Modeling Stellar Ca ii H and K Emission Variations. I. Effect of Inclination on the S-index

Abstract

The emission in the near-ultraviolet Ca ii H and 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 and K emission are still unclear. The amount of measured Ca ii H and 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 the 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 and K spectra synthesized in non-local thermodynamic equilibrium, we validate our model by successfully reconstructing the observed variations of the 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 on both 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 the S-index depends only weakly on the inclination. We provide analytical expressions that model such dependencies.

Faculae Cancel out on the Surfaces of Active Suns

“…Previous studies indicated that such a transition can be reproduced by extrapolating the observed dependencies of solar facular and spot area coverage on the S-index (Shapiro et al 2014). Instead of relying on these extrapolations, which are purely empirical and assume that any trend seen on the Sun continues unchanged to more active stars, we combined our calculations of spot and facular coverages with models of stellar photometric brightness from N20 and Ca II H&K emission developed by Sowmya et al (2021). Namely, we used the model introduced in N20 to calculate the activity-induced alteration in Strömgren (b+y)/2, (b + y)/2 quiet − (b + y)/2 active , where the first term represents the brightness of a star free from any magnetic features and the second term quantifies the brightness in the presence of magnetic activity (so that a positive alteration of Strömgren (b+y)/2 corresponds to an overall brightening with increasing magnetic activity, while a negative alteration corresponds to a dimming).…”

“…These calculations have been performed for the daily snapshots of the disc distributions of magnetic features for all activity levels (s) used in this study (see Fig 1b,c). Then we used the Sowmya et al (2021) model for the Ca II H&K emission to calculate the corresponding S-index values. As a result, we obtained a contemporaneous time series of Strömgren (b+y)/2 and the S-index, by combining all five modelled activity levels into a 55-year time series.…”

“…stars observed pole-on) in comparison to the Lowell and Fairborn data (Radick et al 2018).We note that the inclination affects the variability by changing the disk distribution of magnetic features. For example, on stars like the Sun the magnetic features are mainly concentrated in the near-equatorial bands so that the change of the inclination from i = 90 • to i = 0 • will shift the magnetic features towards the (visible) limb, affecting both photometric variability (see Nèmec et al 2020) and the S-index (see Sowmya et al 2021). In Fig.…”

Characterization of chromospheric activity based on Sun‐as‐a‐star spectral and disk‐resolved activity indices

“…This index serves as a reference standard for the strength of a star's magnetic activity, thus facilitating a direct comparison with the Sun (Baliunas et al 1995; Duncan et al 1991; Hall 1996; Schröder et al 2018). Sowmya et al (2021) pursued a different approach using synthesized Ca ii H & K spectra to calculate a realistic solar S ‐index, which was validated with solar Ca ii H & K imaging and spectral data, to assess stellar magnetic activity.…”

Characterization of chromospheric activity based on Sun-as-a-star spectral and disk-resolved activity indices

“…This index serves as a reference standard for the strength of a star's magnetic activity, thus facilitating a direct comparison with the Sun (Baliunas et al, 1995;Duncan et al, 1991;Hall, 1996;Schröder, Schmitt, Mittag, Gómez Trejo, & Jack, 2018). Sowmya et al (2021) pursued a different approach using synthesized Ca ii H & K spectra to calculate a realistic solar S-index, which was validated with solar Ca ii H & K imaging and spectral data, to assess stellar magnetic activity.…”