Distribution of ﹩\mathrm{log}{R}_{{\rm{HK}}}^{{\prime} }﹩ versus T_eff for different [Fe/H] ranges. The color bar indicates the number density. The red solid line represents the results of Equation (11) 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.