The study, published in the journal Solar Physics, was led by Partha Chowdhury of the University of Calcutta together with Jagdev Singh, V. Muthu Priyal, and Belur Ravindra of the Indian Institute of Astrophysics in Bengaluru. The researchers analyzed digitized images taken in the light of singly ionized calcium, the Ca ii K spectral line, from the Kodaikanal Solar Observatory. These images capture the chromosphere, a thin layer of the solar atmosphere sitting just above the visible photosphere, where magnetic fields heat the gas and make bright regions known as plages blaze in ultraviolet-adjacent wavelengths. Plages are the chromospheric ghosts of sunspots: where magnetic flux crowds the surface, the calcium emission brightens, even when no dark spot is present.

Because plages are visible even when sunspots are not, they offer a more complete census of the Sun’s magnetic activity than sunspot counts alone. The Kodaikanal archive, spanning Solar Cycles 14 through 22, roughly the first nine decades of the twentieth century, is one of the longest continuous records of chromospheric behavior anywhere in the world. After careful digitization and homogenization, a process that corrects for changes in photographic plates, instruments, and observing conditions over the decades, the team measured the total area covered by plages on every available day and compared it with three standard yardsticks of solar activity: the international sunspot number, the total sunspot area, and the 10.7 centimeter radio flux, a microwave emission that tracks coronal magnetic heating.

The correlations the team found are strikingly strong. Across all nine cycles, the chromospheric plage area tracks each of the photospheric and coronal activity indices with correlation coefficients exceeding 0.85, a level of agreement that leaves little doubt that the Sun’s upper and lower atmospheric layers are driven by the same underlying magnetic engine. This matters for more than just bookkeeping. Because plage records extend further back in time than some modern instruments, they can serve as a reliable proxy for reconstructing solar activity across the twentieth century, including the ultraviolet output that subtly influences Earth’s upper atmosphere and climate system.

But the study went beyond simple correlations. The researchers examined whether the plage areas obey two well-known but poorly understood features of the solar cycle. The first is the Gnevyshev-Ohl rule, an empirical oddity noting that in most pairs of consecutive solar cycles, the odd-numbered cycle is stronger than the even-numbered one that precedes it. The team confirmed that plage areas follow this rule, suggesting that the chromosphere inherits the same cycle-to-cycle memory that governs sunspot production. The second feature is the Gnevyshev gap, a temporary dip in activity that often splits the peak of a solar cycle into two humps. The analysis revealed clear Gnevyshev gaps in the plage data during several cycle maxima, confirming that this double-peaked structure is not merely a sunspot quirk but a genuine, whole-Sun phenomenon imprinted on the chromosphere as well.

To dig deeper into the timing of these variations, the team turned to a powerful mathematical technique called Morlet wavelet analysis, which can detect oscillations whose strength and period change over time, something a traditional Fourier analysis cannot do. They supplemented this with wavelet coherence, a method that measures not just whether two signals share a rhythm, but whether those rhythms stay in step with each other, drifting in and out of phase like two musicians who occasionally lose the beat. The technique is widely used in geophysics and climate science, and it is ideally suited to the Sun, whose magnetic activity is famously irregular.

The wavelet analysis uncovered two families of intermediate-term periodicities hiding inside the dominant eleven-year cycle. The first are Rieger-type periods, oscillations of roughly 130 to 190 days. These were first discovered in 1984, when researchers noticed that gamma-ray flares from the Sun seemed to cluster with a period of about 154 days. Since then, similar periodicities have been found in sunspots, flares, and coronal mass ejections, and they are widely interpreted as the signature of magnetic Rossby waves, vast, planet-scale waves of magnetized plasma rolling around the Sun’s interior shear layer known as the tachocline, where the Sun’s differential rotation winds up its magnetic field. The second family comprises quasi-biennial oscillations, or QBOs, with periods of one to four years, which are thought to reflect a secondary magnetic cycle operating in parallel with the main eleven-year one.

Here the story takes an intriguing turn. The Rieger-type periods and QBOs show considerable variability from one solar cycle to the next, and the wavelet coherence analysis reveals that at these intermediate timescales, the chromospheric plage areas and the photospheric activity indices frequently fall out of phase with one another. The rhythms exist, but they do not always march together. This asynchrony suggests that the shorter-period variations may arise from processes that affect the chromosphere and photosphere differently, or from instabilities in the tachocline whose surface manifestations depend on the details of each individual cycle, including the strength of the interior magnetic field at the time.

At the fundamental scale, however, the picture is one of remarkable unity. Within the 9 to 12 year periodicity belt that defines the solar cycle itself, the team found a stable phase synchrony between chromospheric plages and every photospheric and coronal index they examined. In other words, over the long haul, the Sun’s chromosphere and its visible surface rise and fall together like two ends of the same magnetic tide. This tight decadal coupling is exactly what modern solar dynamo models predict: magnetic fields generated by the rotation of plasma at the tachocline buoyantly rise through the convection zone, emerge as sunspots and active regions in the photosphere, and simultaneously light up the overlying chromosphere as plages. The new results provide hard empirical constraints that any credible dynamo model must now reproduce.

The findings also align with theoretical work on tachocline instabilities and magnetic Rossby waves, which have been invoked to explain everything from the double-peaked shape of solar maxima to the so-called seasons of space weather, bursts of intense flaring that come and go over months. By confirming Rieger-type and quasi-biennial signals in a chromospheric dataset spanning nine cycles, the study strengthens the case that these waves are a persistent feature of the solar interior rather than a fluke of a few well-observed cycles. For space weather forecasters, the implications are tantalizing: if the phase relationships between these periodicities and the activity indices can be pinned down well enough, the hidden rhythms of the tachocline might one day help anticipate the timing of the most active and hazardous phases of the solar cycle. For now, the century-old glass plates of Kodaikanal have once again proven that some of the best windows into the Sun’s deepest secrets were captured long before the space age began.

Subject of Research: Long-term chromospheric plage evolution and its relationship to solar activity indices across Solar Cycles 14 to 22

Article Title: Long-term Evolution of Chromospheric Plage Areas from Kodaikanal Observatory Ca ii K Images and Their Relation to Solar Activity Indices

Article References: Chowdhury, P., Singh, J., Priyal, V. M., & Ravindra, B. (2026). Long-term Evolution of Chromospheric Plage Areas from Kodaikanal Observatory Ca ii K Images and Their Relation to Solar Activity Indices. Solar Physics, 301(10), Article 149. https://doi.org/10.1007/s11207-026-02733-y

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02733-y

Keywords: solar physics, chromosphere, Ca ii K, solar plages, solar cycle, sunspots, Rieger periodicity, quasi-biennial oscillations, solar dynamo, tachocline, Rossby waves, Kodaikanal Observatory

The stakes of this archival detective work are higher than they might appear. French solar observations form the primary data source covering the Maunder Minimum, the period from roughly 1645 to 1715 when sunspots became vanishingly rare and Europe shivered through what climatologists call the Little Ice Age. In the 1990s, the astronomer Elisabeth Nesme-Ribes extensively analyzed the Parisian Observatory archives and published a series of influential reconstructions. Tragically, the solar data she compiled have since been lost; only a single figure of average sunspot latitudes survives. That loss made a fresh, independent reduction of the original documents not merely desirable but essential, and the new study delivers exactly that, digitizing measurements that had previously existed only in ink on paper.

The technical challenge of converting seventeenth- and eighteenth-century observations into modern solar coordinates is formidable. La Hire did not simply note that a spot existed; he measured the times at which spots crossed the solar meridian, recorded angular distances from the disk’s limbs, and drew the spots in engravings that captured their shapes and relative positions. To transform these numbers into latitudes and longitudes, the researchers needed the angular size of the solar disk on every observing day, which changes through the year as Earth moves along its elliptical orbit. They interpolated routine meridian measurements published posthumously by Le Monnier in 1741, recovering disk diameters to within a few arcseconds for dates spanning the entire eight-year window. Combining transit timings with these disk sizes, they traced each sunspot’s path across the visible hemisphere and computed daily heliographic coordinates for every individual spot and group.

The reconstruction demanded careful correction of errors scattered through the historical record. The researchers found typos in dates, mislabeled authorship, and arithmetic slips in both the journals and the printed Mémoires. On 31 May 1703, for example, La Hire made an error in a sunspot transit measurement that could only be resolved by consulting his own journal. On 26 June of that year, an engraving appears to have been accidentally reversed and flipped compared with the other drawings, a conclusion supported by the relative positions of the umbrae and by agreement with a drawing by Giovanni Domenico Cassini. On 2 January 1707, a measurement taken seven minutes after noon required a positional correction of about 3.6 degrees toward the solar Equator. Each such fix, the authors note, matters when the goal is a machine-readable catalogue that modern solar physicists can trust.

The Parisian records also proved decisive in resolving puzzles among contemporary observers across Europe. The reconstructed positions resolved an inconsistency in the observations of Johannes Hoffmann and showed that the observer Müller was using a different type of telescope, a finding that changes how his measurements should be interpreted. The team cross-checked La Hire’s data against records from the Kirch family, Hoffmann, Eimmart, Müller, Becker, Hertel, Sturm, Wideburg, Manfredi, and Derham, weaving a continental network of observations into a coherent whole. In one striking episode from January 1704, Giacomo Filippo Maraldi reported two widely separated sunspot groups on the same day, remarking that it had been a long time since such widely separated spots had been seen together, a vivid reminder of how unusual even modest solar activity had become during those years.

Among the technical fruits of the study is a new estimate of the Sun’s sidereal differential rotation during this quiet epoch. For a synodic rotation period of 27.5 days, the sidereal rotation rate works out to 14.08 degrees per day, slightly slower than the 14.18 degrees per day of the modern Carrington frame that serves as the standard reference for solar rotation today. The researchers derived rotation rates from pairs of measurements separated by hours, days, and full disk passages, tabulating them for individual spots and groups. The persistence of Joy’s law, the well-known tendency of sunspot groups to tilt with their leading spots closer to the Equator than their trailing spots, was also verified in these ancient data, suggesting that the underlying dynamics of magnetic flux emergence were operating much as they do now, even at the tail end of a grand minimum.

The time-latitude diagram constructed from the new catalogue, a butterfly-like plot showing where spots appear as the solar cycle progresses, is consistent with the previously available results from the analyses of the Parisian observations, including Nesme-Ribes’s surviving figure of average latitudes. This agreement is reassuring on two fronts: it validates the lost reconstructions of the 1990s and confirms that the new, independently derived dataset can safely replace them. The researchers also documented the Wilson effect in an unexpected place, noting that on 3 June 1703 La Hire observed a sunspot at the very edge of the disk appearing as a small depression in the limb, a phenomenon now understood to arise because spots are shallow structures rather than flat markings on a perfect sphere.

The day-to-day texture of the observations brings the era to life. La Hire frequently worked with telescopes of 16 feet and longer, switching instruments depending on conditions; on 18 January 1704 he could not discern a spot with a 3-foot tube but saw it clearly with a 16-foot one, likely because of poor contrast near the limb. Clouds, fog, and haze repeatedly interrupted the observing campaigns, and the journals candidly record blank Suns, vanished spots, and rare double appearances. In October 1705, two sunspot groups were seen simultaneously, an event the observers flagged as a rarity, and in November 1707 Cassini marveled that a spot had appeared in the northern hemisphere at a latitude of about 13 degrees, an occurrence he called extraordinary. Such details, once mere color, now feed quantitative reconstructions of the solar cycle’s recovery from its deepest recorded lull.

All of the reconstructed sunspot parameters, including daily latitudes, longitudes, areas, and counts, are provided in electronic supplementary materials accompanying the paper, giving modelers of the solar dynamo a fresh, high-resolution window onto the Sun’s behavior as it emerged from the Maunder Minimum. Understanding how the cycle recovered from that grand minimum is not just an exercise in historical astronomy; it informs how scientists assess the Sun’s capacity for prolonged lulls in activity and what such lulls might mean for climate and space weather on timescales of centuries. La Hire, sketching spots with quill and micrometer in the fog above Paris, could not have imagined that his notebooks would one day anchor twenty-first-century dynamo simulations. Three hundred years on, his patience is paying scientific dividends once again.

Subject of Research: Reconstruction of sunspot positions, areas, and counts from Philippe de La Hire's observations at the Paris Observatory during 1703 to 1710, in the late Maunder Minimum.

Article Title: Sunspot Observations by Philippe de La Hire from 1703 to 1710

Article References: Zolotova, N., & Vokhmyanin, M. (2026). Sunspot Observations by Philippe de La Hire from 1703 to 1710. Solar Physics, 301(9), Article 133. https://doi.org/10.1007/s11207-026-02719-w

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02719-w

Keywords: sunspots, Maunder Minimum, solar cycle, solar physics, Philippe de La Hire, Paris Observatory, solar rotation, Joy's law, historical astronomy, sunspot records, solar dynamo, space climate

The chain of causality that makes such reconstructions possible begins far beyond Earth. The Sun’s magnetic field, dragged outward by the solar wind, fills the heliosphere, the vast protective bubble surrounding the solar system. Galactic cosmic rays, high-energy particles arriving from outside, must fight their way through this magnetic shielding to reach Earth. When the Sun is magnetically active, the shielding strengthens and fewer cosmic rays penetrate; when the Sun quiets, the floodgates loosen. Upon entering the atmosphere, cosmic rays collide with nitrogen, oxygen and argon, spawning showers of secondary particles that forge rare radionuclides such as carbon-14 and beryllium-10. Carbon-14, once formed, is incorporated into carbon dioxide, absorbed by trees during photosynthesis and permanently archived in annual growth rings. Because a magnetically active Sun suppresses cosmic ray influx, the abundance of these isotopes in wood and ice is inversely correlated with solar activity, giving scientists a decipherable record stretching back thousands of years.

Deciphering it, however, is harder than it sounds. Previous reconstruction efforts relied on statistical regressions that mapped isotope-derived quantities onto sunspot numbers, and those regressions carried hidden dangers. As the new study’s authors, led by Chitradeep Saha of the University of Reading, point out, even a regression with an impressively high correlation coefficient can misfire if the data contain non-linearities, zero-level offsets, or uneven variance across amplitudes. The most notorious failure mode appears during grand minima, the extended intervals when solar activity collapses, such as the Maunder minimum of the seventeenth century. When regression equations calibrated on modern data are extrapolated to these unusually quiet conditions, they can yield sunspot numbers below zero. Values are often simply clipped to zero, but that crude fix distorts cycle averages and inflates estimates of the Sun’s total irradiance, which in turn muddies attempts to understand the Sun’s influence on past climate.

The Reading-led team, which also includes Mathew Owens, Mike Lockwood and Luke Barnard, together with colleagues at ETH Zurich, the University of Lancashire, the University of Oslo, Lund University and the University of Groningen, took a different path. Rather than inverting the physics with a regression, they ran it forward, over and over, in a Monte Carlo framework. The method, implemented in publicly released code under the name PRISM, begins by generating an ensemble of thousands of hypothetical sunspot cycles drawn from statistical priors: cycle amplitudes sampled from a log-normal distribution, cycle lengths from a Gaussian distribution centred on 10.5 years, and a random start offset for each window of time. Each trial cycle is then passed through a sequence of two semi-empirical forward models that translate sunspot number into open solar flux, the total magnetic flux threading the outer boundary of the corona, and then into the heliospheric modulation potential, a quantity describing how much energy cosmic rays lose as they traverse the heliosphere.

The forward models rest on decades of established solar physics. The first couples sunspot number to the emergence of new magnetic flux through a empirically optimised source function, balanced against a phase-dependent loss rate derived from solar cycles 13 through 24. The second model computes the modulation potential from the open flux together with the tilt and polarity of the heliospheric current sheet, following a formulation calibrated by Owens and colleagues in 2024. Crucially, the open solar flux evolves with memory: it accumulates from past sunspot activity and decays through magnetic reconnection, introducing a hysteresis that makes the inverse problem fundamentally non-unique. Multiple distinct sunspot histories can produce statistically indistinguishable modulation records, which is precisely why simple deterministic inversions break down.

To handle that non-uniqueness, the team employed Approximate Bayesian Computation, a statistical technique that sidesteps the need for an explicit likelihood function. In each sliding ten-to-fifteen-year window, ten thousand Monte Carlo realisations of sunspot cycles are propagated through the forward models and compared directly against the observed modulation potential using a weighted Euclidean distance. The best two percent of candidates, some two hundred realisations, are retained as samples from the approximate posterior distribution, and their spread provides rigorous, quantified uncertainty bounds reported as 68 percent highest-density intervals. Because the sunspot cycle amplitudes are constrained to be non-negative by construction, the resulting reconstruction can never produce the negative values that haunted earlier regression-based approaches, and it requires no post-hoc correction.

To test the method, the researchers applied it to two annual-resolution records of the modulation potential. The first, spanning 1845 to 2020, was derived from geomagnetic observations of open solar flux by Owens and colleagues. When used as the inversion target, the method recovered sunspot numbers and open flux in close agreement with the direct instrumental record maintained by SILSO, with a mean absolute error of just 19.25 megavolts, about three percent of the mean modulation potential. That success validated the technique and justified applying it to the second, far longer dataset: a radiocarbon-based modulation potential record covering 971 to 1932, reconstructed by Nicolas Brehm of ETH Zurich and colleagues from tree-ring carbon-14 measurements. Before feeding the tree-ring record into the inversion, the team cross-calibrated it against the geomagnetic record over their overlapping decades, applying an additive correction of 65.76 megavolts that statistical tests showed produced a near-perfectly symmetric, homoskedastic residual distribution.

The millennial-scale reconstruction that emerged is rich with detail. It captures the familiar grand minima and maxima of the past thousand years, including the Maunder minimum, the Spörer minimum, the Dalton minimum, and the double-peaked grand maximum the Sun passed through between 1900 and 2020. Crucially, the reconstructed open solar flux never falls to zero. Even during the deepest quiet of the Spörer minimum, the unsigned open flux dropped only to about 1.21 times ten to the fourteen webers in 1443, the lowest value in the entire record and well below anything observed in the telescopic era, yet still decisively nonzero. During the Maunder minimum the flux averaged around 2.63 times ten to the fourteen webers. This confirms that the solar dynamo never fully shuts down during grand minima but instead idles in a reduced, finite activity state, a conclusion consistent with flux transport dynamo models in which meridional plasma circulation sustains weak cycles and eventually drives recovery.

The new record also documents some striking extremes at the other end of the scale. The peak annual open solar flux of the twentieth century, reached in 1958, was about 10.96 times ten to the fourteen webers, the highest since the year 1200. Only three years in the entire millennium exceeded it, the largest peaking at roughly 14.21 times ten to the fourteen webers in 981 CE, shortly after the record begins. In other words, the era of telescopic observation has sampled a large fraction, but not all, of the Sun’s true dynamic range; deeper minima and higher maxima both occurred before instruments existed to see them. The reconstruction also flags three intervals around 993, 1052 and 1279 CE where proposed Miyake events, extreme solar particle storms recorded as abrupt radiocarbon spikes, contaminate the cosmic-ray-based record, and the authors conservatively mask these windows from their results.

Beyond its intrinsic appeal as a thousand-year diary of solar magnetism, the work has immediate practical value. Annually resolved, physically consistent sunspot numbers feed directly into reconstructions of total and spectral solar irradiance, which in turn constrain climate models exploring the Sun’s role in terrestrial temperature variability over past centuries. The uncertainty-quantified cycle amplitudes during grand minima provide empirical targets for solar dynamo theorists probing the minimum operating point of the solar cycle engine. The authors note that their forward model templates were built from modern, regular solar cycles, so reconstructions of grand minimum cycles should be treated as indicative rather than definitive, and that the additive cross-calibration between the two modulation potential datasets is itself a simplification. Even so, the framework offers what the team describes as a probabilistic ensemble of physically admissible solar histories rather than a single deterministic answer, and it opens the door to pushing the same technique further back in time as longer and older cosmogenic isotope records become available. The Sun, it turns out, kept meticulous records all along; the trick was learning to read them without breaking the laws of physics.

Subject of Research: Physics-constrained reconstruction of annually resolved sunspot numbers from millennial-scale heliospheric modulation potential records.

Article Title: Physics-Constrained Reconstructions of Sunspot Number from Millennial-Scale Annual Heliospheric Modulation Potential

Article References: Saha, C., Owens, M., Lockwood, M., Barnard, L., Brehm, N., Dalla, S., Herbst, K., Muscheler, R., & Wang, J. (2026). Physics-Constrained Reconstructions of Sunspot Number from Millennial-Scale Annual Heliospheric Modulation Potential. Solar Physics, 301(9), Article 144. https://doi.org/10.1007/s11207-026-02731-0

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02731-0

Keywords: sunspot number, solar cycle, heliospheric modulation potential, cosmogenic isotopes, radiocarbon, open solar flux, Maunder minimum, Spörer minimum, approximate Bayesian computation, space climate, solar dynamo, galactic cosmic rays

The study, published in the journal Solar Physics, was carried out by V. N. Obridko of the Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), M. M. Katsova of the Sternberg Astronomical Institute at Lomonosov Moscow State University, and D. D. Sokoloff of the Faculty of Physics at Lomonosov Moscow State University. Their work draws on the full record of soft X-ray flare monitoring by the Geostationary Operational Environmental Satellites, or GOES, which began in 1975 and has provided the standard classification of solar flares ever since. That continuous, homogeneous dataset is what makes a statistically meaningful look at flare behavior across multiple cycles possible.

Solar flares are classified by their peak soft X-ray brightness as measured by the GOES instruments, with X-class flares representing the most powerful events, each releasing energy equivalent to billions of megatons of TNT. The researchers focused on the great flares, from the relatively moderate X4 class up to the extreme X10 class and beyond, and asked a deceptively simple question: where on the solar disk do these events occur, and how does their location and frequency change as the solar cycle progresses? To answer it, they traced the latitudinal distribution of X-class flares throughout four cycles and compared the flare positions directly with the structure of the Sun’s large-scale magnetic field.

The picture that emerges is one of overlapping magnetic waves. Over the course of a solar cycle, the zones where sunspots and active regions appear migrate steadily from mid-latitudes toward the equator, a pattern known since the nineteenth century as Spörer’s law. At the same time, a second wave of activity belonging to the next cycle begins at higher latitudes and propagates poleward. The new analysis shows that the relatively weak members of the great-flare family, those in the X4 to X7 range, tend to occur at relatively high latitudes of roughly 15 to 20 degrees, precisely where these two waves of activity converge: one moving equatorward as the current cycle matures, and the other, the wave of the following cycle, directed poleward. These events are observed almost continuously during the one to two years before the cycle maximum.

The most powerful flares, however, tell a different story. The total number of powerful X-ray flares increases sharply during the maximum phase of the cycle, as expected from the sheer abundance of magnetically complex active regions. But the greatest events, those of X10 class and stronger, are largely absent during the growth phase of the cycle. Instead, they begin to appear one to two years before the maximum number of sunspots is reached, during the overlapping phase when different kinds of activity waves coexist on the Sun at relatively high latitudes. They then continue to appear throughout the declining phase, at the boundary that separates the wave of local fields from the poleward wave of the following cycle.

This timing is significant because it challenges the simplest expectation that flare intensity should peak exactly when sunspot numbers do. The researchers’ conclusion is that the greatest X-ray flares are not merely a byproduct of having many sunspots, but are tied to a specific magnetic configuration that arises when the outgoing and incoming activity waves overlap. In dynamo theory, the solar cycle is understood as a propagating wave of magnetic field generated by the interplay of turbulent plasma motions and the Sun’s rotation, and the interaction zones between successive waves provide conditions in which magnetic fields of opposite polarity and different origins can be forced together, building up the enormous stresses that power the largest eruptions.

The technical foundation of the analysis rests on comparing flare positions with synoptic maps of the photospheric magnetic field, which chart the distribution of magnetic flux across the solar surface over each solar rotation. The magnetic field data were drawn from the synoptic program at Stanford University’s Wilcox Solar Observatory, while sunspot numbers came from the World Data Center SILSO at the Royal Observatory of Belgium. By overlaying the latitudes of great flares on these magnetic structures, the team could show that flare sites are not randomly distributed within the activity belts but are preferentially located at the interfaces between magnetic regimes, where the wave of local active-region fields meets the large-scale poleward-migrating field of the next cycle.

The practical implications of this finding reach well beyond solar physics. Great X-class flares, particularly when accompanied by coronal mass ejections, are the primary drivers of space weather, capable of disrupting satellite operations, radio communications, GPS navigation, and power grids on Earth. The May 2024 G5-level geomagnetic storm, triggered by a barrage of eruptions from a single enormous active region, offered a vivid recent reminder of how much is at stake. If the largest flares preferentially occur in the years around and after sunspot maximum, and especially at the magnetic boundaries identified in this study, then space-weather forecasting could gain a valuable statistical tool: the periods of greatest extreme-flare risk may extend well past the sunspot peak, rather than ending with it.

The results also connect to a broader body of research on the extended solar cycle and the large-scale magnetic field. Earlier work by members of the same team has traced cyclic variations in the main components of the Sun’s large-scale magnetic field and examined the asymmetry introduced by the extended cycle, in which traces of the next cycle appear years before the current one fades. The new flare analysis adds an independent observational thread to this picture, suggesting that the overlap of activity waves is not a subtle theoretical curiosity but a physically consequential configuration that leaves a measurable imprint on the most energetic events in the solar system.

For now, the study’s conclusions rest on four cycles of GOES data, a sample that is large enough to reveal the pattern but still limited in the sense that each solar cycle has its own character. Some cycles are strong and some are weak, and the recalibration of the greatest GOES soft X-ray flare measurements across two Hale cycles remains an active area of research. Nevertheless, the message of the new work is clear and testable: to understand when the Sun will unleash its very worst, astronomers need to look not only at how many sunspots dot the surface, but at where two great waves of solar magnetism meet and mingle. As the current cycle progresses toward and past its maximum, the boundaries identified in this study will be among the most closely watched regions on the Sun.

Subject of Research: Cycle-dependent latitudinal occurrence of great soft X-ray solar flares in relation to overlapping solar magnetic activity waves

Article Title: Cycle Variation in the Occurrence of Great Soft X-ray Solar Flares

Article References: Obridko, V. N., Katsova, M. M., & Sokoloff, D. D. (2026). Cycle Variation in the Occurrence of Great Soft X-ray Solar Flares. Solar Physics, 301(9), Article 140. https://doi.org/10.1007/s11207-026-02732-z

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02732-z

Keywords: solar flares, X-class flares, solar cycle, space weather, solar magnetic field, GOES, solar dynamo, sunspots, Solar Physics, coronal mass ejections, activity waves, solar maximum

The green line at 530.3 nanometers is the brightest emission line in the solar corona, produced by highly ionized iron atoms, Fe XIV, stripped of thirteen of their electrons by the extreme coronal temperatures of roughly two million kelvin. Unlike the photospheric surface we see with the naked eye, the corona traces magnetic structures that arch high above active regions, and its emission intensity varies with the strength and distribution of the underlying magnetic field. Because ground-based observatories, coordinated through networks that produced the green corona database and the coronal index of solar activity, have monitored this emission consistently since the mid-twentieth century, the green line provides an exceptionally long and homogeneous record of large-scale coronal behavior that modern space-based instruments simply cannot match in duration.

On the sunspot side, the study departs from tradition in a crucial way. Conventional analyses of the solar cycle often rely on the sunspot number or the total sunspot area, both of which collapse the entire two-dimensional distribution of spottedness into a single scalar per day. Takalo instead constructed a Gaussian representation of the sunspot activity field, built from the individual areas and latitudes of every recorded sunspot group. This activity-field model preserves where on the solar disk the magnetic flux emerges, capturing the characteristic equatorward migration of sunspot belts as each cycle progresses and the poleward drift of its remnants. The result is a mathematical description of the large-scale spatial organization of solar magnetic activity that is far more realistic than any single-number index.

The central discovery of the study is a remarkably stable, double-peaked correlation structure in latitude. When coronal green-line emission at each latitude band is correlated against the modeled sunspot activity field at the same latitude, the correlation profile shows two strong maxima that track the well-known active-region belts on either side of the solar equator. These peaks, typically centered in the low and mid-latitudes where sunspot groups preferentially emerge, remain strikingly similar in shape and position from one cycle to the next. Even between weak cycles and strong cycles, and between even-numbered and odd-numbered cycles with their differing amplitudes and parity, the latitude profiles of the corona–sunspot relationship barely change, indicating that the large-scale coupling between photospheric activity and coronal emission is largely independent of how vigorous any particular cycle happens to be.

This finding carries weight because solar cycles are far from identical twins. Cycle 19, which peaked in the late 1950s, was the most active in the observational record, while Cycle 24 was notably feeble, and the even–odd alternation in cycle strength, sometimes called the Gnevyshev–Ohl rule, hints at deep-seated differences in the solar dynamo from one cycle to the next. Yet the corona appears to respond to the sunspot engine in a nearly invariant geometric pattern. The double-peaked structure is a direct signature of the fact that green coronal emission is strongest not randomly across the disk but precisely where active-region magnetic fields cluster, confirming quantitatively what decades of qualitative observation have suggested: the corona is, in a very real sense, a magnetic portrait of the activity belts painted in glowing iron light.

Perhaps the most subtle part of the analysis concerns timing. Using lag-correlation techniques, the study finds that the strongest correlations between the coronal emission and the sunspot activity field generally occur at positive lags, which would naively suggest that the corona follows the sunspots with a specific, measurable delay. But here the author applied a rigorous statistical safeguard. Surrogate-data tests, in which the temporal ordering of one record is scrambled while its statistical properties are preserved, show that these formal lag maxima are usually not statistically distinguishable from the correlations at neighboring lag values. The lag-correlation profiles instead display broad, flat positive-lag plateaus, meaning the apparent delay is not a sharply defined physical delay at all.

What the plateaus do reveal is something arguably more interesting: temporal persistence and memory in the large-scale coronal magnetic structures. Rather than the corona slavishly tracking each new burst of sunspot emergence after a fixed interval, the green-line emission behaves like a slowly evolving reservoir that integrates and smooths the photospheric activity underneath it. Magnetic fields introduced into the corona by emerging active regions persist, relax, and redistribute over extended timescales, so the coronal response is broad and smeared rather than impulsive. This interpretation aligns with a growing body of work emphasizing that the large-scale distribution of magnetic flux, spanning scales far beyond individual sunspots, governs the evolution of the corona as a global system.

The comparison between modeling approaches proved decisive in this regard. When the Gaussian activity-field representation was used as the predictor of coronal emission, it produced substantially stronger and more coherent correlations than conventional sunspot number or sunspot area measures ever achieved. In other words, knowing not just how many sunspots exist but where they sit on the disk at any moment allows a far better reconstruction of the green-line corona’s behavior. This supports the central physical conclusion of the paper: that it is the large-scale spatial distribution of magnetic activity, rather than the presence of individual sunspots alone, that controls the evolution of the large-scale corona. For modelers of the solar atmosphere, this is an invitation to move beyond scalar activity indices toward genuinely two-dimensional descriptions of the emerging flux.

The practical implications extend beyond pure solar physics. The green corona has long served as a proxy for solar activity in space-weather and solar-terrestrial research, and the coronal index built from it has been used to study everything from geomagnetic disturbance to long-term solar variability. Establishing that the corona’s response to sunspot activity is stable in latitude, amplitude-independent, and temporally diffuse strengthens confidence in using coronal records to extend our knowledge of solar behavior backward in time and, potentially, to refine reconstructions of past solar cycles. It also cautions against overinterpreting any single lag measurement as a physical delay mechanism, a lesson in statistical humility that applies across solar-terrestrial science.

Spanning seven decades and seven solar cycles, this analysis demonstrates that beneath the Sun’s famously variable surface behavior lies an unexpectedly disciplined architecture. The green-line corona and the sunspot belts are locked together in a latitude-dependent partnership whose geometry survives even the wildest swings in cycle strength, while their timing relationship reflects the lingering memory of magnetic structures rather than any simple cause-and-effect delay. As the Sun progresses through Cycle 25 and observers accumulate fresh coronal data, the stable patterns documented here provide a robust baseline against which any genuine, long-term change in solar behavior can be recognized. In the quiet green glow of iron atoms two million degrees hot, the Sun has written down, cycle after cycle, a remarkably consistent record of its own magnetic heartbeat.

Subject of Research: Latitude-dependent relationships between green-line coronal emission and sunspot activity across Solar Cycles 18–24

Article Title: Large-Scale Latitude-Time Relationships Between the Green-Line Corona and Sunspot Activity During Solar Cycles 18 – 24

Article References: Large-Scale Latitude-Time Relationships Between the Green-Line Corona and Sunspot Activity During Solar Cycles 18 – 24. (n.d.). https://doi.org/10.1007/s11207-026-02729-8

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02729-8

Keywords: solar corona, green coronal line, sunspots, solar cycle, solar magnetic fields, activity belts, lag correlation, surrogate data, solar physics, coronal index, solar dynamo, space weather

Cross-helicity is a measure of the correlation between the velocity and magnetic fluctuations in a turbulent conducting fluid. Unlike the more familiar magnetic helicity, which quantifies the knottedness and linkage of magnetic field lines and has been studied since the foundational work of H.K. Moffatt in the late 1960s, cross-helicity captures how intimately the swirling plasma motion is coupled to the magnetic structures it carries. When velocity and magnetic fluctuations are strongly correlated, cross-helicity becomes large, and its effects on transport, diffusion, and dynamo action can be profound. Recent reviews by Nobumitsu Yokoi have highlighted what he calls unappreciated cross-helicity effects in plasma physics, including anti-diffusion effects in both dynamo action and momentum transport, hinting that this quantity could reshape how physicists model magnetized turbulence.

The new analysis is grounded in a Kolmogorov-like phenomenology developed within the framework of what Bershadskii terms distributed chaos. In classical turbulence theory, the energy spectrum of a turbulent flow follows well-known power-law scaling relations, first articulated by Andrei Kolmogorov in 1941. But chaotic systems, including turbulent magnetohydrodynamic flows, can produce frequency power spectra whose decaying parts follow exponential rather than power-law forms. Exponential power spectra have been observed in a striking variety of chaotic settings, from magnetically confined laboratory plasmas studied by J.E. Maggs and G.J. Morales, to time series of sunspot numbers examined as far back as R.N. Bracewell’s pioneering analyses in the 1950s. In the distributed chaos picture, the exponential decay of the spectrum encodes the underlying deterministic but unpredictable dynamics of the system.

Bershadskii demonstrates, using results from laboratory dynamo experiments and direct numerical simulations of magnetohydrodynamic turbulence, that when the magnetohydrodynamic turbulence is sufficiently strong in chaotic, swirling flows, cross-helicity comes to dominate the decaying portion of the frequency power spectra of the generated magnetic field. The simulations draw on sparse-mode spectral methods of the kind developed by M. Meneguzzi and colleagues, while the laboratory context connects to experiments such as the Taylor-Green dynamo, in which bistability and chaos have already been documented by R.K. Yadav and collaborators. The essential message is that the interaction between swirl and field, quantified by cross-helicity, is not a minor correction to solar dynamo theory but a leading-order feature when turbulence is vigorous.

To test whether this picture applies to the real Sun, the study turns to observational records of the full-disc solar magnetic field and to the international sunspot number series maintained by the Solar Influences Data Analysis Center in Belgium, along with mean-field measurements from Stanford’s Wilcox Solar Observatory and vector observations from the SOLIS facility. The past two solar cycles have been notably weak in magnetic activity, a period that researchers such as K. Mursula and colleagues have described as a transition away from the Modern Maximum toward a weaker Sun. Bershadskii finds that the full-disc magnetic field during these cycles exhibits deterministic chaotic behavior, with the chaotic dynamics concentrated around the solar equator, precisely the region where sunspot activity emerges and migrates in the familiar butterfly diagram.

The finding that the field’s dynamics are concentrated near the equator resonates with independent evidence about the character of solar interior turbulence. Helioseismic analysis by S. Hanasoge, H. Hotta, and K.R. Sreenivasan has shown that turbulence in the Sun is suppressed on large scales and confined to equatorial regions, a result that surprised much of the community. A dynamo operating in a chaotic, swirling, equatorially concentrated flow environment is exactly the kind of system in which cross-helicity dominance of the spectral decay would be expected, according to the theoretical framework of the new paper. The consistency between theory, simulation, experiment, and observation strengthens the case that the distributed chaos approach captures something real about the solar dynamo.

Deterministic chaos is a concept with a long scientific lineage, tracing back to Edward Lorenz’s celebrated 1963 discovery of deterministic nonperiodic flow in atmospheric convection. A chaotic system obeys definite physical laws, yet its future evolution becomes practically unpredictable beyond a certain horizon because tiny uncertainties grow exponentially. The solar cycle, with its roughly eleven-year rhythm, its irregular amplitudes, and its occasional deep minima, has long tempted scientists to search for such behavior. Studies by C. Letellier and colleagues found evidence for low-dimensional chaos in sunspot cycles, while N. Platt, E.A. Spiegel, and C. Tresser modeled the intermittent character of the cycle, and P. Mininni and collaborators developed stochastic relaxation oscillator models. The new work adds a spectral fingerprint, the exponential decay associated with distributed chaos and cross-helicity, to this body of evidence.

The technical core of the argument lies in how the decaying parts of frequency power spectra distinguish between different underlying regimes. Purely stochastic processes tend to produce power-law spectra, whereas deterministic chaos in turbulent flows produces exponential spectral decay whose slope can be predicted by the Kolmogorov-like phenomenology of distributed chaos. When Bershadskii applies this diagnostic to the full-disc solar magnetic field data from the last two weak cycles, the observed spectra match the theoretical expectations for a system in which cross-helicity dominates. In other words, the correlation between the Sun’s plasma motions and its magnetic fluctuations is strong enough that it governs how magnetic energy is distributed across frequencies, a conclusion with direct implications for how dynamo models should be formulated and how the limits of solar activity prediction should be understood.

The implications extend beyond academic curiosity. Solar magnetic activity drives space weather that can damage satellites, disrupt radio communications, and stress terrestrial power grids. Forecasting the amplitude and timing of future cycles is a major practical goal, and approaches based on mean-field dynamo theory continue to be refined by groups such as V. Obridko and colleagues. If the full-disc magnetic field is genuinely governed by deterministic chaos with cross-helicity-dominated spectral dynamics, then there are hard, quantifiable limits to how far ahead reliable prediction can reach, however good the models become. At the same time, recognizing the system as chaotic rather than purely stochastic opens the possibility of short-term predictability techniques borrowed from nonlinear dynamics, exploiting the deterministic structure that chaos still preserves.

There is also a broader astrophysical payoff. Magnetic cycles and dynamos are observed on stars throughout the galaxy, and the physics uncovered in the solar context applies to magnetized plasmas everywhere, from planetary interiors to accretion disks and the interstellar medium. The study’s synthesis, linking swirling MHD turbulence, laboratory dynamo experiments, numerical simulation, and a half-century of solar monitoring, illustrates how a single theoretical lens, the distributed chaos framework enriched by cross-helicity, can bring coherence to phenomena that have often been treated separately. As the Sun continues its journey away from the Modern Maximum into a period of weaker activity, the chaotic, equator-concentrated dynamics identified in this work offer both a warning about the limits of prediction and an invitation to look more closely at the turbulent, helical plasma churning beneath the solar surface.

Subject of Research: Cross-helicity and deterministic chaotic dynamics of the full-disc solar magnetic field generated by a turbulent magnetohydrodynamic dynamo.

Article Title: Cross-Helicity and Chaotic Dynamics of Full-Disc Solar Magnetic Field

Article References: Bershadskii, A. (2026). Cross-Helicity and Chaotic Dynamics of Full-Disc Solar Magnetic Field. Solar Physics, 301(9), Article 141. https://doi.org/10.1007/s11207-026-02725-y

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02725-y

Keywords: solar dynamo, cross-helicity, magnetohydrodynamic turbulence, distributed chaos, full-disc magnetic field, sunspot number, solar cycle, deterministic chaos, power spectra, Kolmogorov phenomenology, swirling flows, solar physics