovered by McQuillan et al. (2013a) in M-type stars. These observations provide further support for the hypothesis that the period gap is due to stellar astrophysics, rather than a non-uniform star-formation history in the Kepler field.