Modeling Stellar Ca II H and K Emission Variations: Spot Contribution to the S-index

The S-index is a measure of emission in the Ca ii H and K lines and is a widely used proxy of stellar magnetic activity. It has been assumed until now that the S-index is mainly affected by bright plage regions in the chromosphere. In particular, the effect of starspots on the S-index has been neglected. In this study, we revisit this assumption. For this, we analyze high-resolution observations of sunspots recorded in the Ca ii H spectral line at the Swedish 1 m Solar Telescope and determine the contrast of spots with respect to the quiet surroundings. We find that the Ca ii H line core averaged over whole sunspots (including superpenumbrae) is brighter than in the quiet surroundings and that the spot contrast in the line core is comparable to the facular contrast. This allows us to get a first estimate of the influence of spots on the S-index. We show that spots increase the S-index. While this increase is quite small for the Sun, it becomes significantly larger for more active stars. Further, we show that the inclusion of the contribution of spots to the S-index strongly affects the relationship between the S-index and stellar disk area coverages by spots and faculae, and present the new relations.