Exploring spatial and temporal patterns across solar cycles: Focusing on active longitudes

Context. Active longitudes (ALs) are proposed behavioural patterns on the Sun, whereby certain solar phenomena tend to appear at preferred longitudes, with these longitudes shifting over time on a scale of a few Carrington rotations (CRs). The existence of ALs remains a topic of debate, largely due to our limited understanding of their origin, evolution, and physical significance. Aims. This study aims to provide support and further evidence towards the existence of ALs by utilising longer-term sunspot and solar flare datasets. As part of this effort, an artificial test dataset for control was also constructed in which the longitudes of sunspots were randomised, allowing a direct comparison with the observational data. Methods. Kernel density estimation (KDE) was employed to search for longitudinal groupings of sunspot groups and flares on synoptic maps. Furthermore, we explored larger-scale structures by applying a 2D KDE to the peaks of the 1D KDEs (longitude as a function of CR). Finally, we generated artificial solar cycles by simulating sunspots with randomised properties, most notably assigning longitudes from a uniform distribution. Results. Distinguishable features were identified in the 2D KDEs, showing that during certain periods of the solar cycle, a specific longitude range may exhibit heightened activity, which can later switch off entirely, and a new one can appear ∼180° away, consistent with the AL’s flip-flop effect. Although our randomised datasets also exhibited ALs in their 2D KDEs, these differed notably from the observed patterns: inactive longitudes were less pronounced, and active patches appeared shorter-lived and more numerous. We also identified a parameter for a qualitative comparison: the number of KDE peaks (in the 1D KDE) per number of CRs in a solar cycle. This indicator shows a markedly different distribution between the randomised and observed datasets, confirmed by a Cucconi test p value of 0.0177.