We analyzed 3 years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Our automated autocorrelation-based method detected rotation periods between 0.2 and 70 days for 34,030 ( 25.6 % ) of the 133,030 main-sequence Kepler targets ( excluding known eclipsing binaries and Kepler Objects of Interest ) , making this the largest sample of stellar rotation periods to date .
In this paper we consider the detailed features of the now well-populated period-temperature distribution and demonstrate that the period bimodality , first seen by McQuillan , Aigrain & Mazeh ( 2013 ) in the M-dwarf sample , persists to higher masses , becoming less visible above 0.6 M _ { \odot } .
We show that these results are globally consistent with the existing ground-based rotation-period data and find that the upper envelope of the period distribution is broadly consistent with a gyrochronological age of 4.5 Gyrs , based on the isochrones of Barnes ( 6 ) , ( 37 ) and ( 42 ) .
We also performed a detailed comparison of our results to those of ( 49 ) and ( 45 ) , who have measured rotation periods of field stars observed by Kepler .
We examined the amplitude of periodic variability for the stars with detected rotation periods , and found a typical range between \sim 950 ppm ( 5 ^ { th } percentile ) and \sim 22 , 700 ppm ( 95 ^ { th } percentile ) , with a median of \sim 5 , 600 ppm .
We found typically higher amplitudes for shorter periods and lower effective temperatures , with an excess of low-amplitude stars above \sim 5400 K .