Solar PhysicsPub Date : 2026-06-12DOI: 10.1007/s11207-026-02689-z
Charlotte Proverbs, Daniel Brown
{"title":"SSTrack: An Automatic Sunspot Identification and Tracking Algorithm to Support the Measurement of Sunspot Rotation","authors":"Charlotte Proverbs, Daniel Brown","doi":"10.1007/s11207-026-02689-z","DOIUrl":"10.1007/s11207-026-02689-z","url":null,"abstract":"<div><p>Motions of sunspots cause the coronal magnetic field to become deformed with the effect that energy can be stored in the coronal magnetic field. This energy can be released through events such as solar flares. Sunspots are known to rotate about their umbral centres, and this rotation contributes to the build-up of energy within an active region that can be released during an eruptive solar event. To understand the relationship between rotational forms of sunspot dynamics and solar activity, a large, unbiased statistical survey of sunspots is desirable.</p><p>To generate such a statistical sample, a fully automatic sunspot identification and tracking method, SSTrack, is developed. This method is tested on a previously analysed four-month sample of active regions generated using a semi-automatic sunspot rotation tool. The new method is designed to be applied to long periods of observations so that large samples can be efficiently obtained, while working at a high-cadence to effectively capture fine-scale-behaviour, such as sunspot splitting and mergers. SSTrack is able to identify fifty-four of the fifty-six sunspots in the four-month sample as well as an additional forty-three sunspots not found by the semi-automatic method. It is able to identify many of the fifty-four commonly found sunspots earlier and track them for longer than the semi-automatic method. The rotation about umbral centres is calculated for each sunspot using the tracking data from both methods, and when considering only overlapping observations per sunspot the methods show good agreement. The semi-automatic method is found to detect greater rotation when a sunspot undergoes fragmentation due to the changing structure overly influencing the determination of the centre of the sunspot.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02689-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237080","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":"Deep Learning with Magnetic Parameter Constraints for Short-Term Prediction of Solar Active Region Vector Magnetic Fields","authors":"Yuqing Zhou, Hui Liu, Zhenyu Jin, Yuyang Li, Sizhong Zou, Jiaben Lin, Mingfu Shao, Zhuoheng Huang","doi":"10.1007/s11207-026-02687-1","DOIUrl":"10.1007/s11207-026-02687-1","url":null,"abstract":"<div><p>Forecasting the dynamic evolution of solar magnetic fields is a critical technique for enabling space-weather warnings. Addressing the limitations of existing methods in predicting all vector magnetic field components and in maintaining consistency with solar surface magnetic-field-related quantities, this study proposes a deep learning prediction method that integrates dynamic masks of active regions with multiple magnetic parameter constraints. By constructing a three-channel representation of vector magnetic fields, applying dynamic masks to enhance attention to strong-field regions, and incorporating multi-parameter magnetic parameter constraints, we developed an end-to-end short-term (12-hour) predictive model of solar vector magnetic field evolution. Using SDO/SHARP vector magnetogram data, the model predicts and analyses field evolution across all components. Quantitative evaluations demonstrate that our approach achieves horizon-averaged structural similarity index measure (SSIM) of 0.912 (per-hour range: 0.909 – 0.916) and correlation coefficient (CC) of 0.998 for the radial component <span>(B_{r})</span> (root-mean-square error (RMSE) 13.0 – 21.0 G); the horizontal components achieve <span>(B_{phi })</span> SSIM 0.760 – 0.800 (CC 0.910 – 0.945, RMSE 38.5 – 50.0 G) and <span>(B_{theta })</span> SSIM 0.728 – 0.750 (CC 0.895 – 0.920, RMSE 38.5 – 49.0 G). The model maintains unsigned magnetic-flux prediction errors at 7.82% (95% confidence interval (CI): ±0.11%). These results demonstrate strong image-domain performance together with consistency under the magnetic-parameter diagnostics used here, suggesting initial potential for supporting future space weather forecasting efforts.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236891","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}
Solar PhysicsPub Date : 2026-06-08DOI: 10.1007/s11207-026-02688-0
Chloe Pistelli, Momchil E. Molnar, Giuliana de Toma, Joseph Plowman
{"title":"Spectroscopic He i 1083 nm Prominence Eruption Observations in the Middle Corona with MLSO/UCoMP","authors":"Chloe Pistelli, Momchil E. Molnar, Giuliana de Toma, Joseph Plowman","doi":"10.1007/s11207-026-02688-0","DOIUrl":"10.1007/s11207-026-02688-0","url":null,"abstract":"<div><p>Coronal mass ejections (CMEs) are a major driver of space weather as they propagate through the heliosphere. Many CMEs have associated prominence material entangled in their magnetic structure which contains cooler plasma. This cooler CME component contains significant amounts of neutral elements, which emit brightly in permitted atomic lines. It has been hypothesized that permitted transitions of neutral elements in eruptions could be used for inferring the magnetic field in CMEs, which is crucial for space weather forecasting. We present observations made with the Upgraded Coronal Multi-channel Polarimeter (UCoMP) in He <span>i</span> 1083 nm that clearly show the presence of neutral helium in eruptive prominences associated with CMEs as they propagate through the lower and middle corona. We find that solar prominence eruptions can be detected in He <span>i</span> 1083 nm observations up to the edge of the instrument field of view at ≈ 2 solar radii, providing valuable spectral information that complements existing extreme ultraviolet and white-light coronal imaging observations. These results illustrate the capability of UCoMP to probe the dynamic behavior of prominence eruptions, allowing for their line-of-sight velocity estimation, and potentially improving space weather forecasting by enabling earlier and more accurate identification of Earth-directed eruptions.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02688-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236870","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}
Solar PhysicsPub Date : 2026-06-04DOI: 10.1007/s11207-026-02645-x
Vicki Toy-Edens, Wenli Mo, Angelos Vourlidas, James Mason
{"title":"An Algorithm for the Onboard Detection of Solar Flare Onset","authors":"Vicki Toy-Edens, Wenli Mo, Angelos Vourlidas, James Mason","doi":"10.1007/s11207-026-02645-x","DOIUrl":"10.1007/s11207-026-02645-x","url":null,"abstract":"<div><p>The ability to identify solar flare precursors in real-time onboard spacecraft would enable both timely space-weather alerts and dynamic observing mode changes to capture the early phases of flares. In this work, we present a new algorithm capable of predicting flare onset hours in advance. The method leverages the seven extreme ultraviolet (EUV) filters aboard the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA). Our approach triggers on background-subtracted 304 Å regions whose mean values exceed a threshold and then searches for a characteristic signature in the ratios of normalized EUV filters within the triggered region. The algorithm is novel as it is designed from the ground up with onboard computational constraints in mind. The minimum required onboard buffer time to recover 80% of the potential flare detections is 160 minutes. The algorithm, tested on 2587 flares observed by Geostationary Operational Environmental Satellites (GOES) of class ≥ C1.0, achieves a 69.5% detection rate with a 35% false positive rate or a true skill statistic of 34.5%. The performance is comparable to some state-of-the-art flare forecasting methods but with the added advantage of real-time detection designed for spacecraft operations.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172469","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}
Solar PhysicsPub Date : 2026-06-04DOI: 10.1007/s11207-026-02666-6
Arron Augustine D’Awarave, Vemareddy Panditi
{"title":"Statistical Study of Intense Geomagnetic Storms and Their Solar Origins over the Period 1996 – 2025","authors":"Arron Augustine D’Awarave, Vemareddy Panditi","doi":"10.1007/s11207-026-02666-6","DOIUrl":"10.1007/s11207-026-02666-6","url":null,"abstract":"<div><p>Using in situ geomagnetic and solar wind observations, we present a comprehensive list of intense geomagnetic storms (GMSs) that occurred between 1996 and 2025, covering Solar Cycles (SCs) 23, 24, and the ongoing SC 25. The study focuses on storms with (Dst <span>(le -100)</span> nT), primarily driven by interplanetary coronal mass ejections (ICMEs), with the main objective of identifying and characterizing their solar source regions. Remote-sensing observations from the Solar and Heliospheric Observatory (SOHO), Solar TErrestrial RElations Observatory (STEREO), and Solar Dynamics Observatory (SDO) across multiple wavelengths are used to trace GMSs back to their solar origins. A total of 139 intense storms are identified, of which 120 are ICME-driven and 19 are associated with corotating interaction regions (CIRs). ICME-driven storms reach significantly larger intensities (Dst <span>(=-422)</span> nT) compared to CIR-driven storms (Dst <span>(=-130)</span> nT). With six cases being linked to stealth CMEs, this list of storms captures two super storms during SC 25, including the May 2024 event (Dst <span>(=-406)</span> nT), the strongest in two decades. The following statistical conclusions are drawn: i) Storm occurrence and intensity are found to correspond well with solar cycle strength and sunspot number, with SC 23 producing the 87 storms, including 10 super storms, SC 24 producing 26 without super storms, and SC 25 producing 26 storms with two super storms. ii) The CME source regions exhibit a pronounced east–west asymmetry, with a majority (69%) originating from the western solar hemisphere. iii) Storm intensity shows weak dependence on flare strength and CME speed, although extreme storms are associated with higher average CME speeds and large flare strengths. iv) The Dst index has a strong correlation (0.74) with peak southward <span>(B_{z})</span>, total magnetic field strength, and a linear fit arrives at the statistical relation that the Dst is five times the peak <span>(B_{z})</span>. v) The Dst index has a significant correlation with the electric field <span>(E_{y})</span>, with a linear relation Dst <span>(=6.1times E_{y} - 89.3)</span>. These results reinforce the dominant role of ICME magnetic structure in driving severe geomagnetic activity and provide an updated perspective on the solar origins and geoeffectiveness of intense geomagnetic storms across the solar cycles.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172392","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}
Solar PhysicsPub Date : 2026-06-04DOI: 10.1007/s11207-026-02686-2
Varun Soman, Amaranathan Sabarinath
{"title":"Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25","authors":"Varun Soman, Amaranathan Sabarinath","doi":"10.1007/s11207-026-02686-2","DOIUrl":"10.1007/s11207-026-02686-2","url":null,"abstract":"<div><p>Reliable forecasts of solar-cycle activity are important for anticipating space-weather conditions that can affect satellites, communication systems, and power infrastructure. We present a shape-based analog forecasting method that identifies historical solar cycles — or analogs — whose evolution most closely resembles the target cycle, using their subsequent behaviour to project future solar activity. Shape similarity is measured using Dynamic Time Warping (DTW), a technique that can compare cycles with different rise rates, durations, and peak timings.</p><p>The method operates in two modes. In baseline mode, no observations from the target cycle are used, and analogs are selected by comparing historical cycles with a smooth reference curve. In real-time mode, the forecast is updated each month as new observations arrive. Forecast uncertainty is estimated by drawing errors from historical cycles at the same phase as the month being forecast, so that prediction intervals are wider near solar maximum — where errors are largest — and narrower near minimum.</p><p>In strict out-of-sample tests on Solar Cycles 21 – 24, where each target cycle is forecast using only earlier historical cycles, the method achieves a mean absolute error of 26 smoothed sunspots in baseline mode and 19 smoothed sunspots in real-time mode. For Solar Cycle 25, the baseline forecast made without using Cycle 25 observations gives a peak near 189 smoothed sunspots, while the real-time forecast using observations through December 2024 peaks near 173 smoothed sunspots around early 2024, consistent with observations. A baseline projection for Solar Cycle 26 gives a peak near 143 smoothed sunspots.</p><p>Because each forecast is built from named historical analogs, the method is transparent, easy to interpret, and straightforward to update as new observations become available.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172470","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}
Solar PhysicsPub Date : 2026-06-04DOI: 10.1007/s11207-026-02676-4
Pradeep Kayshap, Gayathri Hegde, Z. E. Musielak, K. Murawski, Tobías Felipe
{"title":"Height Variations of Magnetoacoustic Cutoff Frequency in the Solar Atmosphere","authors":"Pradeep Kayshap, Gayathri Hegde, Z. E. Musielak, K. Murawski, Tobías Felipe","doi":"10.1007/s11207-026-02676-4","DOIUrl":"10.1007/s11207-026-02676-4","url":null,"abstract":"<div><p>The determination of the cutoff frequency in real solar observations under different local physical conditions is an important and underexplored aspect of waves in solar physics. This work utilizes the near ultraviolet (NUV) spectrum of the quiet sun (QS), observed by the Interface Region Imaging Spectrograph (IRIS) on November 16th, 2013, in sit-and-stare mode. It contains several absorption and emission lines that form at different heights between the photosphere and chromosphere. Cross-wavelet analysis is performed on Doppler velocity time series of pairs of spectral lines sampling different atmospheric layers to estimate the cutoff frequency at six different heights between the photosphere and chromosphere. It is found that the cutoff frequency increases with height from around 3.0 mHz at 0.38 Mm (photosphere) to around 8.5 mHz at 1.2 Mm (chromosphere). Higher chromospheric heights show indications of standing oscillations. The presented observational results are compared with those previously obtained, and serve as a benchmark to refine theoretical models that predict variations of cutoff frequencies in the solar atmosphere.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02676-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172393","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}
Solar PhysicsPub Date : 2026-06-03DOI: 10.1007/s11207-026-02677-3
S. W. Good, J. Lalueza Puértolas, A.-S. M. Jylhä, E. K. J. Kilpua
{"title":"The Correlation Length of Turbulence in Magnetic Clouds","authors":"S. W. Good, J. Lalueza Puértolas, A.-S. M. Jylhä, E. K. J. Kilpua","doi":"10.1007/s11207-026-02677-3","DOIUrl":"10.1007/s11207-026-02677-3","url":null,"abstract":"<div><p>The large-scale limit or outer scale of turbulence in the solar wind is associated with the correlation length of the magnetic field. Determining correlation lengths from magnetic field time series in magnetic clouds is complicated by the presence of the global flux rope: without removal of the flux rope trend, correlation length measurements will be sensitive to the flux rope as well as the turbulence, and give overestimates of the outer scale when turbulence amplitudes at the outer scale are small relative to the flux rope amplitude. We have used force-free flux rope fits to detrend magnetic field time series measured by <i>Parker Solar Probe</i> in two magnetic clouds and calculated the turbulence correlation length in the clouds using the detrended data. The detrended correlation length in terms of the proton inertial length, <span>(d_{p})</span>, was <span>(2.7times 10^{4} d_{p})</span> in one cloud (observed at 0.77 au) and <span>(1.6times 10^{4}d_{p})</span> in the other (observed at 0.39 au), significantly smaller than the values obtained without detrending. Increments in the flux rope fits scaled equivalently to a <span>(k^{-3})</span> wavenumber power spectrum; this contribution from the flux rope considerably steepened the total spectrum at the largest scales but had a negligible effect in the inertial range, where scaling in both clouds equivalent to <span>({sim}, k^{-5/3})</span> was observed. Finally, we discuss the possible relation of turbulence correlation lengths to mesoscale structure in magnetic clouds.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-026-02677-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172415","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}
Solar PhysicsPub Date : 2026-06-02DOI: 10.1007/s11207-026-02662-w
Bivek Pradhan, Utpal Deka
{"title":"Parametric Decay Instability as a Source of Turbulence in an Open Leakage Permitting Vertical Solar Coronal Domain","authors":"Bivek Pradhan, Utpal Deka","doi":"10.1007/s11207-026-02662-w","DOIUrl":"10.1007/s11207-026-02662-w","url":null,"abstract":"<div><p>The origin and maintenance of turbulence in the solar corona remain a fundamental problem in space plasma physics. Parametric Decay Instability (PDI) as a potential mechanism for generating turbulence in an open leakage-permitting vertical coronal domain is investigated using PLUTO, magnetohydrodynamics (MHD) code. We simulate the evolution of an Alfvén wave driven by a localized broadband (0.07 – 0.71 Hz) Hermite-Gaussian envelope in a plasma of <span>(beta = 0.3)</span>. PDI signatures emerge around <span>(tapprox 20)</span> simulation units, with backward-propagating Alfvén waves growing exponentially alongside compressive (acoustic) fluctuations. Backward-to-forward Alfvén wave ratios approach unity, and compressive amplitudes become comparable to the transverse components, indicating efficient nonlinear energy transfer. Spectral analysis reveals a <span>(k^{-2})</span> power law over a finite range, characteristic of a weak-MHD-like turbulence cascade, while increment Probability Distribution Functions yield non-Gaussian kurtosis, <span>(Kin )</span> 6 - 10, signalling the onset of a weak, intermittent MHD-like turbulent state in this 2.5D configuration.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172308","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}
Solar PhysicsPub Date : 2026-06-02DOI: 10.1007/s11207-026-02661-x
Mariano Poisson, Marcelo López Fuentes, Cristina H. Mandrini, Pascal Démoulin
{"title":"Tilt Angle of Bipolar Active Regions from Solar Cycle 23","authors":"Mariano Poisson, Marcelo López Fuentes, Cristina H. Mandrini, Pascal Démoulin","doi":"10.1007/s11207-026-02661-x","DOIUrl":"10.1007/s11207-026-02661-x","url":null,"abstract":"<div><p>Active regions (ARs) are the photospheric manifestation of magnetic flux ropes (FRs) emerging from the solar interior. A key parameter in their evolution is the tilt angle, defined as the inclination of the AR polarity axis relative to the solar equator. Despite its central role in flux-transport dynamo models, tilt measurements are affected by systematic biases—most notably magnetic tongues—particularly during the emergence phase. In this work we analyze tilt estimates for 108 bipolar active regions from Solar Cycle 23 using two methodologies: (1) the conventional magnetic barycenter method and (2) a Bayesian FR model that fits observed magnetograms with a synthetic model of an emerging twisted toroidal flux tube. We find notable differences between the two estimates, ranging from about <span>(30^{circ })</span> at early stages of emergence to <span>(sim 10^{circ })</span> near the end. Our analysis shows that Joy’s law is already present at the earliest stages of AR emergence, although the tilt dispersion is significantly larger at these times. Tilt rotations are strongest during the early emergence phase, with no preferred sense of rotation, and decrease as ARs approach their maximum magnetic flux, suggesting an important role of near-surface convective motions. We also find that the quantitative characterization of Joy’s law depends on both the magnetic flux of ARs and the method used to estimate their tilt. The Bayesian framework adopted here provides a robust basis for future analyses by allowing known sources of scatter to be explicitly modeled within a consistent statistical formalism.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"301 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172304","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}