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 was conducted by Dr. Roy Yaniv of the Hebrew University of Jerusalem and Sheba Medical Center, together with Prof. Yoav Yair of Reichman University and Prof. Colin Price of Tel Aviv University. Rather than relying solely on models or measurements taken at ground level, the team sent radiation sensors aloft on balloons launched from southern Israel on six occasions between 2014 and 2016. The balloons climbed to approximately 35 kilometres, well above the roughly 10-kilometre ceiling at which most passenger aircraft cruise, allowing the researchers to trace how atmospheric ionization and radiation change continuously from near the surface to the upper stratosphere.

The vertical structure that emerged from the measurements was strikingly clear. As the balloons ascended, radiation levels climbed steadily, reaching a pronounced maximum at around 17 to 20 kilometres above Earth before declining again at even greater heights. This peak is a well-known feature of atmospheric physics called the Regener-Pfotzer maximum. It arises because high-energy cosmic rays entering the atmosphere collide with molecules of air and generate cascades of secondary particles. Near the top of the atmosphere the incoming radiation is intense, but the air is too thin to produce many secondary particles; deeper down, the cascade is fully developed but the overlying atmosphere has already absorbed much of the primary flux. The result is an altitude band where radiation dose rates are at their highest, sitting comfortably above the cruising levels of civil aviation but close enough to influence the environment aircraft operate in.

At approximately 10 kilometres, the altitude at which commercial aircraft typically cruise, the researchers measured gamma-equivalent radiation dose rates of roughly 0.9 to 1.3 microsieverts per hour. Those numbers may sound modest, but they accumulate meaningfully over the thousands of hours that pilots, cabin crews and frequent flyers spend airborne each year. Notably, the levels recorded over Israel were relatively low compared with some higher-latitude regions, a difference the researchers attribute to the stronger geomagnetic shielding found over the Eastern Mediterranean. Earth’s magnetic field deflects charged cosmic particles, and its protective effect is strongest near the equator and weakest near the poles, so geography matters as much as altitude when estimating exposure.

Altitude, however, was only part of the story. The team also found that radiation levels varied systematically with the solar cycle. When the Sun is highly active, its magnetic field is carried outward by the solar wind and forms a protective bubble around the entire solar system, deflecting many of the galactic cosmic rays that would otherwise reach Earth. During periods of low solar activity, this shield weakens, and more of the energetic particles streaming from beyond the solar system penetrate the atmosphere. The balloon measurements reflected this modulation directly: the researchers observed higher radiation levels when solar activity was lower, quantifying the relationship with a negative correlation of r = -0.71. The authors are careful to stress that with only six balloon flights, the number of observations is limited, and the correlation should therefore be considered indicative rather than statistically definitive.

Extrapolating the observed relationship to solar-minimum conditions suggested that radiation levels at commercial aviation altitudes could rise by approximately 40 to 60 percent compared with solar-maximum conditions. The researchers caution that this estimate rests on extrapolation rather than on direct measurements taken under the most extreme quiet-Sun conditions, but the direction and rough magnitude of the effect are consistent with what is known about cosmic-ray modulation. The finding carries practical weight because the Sun is currently progressing through the declining phase of its activity cycle, and solar minima recur roughly every eleven years, meaning the aviation sector periodically operates in precisely the conditions where exposure is greatest.

We tend to think of the atmosphere above us as relatively stable, but the radiation environment at flight altitude is continuously shaped by processes taking place far beyond Earth, the researchers said. Our measurements show that the solar cycle has a measurable effect on the radiation environment experienced at aviation altitudes. By combining direct balloon observations with atmospheric radiation models, we can better understand when and where these levels change and improve the tools used to assess long-term exposure for aircrew and frequent flyers.

To test how well their observations aligned with established prediction tools, the team compared the balloon data with the EXPACS/PARMA atmospheric radiation model. The measured values closely matched the model’s predicted electromagnetic radiation component, generally agreeing within about 10 to 15 percent. The comparison also revealed an important nuance about what the instruments were actually measuring. According to the model, electromagnetic radiation represents only part of the total radiation environment at flight altitude: neutrons account for roughly 40 to 45 percent of the modeled total ambient dose, while photons, electrons and positrons contribute approximately 35 to 40 percent. The Geiger-Müller detectors carried by the balloons were primarily sensitive to photons and charged particles and had little direct sensitivity to neutrons. The reported measurements should therefore not be interpreted as the total radiation dose received by an airline passenger or crew member, but rather as a reliable indicator of the electromagnetic component of the atmospheric radiation field, one that can be used to anchor and validate broader dose assessments.

The findings have particular relevance for aviation, where flight crews and frequent flyers spend extended periods at altitudes where atmospheric protection from cosmic radiation is considerably weaker than at ground level. Occupational exposure limits apply to aircrew in many jurisdictions, and accurate assessment of cumulative dose depends on knowing how radiation varies with altitude, geographical location and solar conditions. The researchers note that continued monitoring is important for understanding long-term occupational exposure, especially as radiation levels shift over the solar cycle and differ substantially between polar and equatorial routes. Beyond aviation, the work offers a clearer picture of how radiation from space interacts with Earth’s atmosphere, and the researchers suggest that similar approaches, pairing relatively inexpensive balloon-borne measurements with established radiation models, could be used to track changes in the atmospheric radiation environment as solar conditions evolve over the coming years.

Subject of Research: Solar-cycle modulation of cosmic radiation dose rates at civil aviation altitudes measured by high-altitude balloons over Israel

Article Title: Cosmic radiation at flight altitudes rises when the sun is less active

Article References: Cosmic radiation at flight altitudes rises when the sun is less active. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: cosmic radiation, solar cycle, aviation, high-altitude balloons, galactic cosmic rays, Regener-Pfotzer maximum, radiation exposure, aircrew, atmospheric ionization, EXPACS/PARMA model, geomagnetic shielding, solar minimum

The research meticulously simulates the journey of high-energy particles, originating from the Sun and the vastness of interstellar space, as they encounter the Moon’s surface and then burrow into its dusty embrace. Solar energetic particles, unleashed during violent solar outbursts, can create intense but transient radiation spikes. In contrast, galactic cosmic rays, accelerated by supernovae and other cataclysmic cosmic events, represent a persistent, high-energy deluge that is far more challenging to shield against. The study tackles the intricate physics of how these charged particles lose energy as they traverse the lunar regolith, a powdery, loosely packed soil composed of fine dust and rock fragments. This energy loss is not uniform; it depends on the particle’s type, its initial energy, and the density and composition of the regolith it encounters, all factors that the simulation carefully accounts for.

One of the most striking aspects of this research is its focus on the subsurface environment. While the surface radiation levels are a known hazard, the way radiation patterns change with depth is critical for designing effective radiation shielding. The study reveals that even a relatively thin layer of regolith can offer significant protection, but the specific depth and thickness required vary dramatically depending on the energy and type of incoming radiation. This nuanced understanding is revolutionary for planning habitats and infrastructure, allowing for optimized use of local lunar materials for shielding, rather than relying solely on heavier, transported materials. The simulations map out radiation levels at various depths, providing a clear picture of where the “sweet spots” for safety and habitability might be found.

The concept of “leakage flux” is another vital contribution of this work. This refers to the amount of radiation that “leaks” through the regolith and continues to penetrate deeper, potentially affecting buried instruments or future underground structures. The simulations quantify this leakage, identifying thresholds below which radiation levels become significantly more manageable. This is particularly important for sensitive electronics used in scientific experiments or life support systems, which could be susceptible to even low levels of persistent radiation over extended periods. By understanding where this leakage is minimized, scientists can make informed decisions about where to place critical equipment and even future subterranean living quarters.

The computational power required for such a complex simulation is immense. The researchers employed advanced modeling techniques, likely incorporating sophisticated numerical solvers and vast datasets of particle interaction cross-sections. The study effectively models the stochastic nature of particle interactions, the scattering events, and the energy deposition processes that occur as these high-energy particles lose their momentum within the regolith. This level of detail allows for a probabilistic understanding of radiation exposure, providing a more realistic assessment of the risks involved in lunar exploration and settlement. It’s a testament to the advancements in computational physics that such intricate scenarios can now be accurately modeled.

The study’s findings have immediate and profound implications for the feasibility of permanent lunar bases. Currently, concepts for lunar habitats often involve extensive shielding, which can be prohibitively heavy and expensive to transport from Earth. However, this research suggests that by strategically utilizing the lunar regolith, substantial protection can be achieved. The simulations provide data that can inform the design of habitats buried beneath the surface or constructed with thick regolith walls, leveraging the Moon’s own material as a natural radiation shield. This reduces reliance on external resources and makes long-term lunar habitation a more attainable goal.

Furthermore, the research sheds light on the long-term radiation effects on lunar assets. Equipment designed for space, even with radiation hardening, has its limits. The persistent bombardment by galactic cosmic rays, even after attenuation by the regolith, can still contribute to degradation over prolonged periods. Understanding these cumulative effects is crucial for ensuring the reliability and lifespan of scientific instruments, communication systems, and the very infrastructure that will support human life on the Moon. The simulations offer a predictive capability, allowing engineers to anticipate and mitigate these long-term degradation pathways.

The simulation models not only proton and heavy ion radiation from solar events but also the high-energy electrons and protons that constitute galactic cosmic rays. Each of these particle types interacts differently with matter, and the research meticulously accounts for these distinct interactions. For instance, heavier ions can cause more localized and intense damage, while high-energy protons can penetrate deeply. The interplay of these different particle fluxes and their modified spectra as they descend into the regolith is visualized and quantified, painting a comprehensive picture of the subterranean radiation environment.

The visual representation of these simulations, while not fully detailed in the text, is suggested to be highly impactful. Imagine intricate cross-sections of the lunar subsurface, color-coded to represent varying radiation intensities at different depths, with particle trajectories mapped out as they are deflected, absorbed, or cascade into secondary particles. Such visualizations would undeniably make the abstract concepts of particle physics tangible and underscore the importance of this research for a wider audience, potentially sparking significant public interest in lunar exploration and astrophysics.

The study’s authors, Wei, Huang, and Cheng, are likely employing sophisticated radiation transport codes, possibly building upon existing frameworks like GEANT4 or MCNP, but with specialized adaptations for the lunar regolith’s unique properties. The accuracy of these simulations hinges on precise knowledge of the regolith’s density, porosity, and elemental composition, which themselves can vary across the lunar surface. Future work might involve validating these simulations with in-situ measurements from lunar surface missions.

The potential for viral dissemination of this research lies in its direct relevance to ambitious future space endeavors, such as the Artemis program and private lunar missions. As humanity gears up to return to the Moon with the intention of establishing a sustained presence, detailed environmental data is critical. This study provides precisely that, offering a scientific foundation for the engineering and safety protocols needed for lunar exploration. The narrative of building a future on another celestial body, made safer by understanding its hidden dangers, is a powerful one.

Beyond human safety, the implications for scientific discovery are also immense. Many proposed lunar science experiments require ultra-low background radiation environments. Understanding how the regolith can shield sensitive detectors from cosmic rays is crucial for siting these observatories. Whether it’s for detecting faint neutrino signals, conducting precise gravitational wave measurements, or searching for evidence of past life, the subterranean radiation environment dictates the feasibility and success of such ventures.

The study’s contribution to the field of astrobiology should also be noted. While the Moon is not considered a primary candidate for extant life, understanding radiation environments on celestial bodies is fundamental to the broader search for life in the universe. The principles and techniques used in this lunar radiation simulation could be adapted to assess the habitability of other planetary bodies, such as Mars, where subsurface protection from radiation is also a critical factor.

In essence, this research acts as a vital blueprint for venturing into the lunar frontier responsibly. It highlights that the Moon, while seemingly barren, possesses its own complex environmental challenges that require deep scientific understanding. By simulating the relentless bombardment of space particles and their intricate interaction with lunar soil, Wei, Huang, and Cheng have provided an invaluable tool for ensuring that humanity’s next steps on the Moon are not only ambitious but also safe and sustainable for the long term.

The very act of simulating the unseen forces that shape potentially habitable environments, even on a seemingly airless body like the Moon, fuels our collective imagination and our drive to explore. This detailed look at particle radiation and its penetration into the lunar subsurface is more than just academic; it’s a crucial step in transforming science fiction dreams of moon colonies into tangible, achievable realities, grounded in rigorous scientific inquiry and advanced computational modeling.

Subject of Research: Subsurface particle radiation and leakage flux on the Moon from solar energetic particles and galactic cosmic rays.

Article Title: Simulation of subsurface particle radiation and leakage flux on the moon from solar energetic particles and galactic cosmic rays

Article References:

Wei, Z., Huang, Y. & Cheng, Y. Simulation of subsurface particle radiation and leakage flux on the moon from solar energetic particles and galactic cosmic rays.
Eur. Phys. J. C 85, 876 (2025). https://doi.org/10.1140/epjc/s10052-025-14619-7

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-14619-7

Keywords**: Lunar radiation, particle physics, space weather, cosmic rays, solar energetic particles, regolith, radiation shielding, space exploration, astrobiology, computational physics