Solar Physics最新文献

{"title":"Large-Scale Latitude-Time Relationships Between the Green-Line Corona and Sunspot Activity During Solar Cycles 18 – 24","authors":"Jouni J. Takalo","doi":"10.1007/s11207-026-02729-8","DOIUrl":"10.1007/s11207-026-02729-8","url":null,"abstract":"<div><p>We investigate the latitude–time relationship between the solar green-line corona and sunspot activity during Solar Cycles 18 – 24 using homogeneous coronal observations and a Gaussian representation of sunspot activity fields. The activity-field model is constructed from individual sunspot areas and latitudes in order to describe the large-scale spatial organization of solar magnetic activity more realistically than traditional sunspot-number or sunspot-area indices. The analysis reveals a stable double-peaked latitude-dependent correlation structure centered on the active-region belts, where the strongest corona–sunspot correlations are observed. The latitude profiles remain remarkably similar from cycle to cycle, indicating that the large-scale relationship between coronal emission and photospheric activity is largely independent of cycle amplitude and parity. The lag-correlation profiles exhibit broad positive-lag plateaus in most cycles. Although formal lag-correlation maxima occur at positive lags, surrogate-data tests indicate that these maxima are generally not statistically distinguishable from neighboring lag values. The results therefore suggest temporal persistence and memory of large-scale coronal magnetic structures rather than a precisely defined physical delay. The Gaussian activity-field representation produces substantially stronger and more coherent correlations with the green-line corona than conventional sunspot measures, supporting the interpretation that the large-scale distribution of magnetic activity, rather than individual sunspots alone, governs the evolution of the large-scale corona.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Closer Look at Streamer Blowout Coronal Mass Ejections: Multi-Wavelength and Multi-Viewpoint Analysis of Morphology and Kinematics","authors":"Leonardo Di Lorenzo,&nbsp;Hebe Cremades,&nbsp;Fernando M. López,&nbsp;Laura A. Balmaceda,&nbsp;Dana-Camelia Talpeanu,&nbsp;Elke D’Huys,&nbsp;Marilena Mierla,&nbsp;Diego Lloveras,&nbsp;Regina Aznar Cuadrado","doi":"10.1007/s11207-026-02724-z","DOIUrl":"10.1007/s11207-026-02724-z","url":null,"abstract":"<div><p>We carry out a detailed multi-viewpoint and multi-wavelength analysis of three candidate streamer blowout coronal mass ejections observed in 2013. Extreme ultraviolet observations from PROBA2/SWAP and STEREO/EUVI were combined with white-light coronagraph data from SOHO/LASCO and STEREO/SECCHI to track the events from their early stage (<span>({&lt;},2~mathrm{R}_{odot })</span>) to heights below <span>(20~mathrm{R}_{odot })</span>. Using tie-point triangulation and Graduated Cylindrical Shell modeling, we derived continuous kinematic profiles of both the prominence and coronal mass ejection leading edge. The significantly longer durations of these events enable more detailed sampling of the coronal mass ejection leading edge, which in turn reveals a change in slope of the height-time profile at greater altitudes than for conventional coronal mass ejections. All three events exhibit a slow to fast kinematic evolution, with an initial slow-rise phase followed by a faster linear ascent. The transition occurs at heliocentric distances that approximately range 3.5 – 4.5 <span>({ mathrm{R_{odot }}})</span> and its sharpness differs from event to event. The third analyzed event shows a particularly shorter streamer swelling phase and a smoother kinematic transition than the other events. Our results highlight that these three events have kinematic signatures that distinguish them among the broader population of conventional coronal mass ejections, particularly regarding their timescales and the height at which the phase transition occurs. Potential field source-surface (PFSS) modeling, together with the observed white-light streamer locations, places the three events within the large-scale streamer-belt environment. However, discrepancies among the extrapolations arising from the use of different input magnetograms and source-surface heights highlight the limitations of PFSS modeling for uniquely determining the underlying magnetic topology of these events. In this respect, our analysis shows that the PFSS analysis and white-light coronagraph observations alone are not sufficient to unambiguously identify streamer blowout events, underscoring the need for magnetic field models that go beyond the simplifying assumptions of PFSS and provide a more realistic representation of the coronal magnetic configuration. The performed analysis was only possible through the use of multi-vantage observations, which were crucial for accurately reconstructing their 3D evolution, constraining their initiation heights, and characterizing their early evolution in relation to the surrounding magnetic configuration.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In-Flight Self-Calibration of the STIX Grid Transmission","authors":"Paolo Massa,&nbsp;Anna Volpara,&nbsp;Muriel Zoë Stiefel,&nbsp;Erhan Bilgili,&nbsp;Maik Degen,&nbsp;Olivier Limousin,&nbsp;Gordon J. Hurford,&nbsp;Säm Krucker","doi":"10.1007/s11207-026-02739-6","DOIUrl":"10.1007/s11207-026-02739-6","url":null,"abstract":"<div><p>The <i>Spectrometer/Telescope for Imaging X-rays</i> (STIX) on board <i>Solar Orbiter</i> provides imaging information on the X-ray sources in solar flares by modulating the emitted radiation with pairs of grids made of stacked tungsten layers. Optical measurements of the grids were taken on the ground and utilized to derive an initial model for the grid transmission. In this work, we describe an in-flight self-calibration procedure of the STIX grid transmission below 20 keV. This technique utilizes fully-illuminated pixels of the STIX Coarse Flare Locator (CFL) as a total flux monitor. The results show that the newly established transmission is lower than what was derived from the optical measurements. This is due to imperfections of the tungsten layers which reduce the effective slit width. Pre-flight optical measurements only measure the outer layers leaving these imperfections undetected. Using the new calibration, the photon spectra derived from individual sub-collimators are consistent within ∼ 2% between 8 and 20 keV. While fitted flare temperatures do not change with the new calibration, emission measure values increase by ∼ 13% compared to those obtained with the initial grid measurements.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02739-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SDOFMv2: A Multi-Instrument Foundation Model for the Solar Dynamics Observatory with Transferable Downstream Applications","authors":"Jinsu Hong,&nbsp;Daniela Martin,&nbsp;Joseph Gallego","doi":"10.1007/s11207-026-02740-z","DOIUrl":"10.1007/s11207-026-02740-z","url":null,"abstract":"<div><p>Foundation models have emerged as a promising paradigm in heliophysics by enabling transferable representations across diverse solar analysis tasks. Recent efforts such as SDOFM, Solaris, and Surya have demonstrated the potential of self-supervised learning for Solar Dynamics Observatory (SDO) data. In this work, we introduce <i>SDOFMv2</i>, a family of foundation models trained on more than 500,000 observations from the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) instruments spanning most of Solar Cycle 24 (2010 – 2018). The framework includes modality-specific and joint AIA+HMI models, a region-aware masking and reconstruction objective that explicitly distinguishes solar-disk, prominence, and background regions, and a denoising refinement stage designed to improve representation quality for challenging magnetic-field observations. Qualitative and quantitative evaluations demonstrate substantial improvements in reconstruction fidelity relative to SDOFMv1. Extensive ablation studies and downstream evaluations against SDOFMv1, Solaris, and Surya reveal that modality-specific and joint foundation models exhibit complementary strengths across reconstruction, solar activity regression, and solar wind classification tasks, providing one of the most comprehensive benchmarking studies of heliophysics foundation models to date. We further evaluate the learned representations on multiple downstream tasks, including missing-channel reconstruction, solar radio flux (<span>(F_{10.7})</span>) regression, and solar wind classification, while comparing against several state-of-the-art heliophysics foundation models. Across these evaluations, SDOFMv2 achieves competitive or superior performance, demonstrating the effectiveness of multimodal masked-autoencoding representations for solar observations. Besides, this study provides a benchmark evaluation framework that facilitates systematic evaluation of representation-learning approaches for solar observations. To facilitate reproducibility and future benchmarking efforts, model weights and source code are publicly available at github.com/Joaggi/sdofmv2.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02740-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bidirectional Autoregressive Tracking Method for Solar Filaments","authors":"Ying Li,&nbsp;Yunfei Yang,&nbsp;Xiaoli Zhang,&nbsp;Song Feng,&nbsp;Wei Dai,&nbsp;Bo Liang,&nbsp;Jianping Xiong","doi":"10.1007/s11207-026-02737-8","DOIUrl":"10.1007/s11207-026-02737-8","url":null,"abstract":"<div><p>Solar filament eruptions are one of the major drivers of hazardous space weather. Fragmented filament evolution, such as splitting, merging, and twisting, may provide important observational clues to pre-eruptive magnetic restructuring and instability. Therefore, precise tracking of the complete lifecycle of solar filaments is important for improving space weather monitoring and forecasting capability. In this study, a total of 630 H<span>(alpha )</span> full-disk solar images from BBSO, SMART, and the GONG network were used to build the dataset, including one training set and five testing sets. They represent different data sources, time intervals, and observation conditions. A new deep learning method, the bidirectional autoregressive tracking method, named BF-TrackFormer, is proposed to detect and track solar filaments. The designed backward autoregressive branch consisting of an ID Embedding Head and a Recheck Network effectively alleviates the problem of incomplete detection of fragmented filaments caused by splitting, as well as the problem of the solar filament lifecycle being divided into multiple discontinuous trajectories due to incomplete and missed detection. The average evaluation metrics <span>(mathit{IDF}1)</span>, <span>(mathit{MOTA})</span>, <span>(mathit{Prec})</span>, <span>(mathit{Reca})</span>, and <span>(mathit{IDSR})</span> of the five testing sets are 70.1%, 46.6%, 75.1%, 70.9%, and 10.1%, respectively. With decreasing intervals, the metrics get better and better. The experimental results show that BF-TrackFormer performs well in detection and tracking solar filaments, especially for fragmented filaments.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solar Doppler Velocity Results from the SDO EVE Level 4 Lines Data Product","authors":"Thomas N. Woods,&nbsp;Phillip C. Chamberlin,&nbsp;Dave Crotser,&nbsp;Andrew Jones,&nbsp;Rita Borelli,&nbsp;Don Woodraska,&nbsp;Gabi Gonzalez","doi":"10.1007/s11207-026-02727-w","DOIUrl":"10.1007/s11207-026-02727-w","url":null,"abstract":"<div><p>NASA’s Solar Dynamics Observatory (SDO) Extreme-ultraviolet Variability Experiment (EVE) observes solar full-disk extreme ultraviolet (EUV) spectral measurements over the spectral range of 6 nm to 106 nm with 0.1 nm spectral resolution. A new EVE data product called the EVE Level 4 Lines data product provides line profile-fit results for intensity, wavelength shift, and line width for 70 emission features. These emission features are from the chromosphere, transition region, and corona. While EVE’s Multiple EUV Grating Spectrographs (MEGS) were not specifically designed to measure intrinsic solar wavelength shifts (Doppler velocities), the high stability of solar pointing by the SDO spacecraft and the very stable thermal environment for SDO in a geosynchronous Earth orbit (GEO) enable detection of solar flare Doppler velocities with MEGS spectra at its modest 0.1-nm resolution. These Doppler velocity results are more accurate after making corrections for MEGS optical wavelength shifts based on wavelength and flare location relative to the MEGS optical center. These Doppler velocity results are most interesting for studying the plasma dynamical behavior during a flare’s impulsive phase and gradual phase. In particular for eruptive flares, there are often wavelength red shifts (downflows) for the transition region emissions with Doppler velocities of about 30 km/s and wavelength blue shifts (upflows) for the corona emissions with Doppler velocities of about − 80 km/s. The Doppler velocity maxima during flare events almost always occur during the impulsive phase of the flares.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02727-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sunspot Observations by Philippe de La Hire from 1703 to 1710","authors":"Nadezhda Zolotova,&nbsp;Mikhail Vokhmyanin","doi":"10.1007/s11207-026-02719-w","DOIUrl":"10.1007/s11207-026-02719-w","url":null,"abstract":"<div><p>French solar observations are the primary sunspot data source covering the Maunder Minimum. In the 1990s, the Parisian Observatory archives were extensively analyzed in a series of articles by Elisabeth Nesme-Ribes. Unfortunately, the solar data she reconstructed have been lost. Only a figure of the average sunspot latitudes is available. In this work, we re-analyze original reports by Philippe de La Hire. We collate measurements from La Hire’s hand-written observational journals with those published by Parisian observers in Memories of the French Royal Academy of Sciences. By combining the measurements with the drawings and engravings, we reconstruct sunspot transits across the solar disk that yield daily latitude and longitude for each individual sunspot and sunspot group. Sunspot areas and sunspot counts are also derived and provided in the electronic supplementary materials. The reconstructed sunspot parameters from La Hire’s observations are compared with contemporary records by the Kirch family, Hoffmann, Eimmart, Müller, Becker, Hertel, Sturm, Wideburg, Manfredi, and Derham. More precisely, the Parisian observations resolved the inconsistency in Hoffmann’s observations and pointed that Müller exploited another type of telescope. The supplementary materials provide the corrected sunspot parameters. The time-latitude diagram derived in this work is consistent with previously available ones from analyses of the Parisian observations, including La Hire. We also estimate the sidereal differential rotation rate and verify the persistence of Joy’s law.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MSTML-CMEP: A Multimodal Spatio-Temporal Feature-Based Machine-Learning Framework for CME Geoeffectiveness Prediction","authors":"Himani Mehta,&nbsp;Arjun Singh Rawat,&nbsp;Lovish Bhatia,&nbsp;V. S. Pandey,&nbsp;Preeti Verma","doi":"10.1007/s11207-026-02734-x","DOIUrl":"10.1007/s11207-026-02734-x","url":null,"abstract":"<div><p>Accurate prediction of coronal mass ejection (CME) geoeffectiveness is essential for space-weather forecasting, where missed geoeffective events and excessive false alarms can both reduce operational reliability. Existing methods based only on tabular CME parameters or isolated image information may not fully capture the combined morphological evolution and physical propagation characteristics of CMEs. In this study, we propose MSTML-CMEP, a multimodal spatio-temporal feature-based machine-learning framework for CME geoeffectiveness prediction using SOHO/LASCO C2 and C3 coronagraph image sequences together with structured CME physical parameters. The dataset comprises 340 CME events spanning 1996 – 2024, selected from the Richardson and Cane ICME catalogue to ensure high-confidence ground-truth labels, with geoeffectiveness defined by the geomagnetic disturbance threshold <span>(mathrm{Dst} leq -50)</span> nT. The proposed framework is therefore evaluated as a second-stage geoeffectiveness classifier for candidate Earth-directed CME events. For each event, frame-level spatial descriptors were extracted independently from C2 and C3 image sequences using a pretrained ResNet50 feature extractor. Temporal mean and standard deviation pooling were then applied to summarize event-level CME evolution. These video-derived descriptors were fused with tabular CME parameters and evaluated using baseline, boosting, and ensemble classifiers under imbalance-handling strategies, including Synthetic Minority Oversampling Technique (SMOTE), Adaptive Synthetic Sampling (ADASYN), and Borderline Synthetic Minority Oversampling Technique (Borderline-SMOTE). XGBoost without resampling achieved the strongest detection of geoeffective events, with 82% accuracy, probability of detection (POD) of 93%, an event-class F1-score of 86%, and skill scores of TSS = 0.594 and HSS = 0.617. Oversampling-based models, particularly Borderline-SMOTE with LightGBM, improved the operational error balance by reducing false-alarm tendency while maintaining competitive geoeffective-event detection. The results demonstrate that fusing LASCO C2/C3 spatio-temporal image descriptors with CME physical parameters provides an informative event-level representation for balancing missed geoeffective events and false alarms in space-weather forecasting.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oscillation Period Properties of Sunspots in the 8 – 10 (mu )m Infrared Band: A Multi-Dataset Analysis","authors":"Suo Liu","doi":"10.1007/s11207-026-02707-0","DOIUrl":"10.1007/s11207-026-02707-0","url":null,"abstract":"<div><p>Sunspot oscillations provide a unique probe of magnetic-plasma interactions in the solar atmosphere. This study investigates oscillation period properties of six single sunspot active regions observed in the 8 – 10 <span>(mu )</span>m infrared band using the Accurate Infra-red Magnetic-field Solar Telescope (AIMS) at Lenghu Observatory. Light curves were extracted from three regions (umbra, penumbra, quiet Sun) and wavelet analysis was applied to determine dominant and weighted mean periods, comparing four methods: pixel-wise wavelet analysis with mean aggregation, pixel-wise wavelet analysis with median aggregation, spatial mean prior to wavelet analysis, and spatial median prior to wavelet analysis. The weighted mean period appears more physically meaningful than the dominant period, better representing the multi-mode nature of solar oscillations. A consistent period sequence holds across all six datasets: umbra (U) &lt; penumbra (P) &lt; quiet Sun (Q), with typical values of 260 – 313 s, 286 – 374 s, and 294 – 382 s, respectively. This key pattern is recovered with 100% consistency by pixel-wise wavelet analysis with mean aggregation, pixel-wise wavelet analysis with median aggregation, and spatial median prior to wavelet analysis. The spatial mean prior to wavelet analysis shows 1/6 full consistency (complete U &lt; P &lt; Q hierarchy), 3/6 partial consistency (U &lt; P and U &lt; Q satisfied, but P ≥ Q), and 2/6 inconsistency (U &gt; P and/or U &gt; Q), with the partial cases preserving the critical umbral period being shortest. Spatial smoothing generally increases measured periods (by up to 21%), with the umbra showing the highest sensitivity. All peak ratios fall below 0.3 (mean <span>(0.14 pm 0.03)</span>), confirming the inherent multi-mode nature of solar oscillations. These findings provide important observational constraints for models of magneto-convection and wave propagation in sunspot atmospheres, establishing the 8 – 10 <span>(mu )</span>m band as a valuable diagnostic window for solar physics.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distribution of Magnetic Helicity and Energy with Height in Solar Atmosphere","authors":"Hongyan Li,&nbsp;Shangbin Yang,&nbsp;Haiqing Xu,&nbsp;Quan Wang,&nbsp;Anda Xiong,&nbsp;Peixin Luo","doi":"10.1007/s11207-026-02723-0","DOIUrl":"10.1007/s11207-026-02723-0","url":null,"abstract":"<div><p>Magnetic helicity and magnetic energy are key to understanding the solar dynamo and eruptions, and their three-dimensional distributions are of great significance. However, how these quantities vary with height remains poorly understood. Moreover, because the three-dimensional distribution depends on magnetic field extrapolation, determining the optimal extrapolation height from physical rather than empirical criteria remains an open problem. To address this issue, this work investigates the vertical distributions of magnetic helicity and magnetic energy in the solar corona within active regions. We analyze 150 active regions observed by the Solar Magnetic Field Telescope (SMFT) from 1988 to 2019, grouped by absolute magnetic flux, perform nonlinear force-free field (NLFFF) extrapolations, and compute the relative magnetic helicity with a finite volume method. It is found that an extrapolation height of at least 81 Mm retains 97% of the total magnetic helicity and energy while reducing computational costs by approximately 38% under the adopted configuration. This work provides important parameter constraints for the long-term statistical study of magnetic helicity in solar active regions.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}