Cross-Scale Phase Relationship of the Ca II K Index with Solar Wind Parameters: A Space Climate Focus

The solar wind, representing one of the most impacting phenomena in the circum-terrestrial space, constitutes one of the several manifestations of the magnetic activity of the Sun. With the aim of shedding light on the scales beyond the rotational period of the Sun (i.e., Space Climate scales), this study investigates the phase relationship of a solar activity physical proxy, the Ca II K index, with solar wind properties measured near the Earth, over the whole space era (last five solar cycles). Using a powerful tool such as the Hilbert–Huang transform, we investigate the dependence of their phase coherence on the obtained time scale components. Phase coherence at the same time scales is found between all the components and is also preserved between adjacent components with time scales ≳ 2 yrs. Finally, given the availability of the intrinsic modes of oscillation, we explore how the relationship of Ca II K index with solar wind parameters depends on the time scale considered. According to our results, we hypothesize the presence of a bifurcation in the phase-space Ca II K index vs. solar wind speed (dynamic pressure), where the time scale seems to act as a bifurcation parameter. This concept may be pivotal for unraveling the complex interplay between solar activity and solar wind, bearing implications from the prediction and the interpretation point of view in Space Climate studies.