  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.
