Stellar Chromospheric Activity Database of Solar-like Stars Based on the LAMOST Low-Resolution Spectroscopic Survey III. Calibrating the Chromospheric Basal Flux and the Connection to Stellar Rotation

Abstract

Based on the Ca\,II H and K lines observed by LAMOST, we employ the photospheric ($R'_{\rm HK}$) and basal ($R^+_{\rm HK,L}$) flux calibrated chromospheric activity indices to examine the relationship between chromospheric activity and the stellar rotation rate. We identify the rotation periods of 11,108 stars observed by Kepler and TESS by cross-matching our chromospheric activity catalog with previous studies. Our statistical results show that chromospheric activity increases with the rotation rate until it reaches a saturation level. As the stellar effective temperature increases from 4950 to 5850 K, the saturation values of the rotation period ($P_{\rm rot}$) vary correspondingly from 4.38 to 1.23 days for $R'_{\rm HK}$ and from 9.88 to 1.33 days for $R^+_{\rm HK,L}$. Similarly, the corresponding saturation Rossby number Ro ranges from 0.200 to 0.032 for $R'_{\rm HK}$ and from 0.302 to 0.107 for $R^+_{\rm HK,L}$. The saturation is also found to be significant in stars with thick convective zones, whereas it is less apparent in stars with higher effective temperatures. For solar-like stars in the $T_{\rm eff}$ range of 4800 to 6000 K, The values of chromospheric activity indicators are saturated when $P_{\rm rot}<1.45 $ days (Ro$<$0.100) and $P_{\rm rot}<2.85 $ days (Ro$<$0.097) for $R'_{\rm HK}$ and $R^+_{\rm HK,L}$, respectively.

Figures (2)

• Figure 1: Distribution of $\log\,\sigma S_L$ and $\log\,(\sigma S_L/S_L)$ versus the observation number. The top panel presents the histogram of observation counts, while the right panels display the corresponding distributions of $\log\,\sigma S_L$ (top right) and $\log\,(\sigma S_L/S_L)$ (bottom right).
• Figure 2: Distribution of $\log R'_{\rm HK}$ versus $T_{\rm eff}$ for different [Fe/H] ranges. The color bar indicates the number density. The red solid line represents the results of Equation \ref{['eq:R_phot_basal_vs_teff-feh']} using the median [Fe/H] value for each metallicity range, while the red dotted line corresponds to the solar metallicity case ([Fe/H] = 0) for comparison.