AI 中文总结
本研究系统探究标准GRB X射线余辉的偏振特性，通过蒙特卡洛模拟评估eXTP/PFA的探测前景，发现其偏振事件率≤1.5%，可捕捉GRB 221009A等稀有亮暴的偏振演化。
AI 中文摘要
伽马射线暴（GRB）余辉的偏振信号是研究其环境和喷流物理的有力诊断工具。本工作系统研究了标准GRB余辉的X射线（2--8 keV）偏振特性，并评估其由增强型X射线时变与偏振卫星（eXTP）上的偏振聚焦阵列（PFA）实现的可探测性。首先进行Morris全局敏感性分析以确定主导参数，随后为这些参数分配符合观测约束的概率分布；具体而言，各向同性能量、半张角和初始洛伦兹因子通过高斯Copula联合采样，以重现经验性的Ghirlanda和Liang关联关系。对10³个余辉开展蒙特卡洛模拟，并通过所选Fermi--Swift样本的观测10 keV流量分布进行验证（10³ s时K--S p值为0.29，10⁴ s时p值为0.18）。模拟结果显示，对于标准GRB X射线余辉，eXTP/PFA的整体偏振事件率≤1.5%，这反映了局限于激波平面的随机磁场产生的本征低偏振。最佳探测窗口出现在喷流断裂附近的晚时段，此时偏振度（PD）达到峰值；但对于GRB 221009A这类异常明亮的事件，其PD在10³--10⁶ s的整个区间内均高于最小可探测偏振度（MDP），表明eXTP/PFA可捕捉这类稀有明亮暴的几乎全部偏振演化过程。
英文摘要
The polarization signatures of Gamma-ray Burst (GRB) afterglows serve as a powerful diagnostic tool for studying their environments and jet physics. This work systematically investigates the X-ray (2--8~keV) polarization properties of standard GRB afterglows and assesses their detectability with the Polarimetry Focusing Array aboard the enhanced X-ray Timing and Polarimetry (eXTP) satellite. A Morris global sensitivity analysis is first conducted to identify the dominant parameters, which are then assigned observationally motivated probability distributions. In particular, the isotropic energy, half-opening angle, and initial Lorentz factor are sampled jointly via a Gaussian copula to reproduce the empirical Ghirlanda and Liang correlations. Monte Carlo simulations of $10^{3}$ afterglows are performed and validated against the observed 10~keV flux distributions of a selected Fermi--Swift sample (K--S $p = 0.29$ at $10^{3}~\mathrm{s}$ and $p = 0.18$ at $10^{4}~\mathrm{s}$). The simulations yield an overall polarization event rate of $\lesssim 1.5\%$ for standard GRB X-ray afterglows with eXTP/PFA, reflecting the intrinsically low polarization produced by a random magnetic field confined to the shock plane. The optimal detection window occurs near the jet break at late times, when the PD peaks. For exceptionally luminous events such as GRB~221009A, however, the PD remains above the MDP over the full interval $10^{3}$--$10^{6}~\mathrm{s}$, demonstrating that eXTP/PFA can capture nearly the entire polarization evolution for such rare, bright bursts.
Comments8 pages, 5 figures, 2 tables, A&A accepted
