Junwei Zhao, Ruizhu Chen, and Aimee A. Norton
W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085

Solar active regions (ARs) are not distributed randomly across the Sun. For more than a century, observations have shown that ARs tend to recur near preferred longitudes over many solar rotations, sometimes persisting for months or even years. These persistent concentrations, often called active longitudes or activity nests, are among the clearest large-scale patterns in solar magnetic activity. Previous studies also found that these preferred longitudes drift relative to the Carrington rotation frame [1], implying that they rotate at slightly different rates. Solar activity additionally shows quasi-periodic variations on timescales ranging from months to years. One well-known example is the 150-160 day Rieger-type periodicity, first discovered in major solar flares [2] and later identified in coronal mass ejections, flare occurrence rates, and sunspot areas. Such periodicities have long been linked to Rossby waves in the solar interior because their characteristic timescales agree closely with theoretical expectations for equatorially trapped Rossby modes. Earlier theoretical work suggested that cyclic variations of the Sun’s toroidal magnetic field may selectively amplify certain Rossby-wave harmonics [3].

Figure 1. (a) Synchronic image of the Sun for 12:00 UT of 2024 July 21, combining near-side magnetic-field observations (green–orange on a gray background) and far-side helioseismic AR images (dark patches on an orange background). The color bars indicate the ranges of magnetic-field strength and acoustic travel-time deficits, separately. (b) Synchronic image of ARs, derived from panel (a) after converting the near-side magnetic field to magnetic flux and degrading the spatial resolution to match that of the helioseismic far-side images.

In this work, we investigate the long-term emergence and clustering patterns of ARs during Solar Cycle 24 using observations from the SDO/HMI. Our analysis combines conventional near-side magnetic-field observations with far-side helioseismic images derived from HMI Doppler measurements through time-distance helioseismology [4] (see Figure 1a). This approach allows us to track solar activity continuously across the entire solar surface, including regions hidden from direct view on the far side of the Sun.

To create a consistent full-sphere dataset, we converted near-side magnetic maps into unsigned magnetic-flux maps by removing polarity information. These maps were then spatially blurred to match the lower resolution of the helioseismic far-side images (Figure 2b). We constructed one full-Sun synchronic magnetic-flux map per day from 2010 June through 2019 December, producing a dataset of about 3500 daily maps spanning nearly the entirety of Solar Cycle 24. For each daily map, we integrated the magnetic flux within the latitude bands 0°-30°N and 0°-30°S separately, generating longitude-dependent activity profiles for the northern and southern hemispheres. Combining these daily profiles produced spatiotemporal maps showing how magnetic activity evolved with longitude and time (Figure 2).

Figure 2. Upper: Three integration bands are identified on the spatiotemporal maps of the northern hemisphere, made of synchronic magnetic-flux maps, corresponding to the highest flux concentrations throughout Cycle 24. Lower: Same as the upper panel but for the southern hemisphere.

The resulting maps reveal that large and long-lived ARs cluster strongly in both space and time rather than emerging randomly. In the northern hemisphere, we identified three narrow longitude bands that contain the highest concentrations of magnetic flux. Although not every AR falls exactly within these bands, most of the largest and strongest regions are located either inside them or nearby. Approximately 63% of the total magnetic flux during the cycle lies within 20° of the three preferred bands. Interestingly, several of the largest ARs appeared near intersections of two or more bands. Two of the three bands drift in the prograde direction relative to the Carrington frame, while one drifts retrograde. Their relative rotation rates are approximately 6.9 ± 0.4, 20.3 ± 0.3, and −12.7 ± 0.4 nHz in the northern hemisphere. Similar behavior is found in the southern hemisphere, with prograde and retrograde drift rates of 6.7 ± 0.3, 17.2 ± 0.2, and −6.9 ± 0.4 nHz.

To quantify these patterns, we computed two-dimensional Fourier power spectra of the spatiotemporal maps shown in Figure 2. The spectra (Figure 3a) show several prominent low-order modes. In the northern hemisphere, two strong prograde modes are prominent with some frequency spread at (m=1, ν = 6.6 ± 1.6 nHz) and (m=1, ν = 19.7 ± 4.2 nHz), and one prominent retrograde mode appears at (m=1, ν = −14.6 ± 3.2 nHz). Figure 3b presents the results for the southern hemisphere. Again, two clusters of prograde power appear at m = 1, with power-weighted frequencies at ν = 6.1 ± 1.7 nHz and 19.4 ± 2.3 nHz. One retrograde mode appears at (m=2, ν = −14.7 ± 2.5 nHz). Note that these mode frequencies are in reasonable agreement with those determined by the tracking rates shown in Figure 2.

Figure 3. (a) Power spectrum calculated from the spatiotemporal magnetic-flux map (Figure 2b), obtained from the latitudinal band of 0° − 30°N. (b) Same as panel (a) but for the southern hemisphere. (c) Power spectrum of the northern hemisphere for m=1, displayed as a function of ν. Arrows point to the dominant
modes. (d) Same as panel (c) but for the southern hemisphere. Note that the unit for power is arbitrary.

We then compared the observed modes with theoretical predictions for magneto-Rossby waves. Using the dispersion relation developed in earlier studies [3], we found that the observed patterns can be reproduced by magneto-Rossby waves associated with a toroidal magnetic field strength of roughly 4 kG near the solar tachocline, the transition layer between the radiative interior and the convection zone. For details of this calculation, please refer to Ref. [5].

Our results suggest that the large-scale clustering and migration patterns of solar active regions are not merely surface phenomena. Instead, they likely reflect global-scale wave dynamics operating deep inside the Sun. In this picture, the emergence of surface magnetic activity carries an imprint of tachocline dynamics, providing a possible observational connection between interior magneto-Rossby waves and the long-term organization of solar activity.

References

[1] Berdyugina, S. V., & Usoskin, I. G. 2003, A&A, 405, 1121
[2] Rieger, E., Share, G. H., Forrest, D. J., et al. 1984, Nature, 312, 623
[3] Zaqarashvili, T. V., Carbonell, M., Oliver, R., & Ballester, J. L. 2010, ApJ, 709, 749
[4] Zhao, J., Hing, D., Chen, R., & Hess Webber, S. 2019, ApJ, 887, 216
[5] Zhao, J., Chen, R., & Norton, A. A. 2026, ApJ, in press, https://arxiv.org/abs/2605.25501