On the Evolution of Rotational Modulation Amplitude in Solar-mass Main-sequence Stars

We investigate the relation between rotation periods P-rot and photometric modulation amplitudes R-per for approximate to 4000 Sun-like main-sequence stars observed by Kepler, using P-rot and R-per from McQuillan et al., effective temperature T-eff from LAMOST DR6, and parallax data from Gaia EDR3. As has been suggested in previous works, we find that P-rot scaled by the convective turnover time tau(c), or the Rossby number Ro, serves as a good predictor of R-per: R-per plateaus at around 1% in relative flux for 0.2 less than or similar to Ro/Ro(circle dot) less than or similar to 0.4, and decays steeply with increasing Ro for 0.4 less than or similar to Ro/Ro(circle dot) less than or similar to 0.8, where Ro(circle dot) denotes Ro of the Sun. In the latter regime we find d ln R-per/d ln Ro similar to 4.5 to -2.5, although the value is sensitive to detection bias against weak modulation and may depend on other parameters including T(eff )and surface metallicity. The existing X-ray and Ca II H and K flux data also show transitions at Ro/Ro(circle dot) - 0.4, suggesting that all these transitions share the same physical origin. We also find that the rapid decrease of R-per with increasing Ro causes rotational modulation of fainter Kepler stars with Ro/Ro(circle dot) greater than or similar to 0.6 to be buried under the photometric noise. This effect sets the longest P rot detected in the McQuillan et al. sample as a function of T-eff and obscures the signature of stalled spin down that has been proposed to set in around Ro/Ro(circle dot) similar to 1.