Michal Švanda1,2, Jan Jurčák1, Markus Schmassmann3
1 Astronomical Institute of the Czech Academy of Sciences, Fričova 298, CZ-25165 Ondřejov, Czech Republic
2 Astronomical Institute, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, CZ-18200 Prague, Czech Republic
3 Institut für Sonnenphysik (KIS), Georges-Köhler-Allee 401A, D-79110 Freiburg im Breisgau, Germany
Why do we average active regions?
Individual ARs vary widely. Some live for just a few days, others persist for weeks. Their spots may be large or small, closely spaced or far apart, and their evolution can be shaped by random interactions with nearby magnetic fields and convection.
Numerical simulations and theory predict that all ARs arise from the same basic mechanism: an Ω-shaped magnetic flux tube rising through the convection zone and piercing the surface[1,2]. Turbulence in the near-surface layers can distort the emerging flux and introduce “noise” into any attempt to identify common patterns.
Ensemble averaging is a statistical approach that reduces random variations by stacking many realizations of the same phenomenon. The trick for ARs is that they differ not only in details but also in scale, both in space and time. Without careful alignment, the average would simply blur away any meaningful structure.
Building the average AR
We selected 36 well-isolated bipolar ARs from SDO observations, each with clear leading and trailing spots and emerging within 60° of the central meridian. We used data from both the HMI – continuum intensity, Doppler velocity, line-of-sight and vector magnetograms – as well as three AIA channels (1600, 304, and 171 Å).
Figure 1. Snapshots of the HMI average intensity of the average normalized AR. Several normalized times are shown, where T= 0 corresponds to the emergence time (see Figure 2) and T= 1 represents the time at which the flux maximum was reached. Gravity centers of the polarities are located on coordinates ±0.5 on the horizontal axis and 0 on the vertical axis. The intensity is relative with respect to the quiet-Sun intensity.
The key innovation was the normalization of each AR in both space and time before averaging:
• Spatial alignment: We automatically detected the barycenters of the leading and trailing magnetic polarities in magnetograms. Each AR was rotated, shifted, and scaled so that its polarity centers lay on a fixed east–west line at the same separation. The leading polarity was set to be negative, so all ARs matched a common orientation.
• Temporal alignment: We defined T = 0 as the start of rapid flux emergence, and T = 1 as the time of peak magnetic flux. For each AR, we linearly scaled the timeline so that these two points matched.
Once normalized, we averaged the data for all ARs at each time step. This gave us a “movie” of the typical AR evolution from a couple of hours before emergence through and slightly beyond peak flux.
What does the average AR look like?
Magnetic field: The averaged vertical field map shows two compact, roughly circular sunspots connected by a horizontal field. The leading spot’s field remains stronger and more coherent than the trailing one, consistent with previous observational analyses (see review Ref [3]). Interestingly, the averaged bipolar pattern is already visible before T = 0, suggesting that in some ARs a weak vertical field structure is in place before the rapid emergence phase.
Figure 2. Similar to Figure 1 but only for vector magnetograms. Colors represent the vertical component of the magnetic field, whereas the arrows indicate the horizontal components.
Intensity: The continuum intensity maps show well-formed dark spots with umbra-penumbra structure. The leading spot is darker and more stable.
Flows: Dopplergrams show downflows co-located with strong magnetic fields, though the interpretation is complicated by projection effects and the convective blueshift. Local correlation tracking of granulation reveals a clear divergent horizontal outflow from the emergence site starting just before T = 0, evolving into moat-like radial outflows around both the leading and trailing spots, being stronger around the leading spot.
Atmosphere: In the AIA 1600 Å channel (upper photosphere/lower chromosphere), brightening appears along the polarity inversion line almost immediately after emergence, peaking early and then spreading into a more diffuse glow. In 304 and 171 Å (transition region and lower corona), brightening is more gradual, suggesting heating above the AR that persists beyond the emergence phase. These patterns are likely linked to ongoing small-scale reconnection as new flux continues to emerge.
Why does this matter?
By carefully normalizing and stacking dozens of ARs, we can identify the robust, repeatable aspects of their structure and evolution. The average AR:
• Confirms the asymmetry between leading and trailing polarities in both field strength and flow patterns.
• Shows that large-scale horizontal outflows begin before spots are visible in magnetograms.
• Reveals systematic atmospheric brightening above the polarity inversion line in the early growth phase.
• The results indicate that the bipolar sunspot groups are indeed spatially invariant, as predicted by theoretical concepts.
Details are available in our recent publication Ref [4]
References
[1] Cheung, M. C. M., Rempel, M. et al. 2010, ApJ, 720, 233
[2] Hotta, H., & Iijima, H. 2020, MNRAS, 494, 2523
[3] van Driel-Gesztelyi, L., & Green, L. M. 2015, Living Rev. Sol. Phys., 12, 1.
[4] Švanda, M., Jurčák, J., & Schmassmann, M. 2025 A&A, 700, A40