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

Abstract

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

24 pages, 20 figures, accepted for publication in ApJ