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