Impact of Spectral Resolution on S-index and Its Application to Spectroscopic Surveys

Utilizing the PHOENIX synthetic spectra, we investigated the impact of spectral resolution on the calculation of $S$-indices. We found that for spectra with a resolution lower than $\approx$30,000, it is crucial to calibrate $S$-indices for accurate estimations. This is especially essential for low-resolution spectral observations. We provided calibrations for several ongoing or upcoming spectroscopic surveys such as the LAMOST low-resolution survey, the SEGUE survey, the SDSS-V/BOSS survey, the DESI survey, the MSE survey, and the MUST survey. Using common targets between the HARPS and MWO observations, we established conversions from spectral $S$-indices to the well-known $S_{\rm MWO}$ values, applicable to stars with [Fe/H] values greater than $-$1. These calibrations offer a reliable approach to convert $S$-indices obtained from various spectroscopic surveys into $S_{\rm{MWO}}$ values and can be widely applied in studies on chromospheric activity.