The enormous sunspot group that crossed the Sun in April 1947 was not observed producing a major flare, but its size points to something more extreme: if a region that large behaved like the most flare-productive regions seen in the modern era, it could in principle have powered a solar flare with a bolometric energy of a few ×10³⁴ erg.
That estimate reaches into the lower end of the energy range associated with so-called superflares on Sun-like stars. It does not mean that such a flare occurred in 1947, or that the Sun routinely produces events of that size. No direct flare measurements or reports exist for the 1947 region. Instead, the estimate comes from an empirical chain linking the size of sunspots to the larger magnetic regions around them, the area involved in flare reconnection, and ultimately the energy released.
The approach was designed to address a long-standing question: how energetic could a solar flare plausibly become?
The answer depends in part on how much magnetic energy is available in a solar active region. Sunspots are the most visible parts of these regions, but the magnetic structure extends beyond the dark spots into surrounding areas. Larger and more magnetically complex active regions tend to produce stronger flares, although size alone does not determine how much energy a particular flare will release.
The researchers therefore looked for an empirical way to connect the largest sunspots in the historical record to the strongest flare behavior actually observed.
Starting with the largest sunspots
The analysis included eight representative large sunspot groups or active regions, spanning the 1859 Carrington event through major modern events in 1989, 2000, 2003, 2014 and 2024.
The largest was the Great Sunspot of April 1947, with a maximum corrected area of about 6,100 millionths of a solar hemisphere. The October 2003 Halloween region reached about 3,500 millionths, while the large active region responsible for the October 2014 flares reached about 4,500 millionths.
The Carrington sunspot group is less certain because observations from 1859 are sparse. Different reconstructions put its maximum corrected area between roughly 2,300 and 3,500 millionths of a solar hemisphere. The researchers adopted 3,100 millionths as a conservative upper estimate, while noting that drawings made by Angelo Secchi suggest the region may have been larger shortly before the famous September 1859 event.
The historical records were not used to reconstruct exactly what happened during those old solar storms. Instead, they supplied the starting point for a hypothetical exercise: given the size of these enormous regions, what flare energies would be possible if they followed the upper end of the relationships measured in modern observations?
That distinction is important because the study is estimating potential energy, not recovering an unobserved historical flare.
From sunspot size to the part that can flare
The researchers first had to account for the fact that a sunspot is only part of an active region.
They estimated total active-region areas in two ways. Where suitable observations existed, they measured the regions directly using solar images and line-of-sight magnetic-field observations. For historical cases, they also used an empirical relationship between sunspot area and the larger areas containing plages and faculae.
For the modern regions, the researchers used observations from instruments including the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager, or HMI, and earlier observations from the Solar and Heliospheric Observatory’s Michelson Doppler Imager. For the 1947 region, they used historical observations including a Mt. Wilson sunspot drawing and Kodaikanal calcium K observations.
The two approaches gave broadly consistent active-region areas for the cases where both could be applied.
But active-region size alone was not enough. The next question was how much of that region might actually participate in a flare.
The flare ribbons provide the next link
During a solar flare, bright structures known as flare ribbons appear in the chromosphere and transition region. They mark the footpoints of newly reconnected magnetic field lines, so their area provides a measure related to the amount of magnetic flux involved in reconnection.
For this part of the analysis, the researchers used a catalog containing measurements for 3,137 flares of GOES class C1.0 and above observed between 2010 and 2016. The catalog included 306 M-class or stronger flares and provided active-region areas, flare-ribbon areas and magnetic reconnection fluxes.
The relationship between active-region area and ribbon area has considerable scatter. A large active region can produce a relatively modest flare, while a smaller region can occasionally produce ribbons that occupy a relatively large fraction of the region.
Because the study was interested in the extreme end of solar activity, the researchers did not use the average relationship. They instead traced the upper envelope of the observed distribution.
They calculated two versions. One represented the 95th percentile of the ribbon-to-active-region area relationship, while the other represented the 99th percentile. The 95th-percentile relation has more events behind it and therefore better statistics. The 99th-percentile relation focuses more strongly on the rarest observed behavior but is based on fewer events.
The researchers then extended those relationships to the much larger active regions represented by the historical sunspots.
The resulting estimates were not treated as strict physical limits. They are statistical upper bounds based on rare but observed flare behavior.
Modern flares provide a test
Before applying the relationships to the historical record, the researchers compared their method with active regions for which actual observations were available.
One particularly useful test was AR 12192, the huge active region that crossed the Sun in October 2014. It is the only region in the sample that is also covered directly by the flare-ribbon catalog used to build the empirical relationships.
Between October 24 and 27, AR 12192 had measured active-region areas between about 3.3 and 4.2 × 10²⁰ square centimeters in the catalog. The researchers’ image-based estimates ranged from about 3.1 to 3.8 × 10²⁰ square centimeters, while their sunspot-to-active-region conversion gave about 4.5 to 4.8 × 10²⁰ square centimeters.
The predicted flare-ribbon areas also agreed reasonably well with the observed values. The researchers regarded this agreement as a check that their empirical scaling was capturing the relationship between active-region size and ribbon area adequately enough to justify extending it toward larger regions.
Another test came from the Bastille Day flare of July 14, 2000. Its active region was the smallest in the sample, with a maximum sunspot area of about 1,400 millionths of a solar hemisphere. An independent analysis had estimated the flare’s bolometric energy at (3.4 ± 1.7) × 10³² erg.
Using direct image measurements, the new scaling produced 3.3 × 10³² erg for its best 95th-percentile estimate. The observed energy therefore fell within the predicted distribution.
The result also illustrates why active-region size cannot be treated as a simple predictor of flare energy. A comparatively modest region can still produce a powerful flare, and large regions do not necessarily release all their available magnetic energy in a single eruption.
The 2003 Halloween events reach the same scale
The Halloween solar storms of October and November 2003 provided another unusually valuable comparison because several of the large flares had bolometric energies estimated from measurements of the Sun’s total irradiance.
The largest region, AR 10486, produced the X25 and X43 flares. The November 4 event, classified as X43 under the revised NOAA scale, had an inferred bolometric energy of about 4.3 × 10³² erg, although the uncertainty was large, reaching about 65% for that event. Two other major flares had inferred energies of about 3.6 × 10³² and 1.4 × 10³² erg.
For AR 10486, the researchers’ image-based 95th-percentile estimate was about 8 × 10³² erg, within the same general range as the directly inferred energy of the strongest Halloween flare. Their statistical upper ranges extended to about 2.3 × 10³³ erg for the 95% prediction interval and about 4.5 × 10³³ erg for the 99% prediction interval.
The empirical active-region estimates were somewhat higher.
These comparisons gave the researchers a way to test whether their scaling method behaved sensibly against observed large flares before using it for regions from eras when direct flare measurements were unavailable.
The 1947 sunspot pushes the estimate into superflare territory
The largest jump comes from the Great Sunspot of April 1947.
Its corrected sunspot area was about 6,100 millionths of a solar hemisphere, making it the largest sunspot group in the record used by the researchers. Applying the empirical relationships gives a best 95th-percentile flare-energy estimate of about 2.3 × 10³³ erg.
The statistical upper ranges are much higher. Depending on the active-region estimate and percentile envelope used, the 95th- and 99th-percentile prediction intervals extend into the range of roughly 6.6 × 10³³ to 1.25 × 10³⁴ erg. The study’s broader extrapolation allows a flare from a region of this size to reach a few ×10³⁴ erg under particularly favorable, extreme conditions.
That is the central result of the analysis.
It overlaps with the lower end of the superflare energy range inferred from observations of Sun-like stars. But the researchers stress that no flare report or bolometric measurement exists for the 1947 region. The calculation therefore says what such a region could plausibly have produced under the empirical scaling, not what it actually produced.
The Carrington region gives a second historical benchmark
The Carrington sunspot group provides a useful comparison because it was associated with the most famous extreme solar storm of the historical record.
Using the adopted corrected sunspot area of 3,100 millionths of a solar hemisphere, the researchers obtain a typical 95th-percentile flare energy of about 1.3 × 10³³ erg. The 99th-percentile prediction interval reaches about 7 × 10³³ erg under exceptionally favorable conditions.
The typical estimate is consistent with independent estimates of the Carrington flare’s X-ray class, which have placed it between about X45 and X146. Those estimates correspond to bolometric energies approaching 10³³ erg, although the conversion carries uncertainties.
The agreement does not provide a direct measurement of the Carrington flare’s energy. Instead, it gives the empirical scaling another historical point of comparison.
Size does not guarantee an eruption
The researchers also found an important qualification in the modern examples.
AR 12192 was exceptionally large and produced numerous X-class flares, but all of its X-class flares were confined rather than eruptive, and its associated solar energetic particle activity was weak. Strong magnetic fields above an active region can suppress the formation of a coronal mass ejection, limiting the escape of particles.
By contrast, the large region associated with the March 1989 Quebec event produced an eruptive X19 flare with substantial space-weather effects.
The contrast means that a large sunspot area can indicate substantial magnetic energy available to a flare, but it does not determine whether that energy will be released in an eruptive event. Magnetic topology and the structure of the surrounding coronal field also matter.
The study therefore distinguishes between the energy that a large active region could potentially release and the actual flare, coronal mass ejection or particle event that might result from its magnetic configuration.
Multiple large regions could complicate the limit
The calculations mostly treat each active region separately. The researchers point out that the Sun does not always produce active regions independently.
Large regions can emerge close to one another in what are known as nests of activity. Statistical studies cited in the research indicate that about 40–60% of sunspot groups are associated with such nests, with nesting becoming more common as solar activity increases.
The Halloween events offer a concrete example. AR 10486, with a sunspot area of about 3,500 millionths of a solar hemisphere, was accompanied by another unusually large region, AR 10488, whose area exceeded 2,500 millionths. The two regions appeared at nearly the same longitude but in different hemispheres.
The study does not calculate what their combined flare energy would have been. Instead, it notes that if large active regions interact or merge, the effective magnetic system involved in reconnection could be larger and more complex than either region considered alone.
A similar pattern appeared during the May 2024 Mother’s Day, or Gannon, event. NOAA AR 13664 underwent a complex evolution in which another region, NOAA AR 13668, and potentially a smaller region emerged and merged into the pre-existing large region. The authors describe this as a plausible way of increasing the complexity and free-energy budget of the system.
But they do not turn this possibility into a numerical upper limit. The ribbon area produced by interacting regions does not necessarily equal the simple sum of their areas. Magnetic connectivity, reconnection geometry and the timing of flux emergence all affect the outcome. A quantitative treatment of these interactions would require a separate analysis of the magnetic topology and flux evolution.
The upper end remains an extrapolation
The study’s central estimates depend on extending relationships measured from modern solar observations into a regime that has not been directly observed.
That creates several layers of uncertainty. The method assumes that the largest historical sunspots had physical properties similar enough to modern active regions for the empirical relationships to remain valid at larger sizes. Uncertainty also enters through the conversion from sunspot area to total active-region area, the scatter in ribbon-to-active-region area ratios, and the relationship between ribbon properties and flare energy.
Measurements of historical regions also involve projection and threshold effects, while active regions evolve over time. The flare productivity of regions with similar sizes can vary substantially.
There is additional uncertainty in converting X-ray measurements to total bolometric flare energy. The apparent total irradiance of a flare can also depend on where it occurs on the solar disk, with events near the limb affected by partial occultation and anisotropic emission.
The authors estimate that these factors can produce discrepancies of up to roughly a factor of two to three in absolute energy.
For that reason, the study does not present precise predictions for individual historical flares. Its purpose is to establish plausible upper bounds based on empirical solar behavior.
The distinction is especially important at the highest energies. The 95th- and 99th-percentile curves describe rare portions of an observed statistical distribution. They are not deterministic physical ceilings that every active region must obey.
Within those limitations, the largest sunspot groups point to a solar flare-energy range that extends beyond the strongest directly measured modern events. The 1947 Great Sunspot provides the highest estimate in the study, with the upper end reaching a few ×10³⁴ erg under the most favorable extrapolated conditions.
The study was published in Philosophical Transactions of the Royal Society A.
