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

We investigate the relation between rotation periods $P_\mathrm{rot}$ and photometric modulation amplitudes $R_\mathrm{per}$ for $\approx 4,000$ Sun-like main-sequence stars observed by Kepler, using from McQuillan et al. (2014), effective temperature $T_\mathrm{eff}$ LAMOST DR6, parallax data Gaia EDR3. As has been suggested in previous works, we find that scaled convective turnover time $\tau_\mathrm{c}$, or Rossby number $\mathrm{Ro}=P_\mathrm{rot}/\tau_\mathrm{c}$, serves as a good predictor of $R_\mathrm{per}$: plateaus around $1\%$ relative flux $0.2 \lesssim \mathrm{Ro}/\mathrm{Ro}_\odot 0.4$, decays steeply with increasing $\mathrm{Ro}$ $0.4 0.8$, where $\mathrm{Ro}_\odot$ denotes Sun. In latter regime $\mathrm{d}\ln R_\mathrm{per}/\mathrm{d}\ln\mathrm{Ro} \sim -4.5$ to $-2.5$, although value is sensitive detection bias against weak may depend on other parameters including surface metallicity. The existing X-ray Ca II H&K also show transitions at $\mathrm{Ro}/\mathrm{Ro}_\odot\sim suggesting all these share same physical origin. rapid decrease causes rotational fainter Kepler $\mathrm{Ro}/\mathrm{Ro}_\odot \gtrsim 0.6$ be buried under noise. This effect sets longest detected (2014) sample function $T_\mathrm{eff}$, obscures signature stalled spin down proposed set 1$.