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

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 ${\rm{d}}\,\mathrm{ln}\,{R}_{\mathrm{per}}/{\rm{d}}\,\mathrm{ln}\,\mathrm{Ro}$ ~ -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.