What does solar chromospheric activity look like under different inclination angles?

Context. Chromospheric observations in the Ca II lines are essential for studying the magnetic activity of stars. In the case of the Sun, the chromospheric plages, the main contributors to the Ca II K emission, are distributed between midlatitude and the equator and never close to the poles. Therefore, we suspect that the inclination angle of the solar rotation axis has an impact on the observable chromospheric emission. Until now, the effect of such an inclination on chromospheric emission has not been extensively studied through direct solar observations. Aims. We reproduce solar images from any inclination to study the effect of the inclination axis on the solar variability by using direct observations of the Sun in the Ca II K line. In the context of the solar-stellar connection, while the Sun is observed from Earth from its near-equator point of view, and the other stars are observed most of the time under unknown inclinations, our results can improve our understanding of the magnetic activity of other solar-type stars. Methods. More than 2700 days of observations since the beginning of the Ca II K observations with the Uccle Solar Equatorial Table (USET), in July 2012, were used in our analysis. For each observation day, we produced synoptic maps to map the entire solar surface during a full solar rotation. Then, by choosing a given inclination, we generated solar-disk views, representing the segmented brightest structures of the chromosphere (plages and enhanced network) as seen under this inclination. The area fractions were extracted from the masks for each inclination and we compared the evolution of those time series to quantify the impact of the inclination angle. Results. We find a variation of the area fraction between an equator-on view and a pole-on view. Our results show an important impact of the viewing angle on the detection of modulation due to the solar rotation. With the dense temporal sampling of USET data, the solar rotation is detectable up to an inclination of about | i | = 70° and the solar cycle modulation is clearly detected for all inclinations, though with a reduced amplitude in polar views. When applying a sparse temporal sampling typical for time series of solar-like stars, the rotational modulation is no longer detected, whatever the inclination, due entirely to the undersampling. On the other hand, we find that the activity cycle modulation remains detectable, even for pole-on inclinations, as long as the sampling contains at least 20 observations per year and the cycle amplitude reaches at least 30% of the solar cycle amplitude. Conclusions. The inclination of the rotation axis of stars relative to our line of sight is unknown most of the time. Based on solar observations, we show that the impact of this inclination is important for the detection of the rotation period but negligible for the detection of the activity cycle period. For other stars, the time series usually have more complicated and scarcer samplings due to restricted target visibility, and this leads to a decrease in the signal of the chromospheric activity cycle. However, our results suggest that the inclination is unlikely to be the primary factor contributing to the relative scarcity of well-established cycles.