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

Abstract

Abstract We investigate the relation between rotation periods P rot and photometric modulation amplitudes R per for ≈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 τ 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 ≲ Ro/Ro⊙ ≲ 0.4, and decays steeply with increasing Ro for 0.4 ≲ Ro/Ro⊙ ≲ 0.8, where Ro⊙ denotes Ro of the Sun. In the latter regime we find d ln R per / d ln Ro ∼ −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⊙ ∼ 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⊙ ≳ 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⊙ ∼ 1.