Chinese Astronomy and Astrophysics最新文献

{"title":"Analysis of Measurement Set Version 4 Data Model and Its Impact on China's Participation in the SKA Project","authors":"Xu Yi-jun ,&nbsp;Wang Feng","doi":"10.1016/j.chinastron.2026.06.010","DOIUrl":"10.1016/j.chinastron.2026.06.010","url":null,"abstract":"<div><div>The Square Kilometre Array (SKA) has entered the construction and commissioning phase. However, the storage and processing of its massive data remain one of the critical challenges that need to be addressed. The construction and operation of the SKA Regional Center (SRC) also heavily rely on efficient data storage and management solutions. To explore the key issues in SKA data storage and management in depth, this paper systematically investigates the development history of Measurement Set (MS) technology, the technical characteristics of its various versions, and their limitations in SKA applications. This paper particularly analyzes the technological innovations in Measurement Set Version 4 (MSV4) and its potential impacts on SKA data management and research. The study indicates that MSV4, by introducing features such as self-description, modular architecture, and efficient storage, is expected to effectively alleviate the bottlenecks in SKA data storage and processing. If MSV4 becomes the standard for SKA data storage, it will significantly influence the construction of SRCs in China and SKA scientific research. Therefore, it is essential to closely monitor the technological development of MSV4 at this stage and to proactively prepare relevant technological reserves to ensure the successful development, upgrading, and transformation of SRC scientific application pipelines and data processing software for SKA scientific research.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 411-430"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research Progress of the Spiral Structure of the Milky Way","authors":"Xu Ye ,&nbsp;Liu De-jian","doi":"10.1016/j.chinastron.2026.06.002","DOIUrl":"10.1016/j.chinastron.2026.06.002","url":null,"abstract":"<div><div>The spiral structure of the Milky Way represents one of the fundamental research topics in astronomy, posing a long-standing challenge. This paper provides a systematic review of the historical and recent advances in our understanding of the Galactic spiral structure. Over the past two centuries, our comprehension has undergone transformative advances-progressing from initial speculative models to direct observational evidence, and from mapping local arm segments in the solar neighborhood to reconstructing the global spiral architecture of the Milky Way. The spiral arms of the Milky Way exhibit complex morphological characteristics; while the four-arm and two-arm models continue to be debated on global scales, the broad arrangement of nearby arms has been largely established, though detailed properties often show discrepancies among different studies. New techniques such as kinematic parameter analysis and measurements of stellar chemical abundances are offering novel avenues for investigating spiral structure.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 260-284"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Asteroid Lightcurves and Inversion of Shape Parameters","authors":"Gao Hao ,&nbsp;Zhao Shun-jing ,&nbsp;Liao Xin-hao ,&nbsp;Lei Han-lun","doi":"10.1016/j.chinastron.2026.06.006","DOIUrl":"10.1016/j.chinastron.2026.06.006","url":null,"abstract":"<div><div>Asteroids are celestial bodies widely present within the solar system. Light curves, which are plots of brightness variation over time obtained from continuous observations of an asteroid, contain information related to its orbital, rotational, shape, and thermophysical parameters. Through light curves, shape inversion of asteroids can be performed to investigate the relationship between the characteristics of light curves and the asteroid's rotational state. Firstly, by comprehensively considering the shape, rotational state, and phase angle of the asteroid, a photometric model is established to simulate and generate asteroid light curves. Based on the triaxial ellipsoid model, the influence of various parameters on light curves is analyzed, and the variations in light curves under principal-axis rotation and non-principal-axis rotation are studied, thereby obtaining the correspondence between light curve features and rotational and shape parameters. Subsequently, parameter fitting of asteroid light curves is performed using both the triaxial ellipsoid model and the convex polyhedron model to invert and obtain the rotational and shape parameters.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 336-358"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Simulation Study on the Origin of Stellar Snakes","authors":"Liang Guo ,&nbsp;Chang Jiang ,&nbsp;Li Jing ,&nbsp;Dai Cai-ping ,&nbsp;Tian Hai-jun","doi":"10.1016/j.chinastron.2026.06.003","DOIUrl":"10.1016/j.chinastron.2026.06.003","url":null,"abstract":"<div><div>Thanks to recent advancements in observational technology, significant progress has been made in the search for open clusters. Among these, binary open clusters have become a key focus of cluster studies due to their unique properties and complex interactions. The open clusters NGC 2232 and Tian 2, which are located at a very close distance from each other, are considered a binary cluster system. Observations show that these two clusters have very young and similar ages (approximately 30–40 Myr). There is a structure formed by stars with a length exceeding 200 pc near the binary star cluster, which is called the “Stellar Snake”. Through a series of high-precision <em>N</em>-body dynamical simulations (<em>N</em>: the number of bodies), the formation of the stellar snake has been dynamically modeled. The simulation results indicate that the two clusters are currently in a non-dynamically bound state, and it remains uncertain whether they were bound at the time of their formation. If the system is initially considered unbound, the two clusters show no significant mass loss after independently evolving for 100 Myr, and their mass loss rate is not significantly higher than that of a single open cluster in the Milky Way under tidal stripping. In contrast, if the two clusters were initially bound at birth and evolved together for 100 Myr, the tidal effects from mutual orbital motion within this bound system significantly accelerated the mass loss of the clusters. As a result, the stripped stars formed a larger tidal structure, but the tidal stream did not effectively form a structure resembling the stellar snake with a span over 200 pc. Additionally, considering the observed stellar snake as a one-sided structure, it does not match the symmetric tidal arms and tails that would be expected from tidal interactions. Therefore, the stellar snake is not likely to be a product of tidal effects, but rather a formation mechanism more consistent with the collapse of primordial gas along a filamentary structure.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 285-306"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Fast Algorithm to Calculate Transits of Inter-satellite Links between Constellation Satellites","authors":"Tang Jing-shi","doi":"10.1016/j.chinastron.2026.06.007","DOIUrl":"10.1016/j.chinastron.2026.06.007","url":null,"abstract":"<div><div>With the development and readiness of inter-satellite link (ISL), it has been widely used in satellite constellations for navigation, communication, and other purposes. As establishing or maintaining ISL can be affected by transits (also known as sun outage), transits of the links need to be calculated and predicted, so the system service can be properly assessed and scheduled. Currently the normal practice to determine and predict the transits, by building scenarios using proven commercial satellite system toolkit or by developing in-house simulation tools, is to calculate the elongation between the ISL and the line-of-sight of the Sun, based on propagated ephemerides. It is simple, straight forward and can be conveniently implemented, however, it bears a significant disadvantage that the computation is extremely CPU-intensive and therefore slow in speed. Although the predicted transits do not have to be very precise in the design phase and the two-body model may suffice, the ephemerides are always limited to small stepsize in order to properly detect the transits. Otherwise transits with short duration may be missed, and the service assessment can be compromised. Regarding the determination and calculation of the transits, a fast algorithm is proposed in this paper. With the equation of the satellite's argument of latitude u at the transit boundary, it can be analytically determined whether a transit may occur or calculated when the transit starts or ends, allowing fast assessment of how transits affect the service. This method is also based on propagated ephemerides, but a much larger stepsize can be accepted. Tests show that the analytical method can outperform the normal practice by detecting more transits while reducing calculation time by two to three orders of magnitude. Even the stepsize of the ephemerides is close to one orbital period, this method is still able to detect more than 99.9% transits. The results are robust against varying stepsizes, where the maximum deviations of calculated start epochs and durations of the transits would not exceed 1 second.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 359-382"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research Progress on Polarization of Repeating Fast Radio Bursts","authors":"Cao Shuo ,&nbsp;Hao Long-fei ,&nbsp;Wang Min ,&nbsp;Li Zhi-xuan","doi":"10.1016/j.chinastron.2026.06.001","DOIUrl":"10.1016/j.chinastron.2026.06.001","url":null,"abstract":"<div><div>To investigate the polarization properties, radiation mechanisms, and origins of repeating fast radio bursts, definitions of polarization-related physical parameters such as Stokes parameters and Faraday rotation measure are first outlined, along with observational analysis methods including <em>Q</em>-<em>U</em> fitting and <em>RM</em> synthesis. By analyzing radiation mechanisms like curvature radiation and inverse Compton scattering, as well as propagation effects such as cyclotron absorption and generalized Faraday rotation, their influences on polarization signals are examined. On this basis, the polarization observational characteristics of six typical repeating FRBs such as FRB 20121102A are highlighted, revealing that repeating FRBs also exhibit high circular polarization, thereby challenging the previous view that circular polarization is unique to non-repeating FRBs. Finally, origin models such as the magnetar model are discussed. The results show that polarization properties can provide key observational constraints for understanding the radiation mechanisms and origins of repeating FRBs, and support the magnetar model as being reasonably plausible.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 229-259"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frequency Averaging Effect on SKA1-LOW Image Based on Simulation","authors":"Liang Wei-jie ,&nbsp;Xie Yang-fan ,&nbsp;Wang Feng ,&nbsp;Deng Hui ,&nbsp;Mei Ying","doi":"10.1016/j.chinastron.2026.06.008","DOIUrl":"10.1016/j.chinastron.2026.06.008","url":null,"abstract":"<div><div>SKA1-Low, the low-frequency component of the Square Kilometre Array (SKA), will undertake critical scientific missions such as probing the Epoch of Reionization (EoR). While frequency averaging can effectively reduce visibility data volume and improve sensitivity, it also introduces “bandwidth smearing”. The specific impact of this bandwidth smearing on SKA1-Low imaging currently lacks comprehensive quantitative analysis. In this study, we employ simulation methods to systematically investigate the effects of frequency averaging. By simulating the full SKA1-Low array, applying frequency averaging, and performing CLEAN deconvolution, we systematically compare restored images generated from multi-channel averaging against those from single-channel data, analyzing the resulting residual maps. Furthermore, we thoroughly examine the impact of frequency averaging on the intensity of observed sources, obtaining quantitative results that detail how peak intensity varies with the number of averaged channels under different imaging weightings. This research provides a valuable reference for selecting the optimal number of channels for frequency averaging during actual SKA1-Low observations, offering significant practical utility for future SKA1-Low scientific operations.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 383-393"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design Scheme and Verification of the Thermal Control System for Balloon-borne Coronagraph in Near Space","authors":"Wang Jing-xing ,&nbsp;Lin Jun ,&nbsp;Kang Kai-feng ,&nbsp;Li Yan ,&nbsp;Song Teng-fei ,&nbsp;Xu Fang-yu ,&nbsp;Liu Da-yang","doi":"10.1016/j.chinastron.2026.06.009","DOIUrl":"10.1016/j.chinastron.2026.06.009","url":null,"abstract":"<div><div>The optical system of the balloon-borne coronagraph typically adopts a small focal ratio design, leading to a slender tube structure that is highly sensitive to fluctuations in ambient temperature. To ensure stable operation under the low-temperature and low-pressure conditions of near-space, this study developed a high-precision thermal control system. The system comprises 12 sets of independently regulated temperature control units, utilizing thermistors as sensors, along with thin-film heaters and a PID (Proportional-Integral-Derivative) control algorithm, to accurately maintain the mirror tube temperature within (<span><math><mrow><mo>−</mo><mn>5</mn><mo>±</mo><mn>3</mn></mrow></math></span>) <span><math><msup><mrow></mrow><mo>∘</mo></msup></math></span>C. By exploiting the differential thermal contraction properties between aluminum alloy and optical materials, the system effectively eliminates structural gaps and mitigates thermal deformation, while an active focusing mechanism compensates for focal shift caused by temperature variations. Through systematic analysis of the structural characteristics of the coronagraph and its operating environment, a heat transfer model specific to near-space conditions was established, identifying the key factors influencing the system temperature, and then a thermal control scheme combining multi-layer insulation and active heating was proposed. On 4 October 2022, a successful flight experiment was conducted in Da Qaidam, Qinghai Province, where the system operated at an altitude of 30 km, acquiring valuable observational data. The recovered data indicates that the temperature control system operates stably, with the temperature fluctuation of the coronagraph tube controlled within the design range. This effectively ensures the normal of the coronagraph in extreme environments, and provides an important technical reference for future similar missions.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 394-410"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radial Velocity Curve Template for RRab Lyrae Star","authors":"Zhang Chen-qian-xi ,&nbsp;Huang Yue ,&nbsp;Liu Gao-chao ,&nbsp;Fang Min ,&nbsp;Zhang Peng ,&nbsp;Liu De-jian ,&nbsp;Chen Yu-xiao","doi":"10.1016/j.chinastron.2026.06.004","DOIUrl":"10.1016/j.chinastron.2026.06.004","url":null,"abstract":"<div><div>As crucial cosmic distance indicator, the RR Lyrae star (RRL) with RRab type plays a significant role in studying the dynamical properties of the Milky Way. However, due to their pulsating nature, the observed radial velocities of RRab stars contain not only the systemic heliocentric velocity but also a substantial component from the stellar pulsation, posing a challenge for accurate kinematic measurements. In this study, we use medium-resolution spectra from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) to construct radial velocity curve templates for RRab stars based on the Mg Ib and H<span><math><mi>α</mi></math></span> absorption lines, with the aim of improving the accuracy of their derived heliocentric radial velocities. Comparative analysis with existing templates shows that the radial velocity curve templates developed in this work yield consistent velocity estimates, with the standard deviations of the resulting heliocentric radial velocities being smaller than 5<span><math><mrow><mtext>km</mtext><mo>·</mo><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. The templates presented here are well-suited for deriving reliable heliocentric radial velocities for RRab stars observed by LAMOST.</div></div>","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 307-325"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Limitation on the Viewing Angles of Long GRBs Based on Amati Relation","authors":"Lin Yi-qing ,&nbsp;Jiang Hua-li","doi":"10.1016/j.chinastron.2026.06.005","DOIUrl":"10.1016/j.chinastron.2026.06.005","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Fermi, Swift, and other observation satellites provided a dataset of 323 Long Gamma-Ray Bursts (LGRBs) with known redshift and well-defined spectral parameters spanning from February 1997 to September 2023. Among these, 123 GRBs (Gamma-Ray Bursts) observed by Fermi-GBM were selected to calibrate the relationship between the isotropic energy &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;iso&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and the peak energy in the cosmological rest frame &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, known as the Amati relation. The analysis revealed that the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;iso&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of five LGRBs (GRB 980425, GRB 061210, GRB 070714B, GRB 071227, and GRB 080123A) significantly deviated from the Amati relation, suggesting that the jet of them may be off-axis to the line of sight. Utilizing the well-established &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;iso&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and Lorentz factor &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mstyle&gt;&lt;mi&gt;Γ&lt;/mi&gt;&lt;/mstyle&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;iso&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; correlations, we estimated the viewing angles &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; for these five LGRBs. The results show, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msubsup&gt;&lt;mn&gt;42&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.14&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;0.29&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for GRB 980425, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msubsup&gt;&lt;mn&gt;27&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.10&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;0.21&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for GRB 061210, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msubsup&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.02&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;0.09&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for GRB 070714B, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msubsup&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.05&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;0.09&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for GRB 071227, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;obs&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;msubsup&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;0.03&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;","PeriodicalId":35730,"journal":{"name":"Chinese Astronomy and Astrophysics","volume":"50 2","pages":"Pages 326-335"},"PeriodicalIF":0.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148214743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}