{"title":"Linking solar magnetism, extreme solar particle events and stellar superflares.","authors":"Valeriy Vasilyev, Ilya Usoskin, Natalie Krivova","doi":"10.1098/rsta.2025.0261","DOIUrl":"https://doi.org/10.1098/rsta.2025.0261","url":null,"abstract":"<p><p>The magnetic field of the Sun drives a wide range of eruptive phenomena, from small-scale nanoflares to large flares and coronal mass ejections. While direct observations of solar activity cover only the past few decades, indirect evidence indicates that the Sun can occasionally produce events orders of magnitude stronger than any recorded ones in the modern era. Two complementary lines of evidence exist. First, extreme solar particle events (ESPEs) have been inferred from prominent spikes in cosmogenic isotope concentrations preserved in precisely dated natural archives such as tree rings and ice cores over the past 15 millennia. Second, high-precision space-borne photometry has revealed superflares on thousands of stars similar to the Sun. Whether these solar and stellar extremes are physically related remains an open question. We summarize the present state of understanding and discuss physical mechanisms that may link them. Although superflares and ESPEs are both extremely energetic manifestations of magnetic energy storage and release, their relationship does not appear to be one-to-one. Their occurrence and energetics probably depend on how magnetic flux and topology govern the partitioning of released energy between radiation, mass ejection and particle acceleration. This article is part of the Theo Murphy meeting issue 'Radiocarbon and cosmic radiation events'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2329","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148920736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maarten Blaauw, Marco A Aquino-López, J Andrés Christen, Elisabetta Dixon, Timothy Heaton
{"title":"'Ats us nai'-adaptive sampling strategies for the radiocarbon wiggle-match dating of trees.","authors":"Maarten Blaauw, Marco A Aquino-López, J Andrés Christen, Elisabetta Dixon, Timothy Heaton","doi":"10.1098/rsta.2025.0258","DOIUrl":"https://doi.org/10.1098/rsta.2025.0258","url":null,"abstract":"<p><p>Wiggle-match dating is an approach to obtaining very precise age estimates for 'floating' trees by combining multiple radiocarbon-dated annual rings with the known relative dating information contained within the tree's rings. Whereas individual radiocarbon dates often have multi-decadal to centennial uncertainties, wiggle-match dating can result in annual precision of both a tree's felling age and the ages of all other rings. Here, we develop a numerical sampling strategy, with the aim of helping researchers decide which rings to date in order to obtain annual precision with as few radiocarbon dates as possible so that they can say, 'ats us nai' ('that's us now' or 'we're done'). The sampling score is tested on a real-world case study as well as on simulated trees. The latter are used to investigate the effect of dating scatter, a tree's timespan and its felling age on both the precision and accuracy of the felling age estimates. The results are used to provide advice for future studies that aim to use wiggle-match dating to place trees on a secure calendar scale. This article is part of the Theo Murphy meeting issue 'Radiocarbon and cosmic radiation events'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2329","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148920725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Radiocarbon dating of subfossil trees from the southern French Alps and the extreme solar particle event at ca 14 300 cal yr BP.","authors":"Edouard Bard, Cécile Miramont, Frauke Rostek, Thibaut Tuna, Frédéric Guibal, Christian Marschal, Timothy Heaton","doi":"10.1098/rsta.2025.0289","DOIUrl":"https://doi.org/10.1098/rsta.2025.0289","url":null,"abstract":"<p><p>Subfossil pines from the banks of the Drouzet River in the southern French Alps provide a unique Late Glacial archive for reconstructing past solar activity. Dendrochronological analyses produced three floating chronologies together spanning ≈ 700 calendar years. High-precision 14C measurements obtained at CEREGE with the AixMICADAS accelerator mass spectrometer, and calibrated by Markov Chain Monte Carlo wiggle-matching against the IntCal20 absolute chronology, reveal a large and abrupt Δ14C increase of ≈ 30‰ at 14 300 cal yr BP. Carbon cycle model simulations forced with the GRIP 10Be flux record are compatible with this spike, confirming a sharp enhancement in cosmogenic isotope production linked to an extreme solar particle event (ESPE). Lower geomagnetic field intensity and reduced atmospheric CO₂ during the Late Glacial contributed to amplifying the ∆14C signal. Recent three-dimensional atmospheric 14C modelling indicates that this event represents the most powerful ESPE evidenced so far, much stronger than the largest ground-level enhancement of cosmic rays observed over the last 80 years of instrumental data. These results extend the ESPE record beyond the Holocene and demonstrate that subfossil wood has the potential to offer annually resolved evidence of ancient solar events, providing new constraints for radiocarbon calibration and solar-terrestrial interaction studies. This article is part of the Theo Murphy meeting issue 'Radiocarbon and cosmic radiation events'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2329","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148920695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fusa Miyake, A J Timothy Jull, Katsuhiko Kimura, Mihaly Molnar, Toru Moriya, Vladimir Myglan, Irina P Panyushkina, Andrea Scifo, Mirei Takeyama, Fuyuki Tokanai, Ilya Usoskin, Lukas Wacker
{"title":"Reassessment of a cosmic ray increase event in 1279/1280 CE using carbon-14 records of tree rings.","authors":"Fusa Miyake, A J Timothy Jull, Katsuhiko Kimura, Mihaly Molnar, Toru Moriya, Vladimir Myglan, Irina P Panyushkina, Andrea Scifo, Mirei Takeyama, Fuyuki Tokanai, Ilya Usoskin, Lukas Wacker","doi":"10.1098/rsta.2025.0264","DOIUrl":"https://doi.org/10.1098/rsta.2025.0264","url":null,"abstract":"<p><p>Extreme solar energetic particle events (ESPEs) rarely occur on the Sun, as known from cosmogenic isotope proxies, the primary being 14C measured in tree rings. Several such events have been identified in tree-ring 14C data as sharp spikes. The most recent spike, around 1279 CE, has been reported in several previous studies, but the results were controversial. Here, we investigated the possible occurrence of an ESPE around 1279 CE by analysing new high-precision Δ14C data from Japanese cedar and Altai larch tree samples for the period 1274-1288. Cross-comparisons of our datasets from different accelerator mass spectrometry facilities demonstrated their high reproducibility. Although our independent measurements do not yield a statistically significant single-year 14C spike, the result supports a small but significant Δ14C enhancement around 1279-1280. The Δ14C data were analysed by using two different carbon-transport models, Ticktack and SOCOL:14C-Ex, showing a robust result. We examined possible causes for the 14C increase, that is, ESPE and variations in galactic cosmic rays and concluded that the two scenarios cannot be distinguished with the existing datasets. Further investigations using ice-core records and 14C data from the southern hemisphere will be crucial to determine the cause of this event. This article is part of the Theo Murphy meeting issue issue 'Radiocarbon and cosmic radiation events'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2329","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148920816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Formal moduli problems and derived Lie algebras.","authors":"Joost Nuiten","doi":"10.1098/rsta.2024.0405","DOIUrl":"https://doi.org/10.1098/rsta.2024.0405","url":null,"abstract":"<p><p>We show that derived Lie algebras and restricted Lie algebras classify formal moduli problems on Artin divided power algebras and truncated algebras respectively. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derived deformation functors, Koszul duality and Maurer-Cartan spaces.","authors":"Jonathan Pridham","doi":"10.1098/rsta.2024.0407","DOIUrl":"https://doi.org/10.1098/rsta.2024.0407","url":null,"abstract":"<p><p>We summarize the chain of comparisons (Pridham 2011 Unifying derived deformation theories. Adv. Math. 224(3), 772-826, 2010. Corrigendum 228, 2554-2556 (doi:10.48550/arXiv.0705.0344)) showing Hinich's derived Maurer-Cartan functor gives an equivalence between differential graded Lie algebras and derived Schlessinger functors on Artinian differential graded-commutative algebras. We include some motivating deformation problems and analogues for more general Koszul dual pairs of operads. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic models and motivic structure on homotopy types.","authors":"Geoffroy Horel","doi":"10.1098/rsta.2024.0504","DOIUrl":"https://doi.org/10.1098/rsta.2024.0504","url":null,"abstract":"<p><p>We review some algebraic models for rational or integral homotopy types with the motivation of formalizing what it means for affine algebraic group to act on a homotopy type. We give some applications to the construction of a motivic structure on the homotopy type of algebraic varieties. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effective integration of Lie type algebras.","authors":"Bruno Vallette","doi":"10.1098/rsta.2024.0409","DOIUrl":"https://doi.org/10.1098/rsta.2024.0409","url":null,"abstract":"<p><p>This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Poincaré-Birkhoff-Witt theorems in higher algebra.","authors":"Omar Antolín-Camarena, Lukas Brantner, Gijs Heuts","doi":"10.1098/rsta.2024.0410","DOIUrl":"https://doi.org/10.1098/rsta.2024.0410","url":null,"abstract":"<p><p>We extend the classical Poincaré-Birkhoff-Witt (PBW) theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic relation between operads in spectra: the commutative operad is the quotient of the associative operad by a right action of the spectral Lie operad. This statement, in turn, is a consequence of a fundamental relation between different En-operads, which we articulate and prove. We deduce a variant of the Poincaré-Birkhoff-Witt theorem for relative enveloping algebras of En-algebras. Our methods also give a simple construction and description of the higher enveloping En-algebras of a spectral Lie algebra. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148841053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An operadic proof of the Bogomolov-Tian-Todorov theorem.","authors":"Joana Cirici, Geoffroy Horel","doi":"10.1098/rsta.2024.0399","DOIUrl":"https://doi.org/10.1098/rsta.2024.0399","url":null,"abstract":"<p><p>In this article, we explain an operadic proof of the Bogomolov-Tian-Todorov (BTT) theorem stating that the deformation theory of Calabi-Yau varieties is unobstructed. We also provide a short new proof of the non-commutative BTT for Calabi-Yau dg categories. Finally, we observe that our proof also produces partial results in positive characteristic. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2328","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148840936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}