Quantifying sunspot group nesting with density-based unsupervised clustering

TL;DR

This paper tackles the problem of quantifying sunspot-group nesting in longitude–time space by combining a smooth density representation with density-based clustering (DBSCAN) to identify nests across 151 years of RGO and KMAS observations. The authors validate the method on synthetic data, calibrate it on two independent solar catalogs, and apply it to study how nesting depends on latitude, cycles, and activity. They find a mean nesting degree of about 0.61, with a strong mid-latitude peak around 10°–20°, and a positive correlation between nesting and cycle strength, yet no persistent active longitudes emerge in cycle-averaged analyses due to longitudinal drift and differential rotation. The approach provides a robust, automated framework for quantifying spatial–temporal clustering of solar magnetic flux and has potential extensions to full 3D clustering and to stellar photometric data for Sun-like stars.

Abstract

Sunspot groups often emerge in spatial-temporal clusters, known as nests or complexes of activity. Quantifying how frequently such nesting occurs is important for understanding the organisation and recurrence of solar magnetic fields. We introduce an automated approach to identify nests in the longitude-time domain and to measure the fraction of sunspot groups that belong to them. The method combines a smooth representation of emergence patterns with a density-based clustering procedure, validated using synthetic solar-like cycles and corrected for variations in data density. We apply this method to 151 years of sunspot-group observations from the Royal Greenwich Observatory Photoheliographic Results (RGO, 1874-1976) and Kislovodsk Mountain Astronomical Station (KMAS, 1955-2025) catalogues. Across all cycles and latitude bands, the mean nesting degree is $\langle D\rangle = 0.61 \pm 0.12$, implying that about 60 percent all sunspot groups emerge within nests. Nesting is strongest at mid-latitudes (10$^\circ$-20$^\circ$), and results from the two independent datasets agree in the period of overlap. The identified nests range from compact clusters to long-lived, drifting structures, offering new quantitative constraints on the persistence and organisation of solar magnetic activity.

Figures (8)

• Figure 1: Injection-recovery validation of DBSCAN clustering for synthetic SG-emergence data of solar-like cycles, showing recovered vs. injected nesting degree (left) and the corresponding bias as a function of the injected degree (right). Red symbols show mean values with error bars indicating standard deviation over 160 independent realisations.
• Figure 2: Carrington longitudes and times of SG emergence from KMAS data, during solar cycle 21 across the latitude band $10^\circ-15^\circ$ of the northern (left panel) and southern (right panel) hemisphere. Grey-scale background show the SG-area-weighted KDE density distribution where the areas were taken in their peak value. The coloured circles denote nest members and grey crosses non-members according to the area-weighted DBSCAN. Yellow plus signs show the area-weighted centres of nests. The nesting degree, total SG area, adopted $\varepsilon$, and the adjusted KDE bandwidth (bw_adjust), and the number of significant vs. total nests are given on plot titles.
• Figure 3: Comparison of nesting degrees from RGO and KMAS during overlap period (Cycles 19--20, 1954--1976). Red circles: Cycle 19 ($n=14$); blue squares: Cycle 20 ($n=14$). Strong correlation ($r=0.777$) with systematic offset following $D_{\rm RGO} = 0.66 \, D_{\rm KMAS} + 0.31$ (RMS = 0.158).
• Figure 4: Example comparison for Cycle 19, latitude band $15^\circ$--$20^\circ$. Left: RGO detects substantially more groups ($D=0.768$). Right: KMAS shows sparser coverage ($D=0.671$) for the identical temporal and spatial window. Both datasets identify similar large-scale nesting structures, but RGO's superior completeness captures additional small groups that increase the recovered nesting degree.
• Figure 5: Distribution of nesting degrees across latitude bands from the combined RGO (cycles 12--20) and KMAS (cycles 21--25, calibrated) dataset. Box plots show distributions across 95 independent full-cycle analysis windows in 10$^\circ$-wide latitude bands. Box boundaries mark the first and third quartiles (25th and 75th percentiles), with the median indicated by the horizontal orange line and the mean by red diamonds. Whiskers extend to 1.5 times the interquartile range, with outliers shown as circles. Sample sizes ($n$) indicate the number of analysis windows contributing to each band. The Kruskal--Wallis test ($H=36.6$, $p=5.5\times 10^{-8}$) confirms highly significant latitude dependence.