Scientific Methods for Analyzing Observational Data of Gamma-Ray Bursts and Related High-Energy Transients

doi:10.11871/jfdc.issn.2096-742X.2025.04.009

Abstract

Abstract:

[Context] Astronomical research heavily relies on the acquisition and analysis of observational data. For high-energy transients such as gamma-ray bursts (GRBs), radiation undergoes rapid and intense variations over extremely short timescales, characterized by significant temporal and spectral evolution. Efficiently and accurately extracting these dynamic features from complex observational data has become a critical technical challenge in high-energy time-domain astrophysics. [Objective] This study aims to develop a scientific data analysis pipeline tailored for GRBs and related high-energy transient sources, with a particular focus on the development and application of key algorithms and core technologies that ensure high efficiency and precision. [Methods] For temporal analysis, we propose an automated signal identification and background fitting algorithm that integrates baseline correction, Bayesian block segmentation, significance calculation, and polynomial fitting. For spectral analysis, we construct a Bayesian inference-based spectral fitting framework designed to robustly estimate model parameters and their uncertainties. [Results] The proposed analysis pipeline and its key algorithms have been successfully applied to real observational data of GRBs. The approach effectively identifies and separates signal from background and enables reliable estimation of key spectral parameters through a Bayesian inference algorithm. [Conclusion] The data analysis framework presented in this work significantly improves the efficiency and accuracy of observational data analysis for GRBs and related high-energy transient sources. It offers a reusable technical approach for the automated analysis of high-energy astrophysical explosion phenomena and holds substantial potential for broad application and scientific advancement.

Key words: gamma-ray bursts, transient sources, astronomical data processing methods, signal identification, Bayesian inference

YANG Jun, ZHANG Binbin. Scientific Methods for Analyzing Observational Data of Gamma-Ray Bursts and Related High-Energy Transients[J]. Frontiers of Data and Computing, 2025, 7(4): 101-117, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2025.04.009.

Figures/Tables 10

Table 1

Table 2

Alg.1

Alg.2

The algorithm for automated signal recognition and background fitting"

自动化信号识别与背景拟合算法
Input：总光变曲线$\mathit{A}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i}}\right)\right\}$
Output：分离出的信号光变曲线$\mathit{S}\left(\mathit{T}\right)$和背景光变曲线$\mathit{B}\left(\mathit{T}\right)$
/* 基线矫正 */
使用DRPLS算法进行基线矫正，得到初步背景估计$\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i},\mathit{b}\mathit{c}}\right)\right\}$
/* 贝叶斯块 */
使用贝叶斯块算法对$\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i}}\right)\right\}$进行自动分段，得到分段边界$\left\{{\mathit{T}}_{\mathit{k}}\right\}$
/* 显著性计算 */
For 每个贝叶斯块$\left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]$ do
计算该时间区间内的总光子数：${\mathit{C}}_{\mathit{k}}=\sum _{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}{\mathit{R}}_{\mathit{i}}\mathrm{\Delta }\mathit{t}$
计算该时间区间内的背景光子数：${\mathit{C}}_{\mathit{k},\mathit{b}\mathit{c}}=\sum _{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}{\mathit{R}}_{\mathit{i},\mathit{b}\mathit{c}}\mathrm{\Delta }\mathit{t}$
计算信号显著性：${\mathit{S}}_{\mathit{k}}=\sqrt{2\mathbf{l}\mathbf{o}\mathbf{g}\frac{{\mathit{L}}_{1}\left({\mathit{\theta }}_{1}^{\mathbf{m}\mathbf{l}\mathbf{e}}\right)}{{\mathit{L}}_{0}\left({\mathit{\theta }}_{0}^{\mathbf{m}\mathbf{l}\mathbf{e}}\right)}}$
If ${\mathit{S}}_{\mathit{k}}\ge {\mathit{S}}_{\mathbf{t}\mathbf{h}}$ then
标记该贝叶斯块为信号区间$\left[{\mathit{T}}_{\mathit{k}}^{\mathit{S}},{\mathit{T}}_{\mathit{k}+1}^{\mathit{S}}\right]$
标记该贝叶斯块内的数据为信号${\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{S}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{S}}\right)\right\}}_{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}$
End
Else
标记该贝叶斯块为背景区间$\left[{\mathit{T}}_{\mathit{k}}^{\mathit{B}},\mathrm{ }{\mathit{T}}_{\mathit{k}+1}^{\mathit{B}}\right]$
标记该贝叶斯块内的数据为信号${\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{B}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{B}}\right)\right\}}_{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}$
End End
/* 多项式拟合 */
构建m阶多项式$\mathit{f}\left(\mathit{t},\mathrm{ }\mathit{\beta }\right)=\stackrel{\mathit{m}}{\sum _{\mathit{j}=0}}{\mathit{\beta }}_{\mathit{j}}{\mathit{t}}^{\mathit{j}}$拟合背景数据$\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{B}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{B}}\right)\right\}$
采用加权最小二乘法求解最优多项式系数$\widehat{\beta }$及其协方差矩阵 $Cov\left(\widehat{\beta }\right)$
生成背景光变曲线$\mathit{B}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},\mathrm{ }\mathit{f}\left({\mathit{T}}_{\mathit{i}},\mathrm{ }\widehat{\beta }\right)\right)\right\}$
生成信号光变（净光变）曲线$\mathit{S}\left(\mathit{T}\right)=\mathit{A}\left(\mathit{T}\right)-\mathit{B}\left(\mathit{T}\right)$
Return $\mathit{S}\left(\mathit{T}\right)$，$\mathit{B}\left(\mathit{T}\right)$

Alg.2

Fig.1

Fig.2

Alg.3

The algorithm for extracting the gamma-ray background spectrum"

伽马射线背景能谱提取算法
Input：光子事件列表$\left\{\left({\mathit{t}}_{\mathit{i}},\mathrm{ }{\mathit{p}}_{\mathit{i}}\right)\right\}$，时间切片$\left[{\mathit{T}}_{\mathit{l}},\mathrm{ }{\mathit{T}}_{\mathit{r}}\right]$
Output：背景能谱$\left\{\left(\mathit{I},{\mathit{C}}_{\mathit{I}}^{\mathit{B}},{\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}\right)\right\}$
提取总光变曲线$\mathit{A}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},\mathrm{ }{\mathit{R}}_{\mathit{i}}\right)\right\}$
应用信号识别与背景拟合算法，确定信号区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{S}}\right\}$和背景区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{B}}\right\}$
For 每一个能道$\mathit{I}\in \left\{1,\mathrm{ }2,\cdots,\mathit{N}\right\}$ do
提取光子事件列表$\left\{\left({\mathit{t}}_{\mathit{i}},\mathrm{ }{\mathit{p}}_{\mathit{i}}\right)\|{\mathit{p}}_{\mathit{i}}=\mathit{I}\right\}$
提取光变曲线${\mathit{A}}_{\mathit{I}}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i},\mathrm{ }\mathit{I}},{\mathit{R}}_{\mathit{i},\mathrm{ }\mathit{I}}\right)\right\}$
使用多项式拟合背景区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{B}}\right\}$内的${\mathit{A}}_{\mathit{I}}\left(\mathit{T}\right)$
获取背景光变曲线的多项式模型${\mathit{B}}_{\mathit{I}}\left(\mathit{t}\right)$及其误差${\mathit{\sigma }}_{{\mathit{B}}_{\mathit{I}}}\left(\mathit{t}\right)$
计算背景光子数：${\mathit{C}}_{\mathit{I}}^{\mathit{B}}=\stackrel{{\mathit{T}}_{\mathit{r}}}{\underset{{\mathit{T}}_{\mathit{l}}}{\int }}{\mathit{B}}_{\mathit{I}}\left(\mathit{t}\right)\mathit{d}\mathit{t}$
计算背景光子数的统计误差：${\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}=\stackrel{{\mathit{T}}_{\mathit{r}}}{\underset{{\mathit{T}}_{\mathit{l}}}{\int }}{\mathit{\sigma }}_{{\mathit{B}}_{\mathit{I}}}\left(\mathit{t}\right)\mathit{d}\mathit{t}$
End
Return $\left\{\left(\mathit{I},{\mathit{C}}_{\mathit{I}}^{\mathit{B}},{\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}\right)\right\}$

Alg.3

Alg.4

Alg.4 Bayesian inference-based algorithm for astronomical spectral fitting"

基于贝叶斯推断的天文能谱拟合算法
Input：观测光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$，仪器响应矩阵${\mathit{R}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},{\mathit{J}}_{\mathit{n},\mathit{g}}\right)$，参数化能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$
Output：参数后验概率分布$\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$
/* 模型构建 */
构建参数化能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$，其中$\mathit{\theta }$为待估参数
/* 数据准备 */
准备观测光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$和仪器响应矩阵${\mathit{R}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},{\mathit{J}}_{\mathit{n},\mathit{g}}\right)$
/* 贝叶斯推断 */
结合先验认知，设定参数的先验分布$\mathit{P}\left(\mathit{\theta }\right\|\mathit{M})$
根据数据的统计假设，定义似然函数$\mathit{P}\left(\mathit{D}\right\|\mathit{\theta },\mathit{M})$
采样器根据参数先验分布在多维参数空间中进行采样
While 未满足收敛条件do
采样获得当前参数值$\mathit{\theta }$
计算能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$
计算模型预测的光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}^{\mathit{p}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$
计算拟合统计量$\mathit{S}$
更新采样状态，并检查是否满足收敛条件
End
计算参数后验概率分布$\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$
Return $\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$

Alg.4

Fig.3

Fig.4

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参数	类型	单位	解释
TIME	8字节实数	s	光子事件的到达时间
PHA	2字节整数	—	脉冲高度分析器通道编号

参数	类型	单位	解释
TIME	8字节实数	s	光子事件的到达时间
X	2字节整数	pixel	光子在天球坐标系中的X坐标
Y	2字节整数	pixel	光子在天球坐标系中的Y坐标
RAWX	2字节整数	pixel	光子在原始探测器坐标系中的 X坐标（未线性化前）
RAWY	2字节整数	pixel	光子在原始探测器坐标系中的 Y坐标（未线性化前）
DETX	2字节整数	pixel	光子在线性化探测器坐标系中的 X坐标
DETY	2字节整数	pixel	光子在线性化探测器坐标系中的 Y坐标
PHA	4字节整数	—	脉冲高度分析器通道编号
PI	4字节整数	—	脉冲不变通道编号
GRADE	2字节整数	—	光子事件的等级
STATUS	16位无类型	—	光子事件的数据质量标志

光变曲线提取算法
Input：光子事件列表${\left\{\left({\mathit{t}}_{\mathit{i}},{\mathit{E}}_{\mathit{i}}\right)\right\}}_{\mathit{i}=1}^{\mathit{n}}$，时间区间$[{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}},{\mathit{T}}_{\mathbf{e}\mathbf{n}\mathbf{d}}]$，能量范围$[{\mathit{E}}_{\mathbf{m}\mathbf{i}\mathbf{n}},\mathrm{ }{\mathit{E}}_{\mathbf{m}\mathbf{a}\mathbf{x}}]$，时间步长$\mathrm{\Delta }\mathit{t}$
Output：光变曲线$\left\{\right({\mathit{T}}_{\mathit{j}},{\mathit{C}}_{\mathit{j}},{\mathit{\sigma }}_{\mathit{j}}\left)\right\}$
计算时间箱的总数：$\mathit{M}=\left[({\mathit{T}}_{\mathbf{e}\mathbf{n}\mathbf{d}}-{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathrm{t}})/\mathrm{\Delta }\mathit{t}\right]$；
For $\mathit{j}=1$ 到 $\mathit{M}$ do
	计算当前时间箱的时间范围： $\left[{\mathit{T}}_{\mathit{j}}^{1},\mathrm{ }{T}_{\mathit{j}}^{2}\right]=[{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}}+\left(\mathit{j}-1\right)\mathrm{\Delta }\mathit{t},\mathrm{ }{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}}+\mathit{j}\mathrm{\Delta }\mathit{t}]$
	统计落入特定时间范围和能量范围内的光子数：${\mathit{C}}_{\mathit{j}}=\stackrel{\mathit{n}}{\sum _{\mathit{i}=1}}1$，满足${\mathit{T}}_{\mathbf{j}}^{1}\le {\mathit{t}}_{\mathit{i}}<{\mathit{T}}_{\mathit{j}}^{2}$，${\mathit{E}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\le {\mathit{E}}_{\mathit{i}}\le {\mathit{E}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$
	计算当前时间箱的泊松误差：${\mathit{\sigma }}_{\mathit{j}}=\sqrt{{\mathit{C}}_{\mathit{j}}}$
End
Return $\left\{\right({\mathit{T}}_{\mathit{j}},\mathrm{ }{\mathit{C}}_{\mathit{j}},\mathrm{ }{\mathit{\sigma }}_{\mathit{j}}\left)\right\}$