Modeling stellar Ca II H & K emission variations. I. Effect of inclination on the S-index

TL;DR

This paper develops a physics-based model to understand how the inclination angle of a star affects the observed Ca II H & K emission, which is a key indicator of stellar magnetic activity, and validates it using solar data.

Contribution

The study introduces a novel model that quantifies the impact of stellar inclination on the S-index, enhancing interpretation of stellar magnetic activity measurements.

Findings

S-index amplitude decreases with inclination, more so on rotational timescales.

The absolute S-index value is only weakly affected by inclination.

The model successfully reconstructs solar activity variations over four cycles.

Abstract

The emission in the near ultraviolet Ca II H & K lines is modulated by stellar magnetic activity. Although this emission, quantified via the S-index, has been serving as a prime proxy of stellar magnetic activity for several decades, many aspects of the complex relation between stellar magnetism and Ca II H & K emission are still unclear. The amount of measured Ca II H & K emission is suspected to be affected not only by the stellar intrinsic properties but also by the inclination angle of the stellar rotation axis. Until now such an inclination effect on S-index has remained largely unexplored. To fill this gap, we develop a physics-based model to calculate S-index, focusing on the Sun. Using the distributions of solar magnetic features derived from observations together with Ca II H & K spectra synthesized in non-local thermodynamic equilibrium, we validate our model by successfully reconstructing the observed variations of solar S-index over four activity cycles. Further, using the distribution of magnetic features over the visible solar disk obtained from surface flux transport simulations, we obtain S-index time series dating back to 1700 and investigate the effect of inclination on S-index variability, both on the magnetic activity cycle and the rotational timescales. We find that when going from an equatorial to a pole-on view, the amplitude of S-index variations decreases weakly on the activity cycle timescale and strongly on the rotational timescale (by about 22% and 81%, respectively, for a cycle of intermediate strength). The absolute value of S-index depends only weakly on the inclination. We provide analytical expressions that model such dependencies.