Expectation on observations of Fermi-LAT gamma-ray sources using the HADAR experiment

Sun Hui-Ying; Qian Xiang-Li; Chen Tian-Lu; Danzengluobu; Feng You-Liang; Gao Qi; Gou Quan-Bu; Guo Yi-Qing; Hu Hong-Bo; Kang Ming-Ming; Li Hai-Jin; Liu Cheng; Liu Mao-Yuan; Liu Wei; Qiao Bing-Qiang; Wang Xu; Wang Zhen; Xin Guang-Guang; Yao Yu-Hua; Yuan Qiang; Zhang Yi

doi:10.7498/aps.72.20230977

Abstract

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1. 引　言
2. HADAR实验
3. Fermi-LAT源能谱的外推方法
3.1 Fermi-LAT数据
3.2 EBL吸收
3.3 伽马射线源SED的外推
4. 河外源的预期能谱
5. HADAR对伽马射线源的观测显著性预期
5.1 模拟方法
5.2 结果
6. 结　论

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Abstract

High altitude detection of astronomical radiation (HADAR) is an innovative array of atmospheric Cherenkov telescopes that employs pure water as its medium. By utilizing large-aperture hemispherical lenses, HADAR can capture atmospheric Cherenkov light, enabling the detection of gamma rays and cosmic rays in the energy range of 10 GeV to 10 TeV. Compared to traditional Imaging Atmospheric Cherenkov telescopes, HADAR offers distinct advantages such as a low energy threshold, high sensitivity, and a wide field of view. The telescope mainly consists of a hemispherical lens with a diameter of 5 m acting as a Cherenkov light collector, a cylindrical metal tank with a 4 m radius and 7 m height, and an imaging system at the bottom of the tank. The sky region covered by HADAR is much larger than the current generation of Imaging Atmospheric Cherenkov Telescopes. The field of view of HADAR can reach up to 60 degrees. Its continuous scanning capability allows for comprehensive observations of gamma-ray sources throughout the entire celestial sphere, making it an ideal instrument for studying transient and variable sources. In this study, the observational capabilities of HADAR are thoroughly investigated using the latest 4FGL-DR3 and 4LAC-DR3 gamma-ray source catalogs from Fermi-LAT. For extragalactic sources, the energy spectra in the high energy range have been extrapolated to the very high energy range, taking into account the absorption effect caused by extragalactic background light. By comparing the extrapolated results with existing VHE experimental data, the feasibility of this extrapolation method has been demonstrated. Through simulated analyses of the significance of these sources, it is anticipated that HADAR will detect a total of 93 gamma-ray sources with a significance exceeding 5 standard deviations during one year of operation. These sources comprise 45 galactic sources, 39 extragalactic sources, 3 sources of unknown type, and 6 unassociated sources.

Keywords:

PACS:

95.55.Ka	(X- and γ-ray telescopes and instrumentation)
95.55.Cs	(Ground-based ultraviolet, optical and infrared telescopes)
29.40.Ka	(Cherenkov detectors)
98.70.Rz	(γ-ray sources; γ-ray bursts)

Authors and contacts

1.
School of Intelligent Engineering, Shandong Management University, Jinan 250357, China
2.
Key Laboratory of Cosmic Rays, Ministry of Education, Tibet University, Lhasa 850000, China
3.
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
4.
University of Chinese Academy of Sciences, Beijing 100049, China
5.
College of Physics, Sichuan University, Chengdu 610064, China
6.
Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
7.
Suzhou Aerospace Information Research Institute, Suzhou 215000, China
8.
College of Physics, Chongqing University, Chongqing 401331, China
9.
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China

Corresponding author: Qian Xiang-Li, qianxl@sdmu.edu.cn ; Guo Yi-Qing, guoyq@ihep.ac.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12263005, 12005120, 12147218, U1831208, U2031110) and the Key Laboratory of Cosmic Ray of the Ministry of Education of China, Tibet University (Grant No. KLCR-202201)

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1. 引　言

宇宙线被认为是组成非热宇宙的重要成分, 然而由于宇宙线是带电粒子, 在传播过程中受到银河系内磁场的作用容易发生偏转, 因此很难确定其起源. 当带电粒子被加速到相对论能量时, 会通过多种相互作用过程产生伽马射线, 而伽马射线是电中性, 在传播过程中不受磁场影响偏转, 可以指向伽马射线的产生区域, 因此伽马射线尤其是甚高能(very high energy, VHE; E ≥ 30 GeV)伽马射线成为研究宇宙线产生和加速的重要手段. 对非热辐射过程产生的VHE伽马射线及其辐射体的探测成为探测宇宙结构及其电磁成分的重要探针. 除此之外, 通过VHE伽马射线还可以研究各种天体辐射源的辐射机制及其辐射区域信息, 也是研究伽马射线暴、洛伦兹破缺及间接测量暗物质的重要手段.

过去二十多年, 已经观测到超过270个不同类型的VHE伽马射线源. 这主要得益于地面成像大气切伦科夫望远镜阵列实验(imaging atmospheric Cherenkov telescopes, IACTs)和地面空气簇射阵列(extensive air shower detector array, EAS)实验的发展, 且实验的探测灵敏度逐渐提高. 以对蟹状星云(Crab Nebula)的观测为例, 现代IACT阵列实验, 比如H.E.S.S.^[1], MAGIC^[2]和VERITAS^[3], 只需几分钟时间就可以探测到该源5倍显著性超出. 下一代的切伦科夫望远镜阵列实验(Cherenkov telescope array, CTA)^[4], 将在灵敏度和分辨率方面有显著提高, 将灵敏度再提高1个量级, 不到1 min便可探测到Crab源的显著性超出. 因此, 随着IACTs和EAS实验灵敏度的提高, 预计会有更多VHE伽马射线源被探测到.

VHE伽马射线来源于多种宇宙线源, 像超新星遗迹(supernova remnant, SNR)^[5]、脉冲星风星云(pulsar wind nebula, PWN)^[6]、脉冲星(pulsar, PSR)等, 这些源主要集中在银河系内. 银河系外的VHE伽马射线源也被观测到, 主要产生于活动星系核(active galactic nuclei, AGN)的相对论性喷流, 或者恒星快速形成区域(star-forming region, SFR), 比如星暴星系(starburst galaxies, SBG)和伽马射线暴(gamma-ray bursts, GRBs)的余辉辐射等. 还有一些未确定类型(unknown, UNK)的伽马射线源, 这些源主要分布在银道面上, 其类型尚未被其他波段观测实验确定.

对银河系内伽马射线源的观测, 银道面是主要观测区域, 现代IACT实验都对其进行了观测. 位于南半球的H.E.S.S.实验以小于1.5% Crab流强的灵敏度和0.08°的角分辨对银道面区域进行了扫描观测^[7], 共观测到78个VHE源和47个未确定类型的源. 位于北半球的VERITAS实验对Cygnus区域进行了详细观测^[8], 将延展源VER J2019+368区分为两个候选源(VER J2018+367*和VER J2020+368*), 并且对超新星遗迹区域Gamma-Cygni的形态轮廓进行了详细观测研究. 位于北半球的水切伦科夫观测实验HAWC对北天区进行了观测^[9], 共发现65个TeV以上的源, 其中大部分位于银道面, 且有脉冲星对应体.

银河系外的伽马射线主要来自AGN产生的辐射, AGN主要包括耀变体(blazar)、未确定类型的耀变体候选体(blazar candidates of uncertain type, BCUs)、射电星系(radio galaxies, RDGs)、类星体(quasar)和赛弗特星系(seyfert galaxy, SEY)等类别, 其中大部分是耀变体. 耀变体是一类活动非常剧烈的AGN, 通过具有大洛伦兹因子( ≥ 10)的相对论性喷流产生伽马射线, 且喷流的方向与视线的夹角较小, 具有快速光变、高偏振、强辐射等特征. 关于耀变体的辐射模型, 人们普遍接受的是相对论喷流、黑洞、吸积盘三者相统一的辐射模型^[10,11]. 耀变体的非热辐射, 被认为是黑洞通过吸积盘吸积物质, 然后相对论粒子以接近光速喷流出来, 并通过相互作用过程产生伽马辐射. 其中产生伽马射线的辐射机制还不是完全清楚, 大部分辐射属于轻子起源, 比如相对论电子在黑洞周围磁场中的同步辐射, 相对论电子与周围软光子场(光子来自同步辐射的光子和喷流以外的区域^[12])的逆康普顿散射. 还有一种辐射属于强子起源, 主要是喷流中的高能质子与周围的软光子发生p-γ作用, 产生级联辐射, 或者是质子直接参与的同步辐射^[13-16]. 除此之外, 还有一些轻子-强子混合模型^[17]也被用来解释耀变体的VHE能谱结构.

耀变体根据光谱发射线强度的等值宽度大小分为平谱射电类星体(FSRQ, 强发射线)和蝎虎状天体(BL Lacs, 无或弱发射线)^[18], 根据同步辐射峰频的位置分为低峰频同步辐射峰(LSP, 频率 < 10¹⁴ Hz)(包含FSRQs和LBLs)、中峰频同步辐射峰(ISP, 10¹⁴ Hz < 频率 < 10¹⁵ Hz)(包含LBLs和IBLs)、高峰频同步辐射峰(HSP, 10¹⁵ Hz < 频率 < 10¹⁷ Hz)和极高峰频同步辐射峰(EHSP, 频率 > 10¹⁷ Hz)^[19,20](大部分是HBLs). 耀变体的光谱遍布整个电磁波谱, 从射电波段、光学、X射线到伽马射线波段. 耀变体的一个主要特征是具有显著的光变, 时间周期从几分钟到几年不等. 耀变体的谱能量分布(spectral energy distribution, SED)在 $\log{\nu}$ - $\log{\nu}{F_{\nu}}$ 呈现一个典型的双峰结构, 其结构可以由喷流中高能相对论粒子的非热辐射机制进行解释. 对耀变体的观测, 在过去几十年里已经成功探测到耀变体的高能(E > 100 MeV)伽马射线辐射, 通过高能伽马射线实验望远镜(EGRET)和费米空间望远镜搭载的大面积望远镜(Fermi large area telescope, Fermi-LAT)的巡天观测, 很多伽马射线的源表和AGN源表已经发布.

然而Fermi-LAT等空间望远镜由于接收面积有限(约1 m²), 不适合观测能量高于100 GeV的伽马射线. VHE能量伽马射线的观测主要是通过IACTs和EAS实验来完成. IACTs具有大的有效面积(约10⁵ m²)、好的角分辨和能量分辨, 因此在观测短时标变化的伽马射线源方面具有一定优势. 然而, 由于观测视场相对较小(~3.5°—5°)、占空比较小( < 10%), 只能对单一的源进行观测, 对一些快速瞬变源不能及时跟踪观测, 且不能长期观测. 地面EAS实验虽然具有大的观测视场, 能对视场内的源进行连续观测, 但往往观测阈能偏高(几百GeV)、角分辨较差. 因此, 一种具有大视场、低阈能的地面望远镜实验阵列——高海拔天体辐射探测实验(high altitude detection of astronomical radiation, HADAR)被提出. HADAR由我国科研人员自主提出, 是一种采用新技术的成像大气切伦科夫望远镜阵列, 采用折射式透镜聚焦宇宙线和伽马射线产生的大气切伦科夫光, 以实现对10 GeV至10 TeV伽马射线辐射的观测.

HADAR是地面式的宽视场望远镜, 具有宽视场优势, 能以较高灵敏度对其天空视场区域进行连续扫描观测, 包括点源、暂现源和时变源等. 这非常有利于对耀变体这类流强连续变化的源进行观测, 可以充分研究耀变体的耀变行为, 研究其能谱结构、喷流的辐射机制等. 除了流强快速变化的伽马射线源外, 对一些空间上扩展的源, 宽视场探测器HADAR在观测这类源方面也有优势, 这是窄视场的IACTs实验所不具备的.

本文利用HADAR实验的性能, 基于Fermi-LAT对伽马射线源的观测数据, 模拟研究HADAR对银河系内和银河系外伽马射线源的观测预期. 第2节简单介绍HADAR实验及其性能; 第3节介绍基于Fermi-LAT源的能谱外推方法; 第4节讲述HADAR对河外源的预期能谱; 第5节给出源的观测显著性预期; 第6节是结论.

2. HADAR实验

HADAR实验是一个由广角切伦科夫透镜和闪烁体探测器组成的复合阵列, 阵列结构如图1(a)所示, 通过探测宇宙线和伽马射线产生的切伦科夫光, 以达到探测和区分伽马射线的目的. 单个广角切伦科夫透镜(水透镜)的结构如图1(b)所示, 与现代IACT采用反射式透镜不同, HADAR采用新型水透式折射透镜, 以克服传统反射式望远镜视场小、离轴大角度时成像差等缺点. 整个系统由折射透镜、水介质、光聚焦系统和圆柱形罐体4部分组成. 透镜设计为球冠形状, 直径为5 m, 以实现大的视场角, 用来收集切伦科夫光. 透镜材质采用亚克力玻璃材质. 折射后的光经过高透射率的高纯水后到达望远镜聚焦成像系统, 成像系统放置在透镜的焦平面上, 以实现对切伦科夫光成像的探测, 透镜的焦距为6.8 m, 望远镜的视场角为60°. 望远镜系统的各部分结构尺寸如图1(b)所示.

$图 1 HADAR阵列示意图　(a)阵列分布图; (b)单个水透镜详细结构图[21]\r\nFig. 1. Schematic of HADAR: (a) Layout of the HADAR experiment; (b) detailed design of a water-lens telescope[21].$

图 1 HADAR阵列示意图　(a)阵列分布图; (b)单个水透镜详细结构图^[21]

Fig. 1. Schematic of HADAR: (a) Layout of the HADAR experiment; (b) detailed design of a water-lens telescope^[21].

下载: 全尺寸图片幻灯片

HADAR的有效面积、角分辨、时间分辨等性能模拟可以参考文献[21-23], HADAR实验覆盖的天区面积远大于IACTs等实验, 因此在巡天观测伽马射线源方面具有重要优势. 图2是HADAR与Fermi^[24], MAGIC^[25], H.E.S.S.^[7], ARGO-YBJ^[26], HAWC^[27], Tibet-ASγ^[28], LHAASO^[29]和CTA^[4]的灵敏度曲线对比图, IACT实验的曝光时间为50 h, EAS实验的曝光时间为1 a. 从图2可以看出, 在HADAR的低能段, 其灵敏度好于Fermi-LAT卫星实验; 在高能段, 其灵敏度好于HAWC等地面EAS实验, 与IACT实验MAGIC和H.E.S.S.的灵敏度相当, 因此可以弥补已有地面实验和卫星实验的能段空缺. HADAR在1 TeV的灵敏度约为1% Crab流强^[22], 虽然该灵敏度没有超过MAGIC和H.E.S.S.实验, 但是HADAR具有IACT实验所没有的宽视场优势, 十分有利于对视场内的点源、瞬变源进行连续观测. 表1列出了HADAR与其他实验的性能参数对比.

$图 2 HADAR及其他伽马射线实验的灵敏度曲线对比图[23]\r\nFig. 2. Comparisons of the sensitivity of HADAR with other γ-ray instruments[23]$

图 2 HADAR及其他伽马射线实验的灵敏度曲线对比图^[23]

Fig. 2. Comparisons of the sensitivity of HADAR with other γ-ray instruments^[23]

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表 1 HADAR及其他IACT和EAS实验的性能对比, 表中列出了各实验的名称、覆盖天区、视场、能量阈值、角分辨、观测点源的灵敏度和参考文献

Table 1. Comparison of the performance of HADAR and other IACT/EAS experiments. For each experiment, the name, spatial coverage, field of view, energy threshold, angular resolution, point-source ssensitivity and reference are given.

Experiment	Hemisphere/(N, S)	FOV/sr	Energy threshold	Angular resolution/(°)	Sensitivity/Crab	Ref.
Fermi-LAT 2FHL	space	2.7	10 GeV–2 TeV	0.1°(30 GeV)	3%–4%	[24]
LHAASO-WCDA	N	1.5	100 GeV–30 TeV	0.4°(2 TeV)	< 10%	[29]
HAWC	N	1.5	100 sGeV–10 sTeV	~0.5°	5%–10%	[9]
H.E.S.S.	S	0.006	30 GeV–100 TeV	0.08°	0.4%–2.0%	[7]
MAGIC	N	0.003	50 GeV–10 TeV	~0.1°	~0.7%	[25]
CTA	N, S	0.0048–0.015	20 GeV–300 TeV	0.07°(1 TeV)	0.2%–0.4%	[4]
HADAR	N	0.84	10 GeV–10 TeV	0.4°(100 GeV)	1.3%–2.4%	[22]

下载: 导出CSV

| 显示表格

HADAR实验计划布置在海拔4300 m的西藏羊八井宇宙线观测站, 比IACT实验海拔更高, 探测阈能相对更低, 有潜力探测几十GeV能量的伽马辐射. 实验硬件建设方面, 2016年已完成0.9 m口径球冠薄透镜原理样机系统的验证, 成功观测到宇宙线事例^[30,31], 在可行性方面得到初步验证. 第二步实验计划, 用2个或3个直径2 m的半球作为透镜主体进行实验, 目前透镜主体已经加工完成, 探测实验将在近期展开. 第三步将进行HADAR四个5 m口径望远镜的计划.

3. Fermi-LAT源能谱的外推方法

为了正确估计HADAR对河内和河外伽马射线源的观测能力, 我们基于现有Fermi-LAT的观测数据, 利用其能谱信息, 结合HADAR实验的观测性能进行合理估计. Fermi-LAT的能量范围主要集中在低能段, 而HADAR可以观测至10 TeV能量, 因此对甚高能段源的能谱, 需要进行能谱外推. 外推一方面要基于伽马射线辐射产生的物理机制, 另一方面伽马光子与河外背景光(extragalactic background light, EBL)相互作用导致的伽马射线的衰减(不透明度)也需要正确估计.

3.1 Fermi-LAT数据

费米伽马射线空间望远镜于2008年发射, Fermi-LAT^[32]开始在GeV能段进行连续巡天观测, 合作组2022年发布了最新的四期源表4FGL-DR3^[33]和4LAC-DR3^[34], 提供了50 MeV—1 TeV能段12年间的伽马射线观测结果. 其中, 4FGL-DR3包含6658个置信水平在4σ以上的源, 包括河内源和河外源. 相比于4FGL (4FGL-DR1)^[35]源表, 4FGL-DR3对所有源的谱参数、谱能量分布、年光变曲线和关联体等做了更新, 对脉冲星采用了更优化的参数化拟合, 增加了1607个新的点源和一些新关联的源^[33].

4LAC (4LAC-DR1)^[36]是基于与4FGL相同的数据, 重点介绍河外源AGN, 并对源的性质做了一些补充, 例如增加了河外源的红移估计和耀变体分类信息等, 是AGN类伽马射线源数据的重要参考. 在4FGL-DR3包含的6658个源中, 共分为27类, 其中AGN (4LAC-DR3)包含3814个源, 9个子类, 包括792个FSRQ, 1458个BL Lacs, 1493个BCUs和71个非耀变体类型的AGN (Nonblazar AGN, 包含6个子类). 4LAC-DR3相比于4LAC-DR1新增了591个AGNs源, 其中包含587个耀变体(75个FSRQs、117个BL Lacs和395个BCUs)和4个射电星系. 新增加的BCUs中大部分具有较软的谱指数, 因此FSRQs类型可能占的比例要大些, 这一特征在4LAC-DR1中是没有的, 原因可能是由于FSRQs具有较强的耀变活动.

3.2 EBL吸收

在VHE伽马射线从源处产生到传播至地球的过程中, 将穿过EBL辐射场并与EBL光子发生相互作用, 导致正负电子对的产生, 即 $\gamma_{\rm VHE}+\gamma_{\rm EBL}\rightarrow$ ${\rm{e}}^{+}+{\rm{e}}^{-}$ . 该相互作用将导致观测的伽马射线能谱的衰减, 即对VHE光子的不透明度, 该不透明度跟伽马射线的能量、源的红移和EBL强度(由EBL模型预测)有关. 图3是伽马射线衰减因子随伽马射线能量的变化图^[37], 分别给出了不同红移下的曲线, 可以看出, 随着红移的增加, 吸收效应变大, 但在低能段(<50 GeV)吸收效应相对较弱. 由于Fermi-LAT观测到的大部分伽马辐射发生在能量小于50 GeV的区域, 因此基本上不受EBL吸收的影响, 尤其是对红移 $z\leqslant1$ 的源. 因此, Fermi-LAT伽马射线源的能谱可以认为是未被吸收的内禀谱. 在此基础上对VHE源能谱进行预期, 需要加入EBL吸收效应. 该效应可用公式表示为

$图 3 伽马射线衰减因子与能量的关系图, 分别对应红移为0.03, 0.1, 0.25, 0.5和1.0处的源. 实线代表基于威尔金森微波各向异性探测器卫星(WMAP5)数据的模型, 作为对比, 基于固定参数的WMAP5模型(紫色点划线)和Domínguez模型[38] (红色点划线)也分别画出. 可以看出伽马射线的衰减主要集中在甚高能段, 随着红移的增加吸收效应逐渐变强, 且衰减逐渐向低能段发展. 低红移时在1—10 TeV能量区间存在一个较平缓的变化[37]\r\nFig. 3. Attenuation ${\rm{e}}^{-\tau}$ of gamma-rays versus gamma-ray energy, for sources at z = 0.03, 0.1, 0.25, 0.5 and 1.0. Results are compared for Wilkinson microwave anisotropy probe 5-year (WMAP5, solid) and WMAP5 + fixed (dash-dotted violet) models, as well as the model of Domínguez[38] (dash-dotted red). Increasing distance causes absorption features to increase in magnitude and appear at lower energies. A plateau can be seen between 1–10 TeV at low redshift[37]$

图 3 伽马射线衰减因子与能量的关系图, 分别对应红移为0.03, 0.1, 0.25, 0.5和1.0处的源. 实线代表基于威尔金森微波各向异性探测器卫星(WMAP5)数据的模型, 作为对比, 基于固定参数的WMAP5模型(紫色点划线)和Domínguez模型^[38] (红色点划线)也分别画出. 可以看出伽马射线的衰减主要集中在甚高能段, 随着红移的增加吸收效应逐渐变强, 且衰减逐渐向低能段发展. 低红移时在1—10 TeV能量区间存在一个较平缓的变化^[37]

Fig. 3. Attenuation

${\rm{e}}^{-\tau}$

of gamma-rays versus gamma-ray energy, for sources at z = 0.03, 0.1, 0.25, 0.5 and 1.0. Results are compared for Wilkinson microwave anisotropy probe 5-year (WMAP5, solid) and WMAP5 + fixed (dash-dotted violet) models, as well as the model of Domínguez^[38] (dash-dotted red). Increasing distance causes absorption features to increase in magnitude and appear at lower energies. A plateau can be seen between 1–10 TeV at low redshift^[37]

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$\begin{align} {\left(\frac{{\rm{d}}N}{{\rm{d}}E}\right)}_{{\rm{obs}}}={\left(\frac{{\rm{d}}N}{{\rm{d}}E}\right)}_{{\rm{int}}}\times {\rm{e}}^{-\tau(E,z)} \end{align},$

(1)

其中, $\Big(\dfrac{{\rm{d}}N}{{\rm{d}}E}\Big)_{{\rm{obs}}}$ 是观测到的伽马射线源能谱, $\Big(\dfrac{{\rm{d}}N}{{\rm{d}}E}\Big)_{{\rm{int}}}$ 是内禀谱, ${\rm{e}}^{-\tau(E, z)}$ 是衰减因子.

3.3 伽马射线源SED的外推

基于Fermi-LAT伽马射线源的能谱数据估计HADAR对这些源的观测能力, 需要将源能谱的能量外推至甚高能段. 对河外源耀变体来说, 大多数耀变体的流强是变化的, 在许多情况下对同一个耀变体可以观测到不同耀发态时的多个能谱, 同时, 不同时间段观测到的能谱可能也不一样. 但总体来说, 源的大部分时间是处在稳态, 耀发态的持续时间较短且不规则. Fermi-LAT的观测数据一般是几年观测的平均辐射, 而IACTs实验观测到的一般是在几小时或几天时间内的耀发态时的辐射. 这里将Fermi-LAT的SED进行外推, 由于Fermi-LAT的内禀谱存在多种模型, 作为对比, 将这几种内禀谱模型分别加上EBL吸收效应来进行外推. 同时, 为了更好地评估SED外推到VHE高能段的可靠性, 将某些源已有的VHE实验观测数据与Fermi-LAT外推的能谱进行了对比, VHE数据主要采用VERITAS实验的VTSCat数据^[39], 该数据分别包含稳态和耀发态时的数据.

Fermi-LAT采用的内禀谱函数模型主要有以下4种.

幂律谱型(power law, PL):

$\begin{align} \phi_{{\rm{int}}}({{E}})={{F}}_0\left( {{{E}}}/{{{E}}_0}\right)^{-\varGamma}. \end{align}$

(2)

对数抛物线型(log parabola, LP):

$\begin{align} \phi_{{\rm{int}}}({{E}})={{F}}_0\left( {{{E}}}/{{{E}}_0}\right)^{-\varGamma-\beta {\rm{ln}}( {{{E}}}/{{{E}}_0})}. \end{align}$

(3)

带指数能量截断的幂律谱型(PL with exponential cut-off, PLEC):

$\begin{align} \phi_{{\rm{int}}}({{E}})={{F}}_0\left( {{{E}}}/{{{E}}_0}\right)^{-\varGamma}{\rm{e}}^{- {{{E}}}/{{{E}}_{{\rm{cut}}}}}. \end{align}$

(4)

带指数能量截断的对数抛物线型(LP with exponential cut-off, ELP):

$\phi_{{\rm{int}}}({{E}})={{F}}_0\left( {{{E}}}/{{{E}}_0}\right)^{-\varGamma-\beta {\rm{ln}}( {{{E}}}/{{{E}}_0})}{\rm{e}}^{-{{{E}}}/{{{E}}_{{\rm{cut}}}}},$

(5)

其中, $F_0$ 是参考能量 $E_0$ 下的归一化流强, Γ是能谱指数, β是log抛物线谱型的曲率参数, $E_{{\rm{cut}}}$ 是能谱在高能段的截断能量. 模拟中, 对不同类型的耀变体 $E_{{\rm{cut}}}$ 设置了不同的能量截断值^[40,41].

图4是能量外推得到的伽马射线源谱能量分布图, 分别列举了3C 66A, 1ES 1218+304, PKS 1424+240和PG 1553+113共4个源, 这些源都位于HADAR视场内. 能谱中蓝色数据点是Fermi-LAT源表的数据, 黄色数据点是VTSCat的数据, 分别列举了低态和耀发态时的数据. 不同的线条代表不同的内禀谱函数模型, 谱的模型采用Fermi-LAT的模型参数信息, 能谱中加入EBL吸收效应, EBL模型采用Domínguez模型^[38]. 将外推的吸收能谱与VHE能段的观测数据进行对比, 可以看出采用内禀谱函数和EBL吸收外推的能谱能较好地描述VHE能段的实验数据, 能谱外推的方法是可行的. 表2列出了这4个源的具体参数信息, 其中每个源列出的是Fermi-LAT提供的最佳能谱模型及其在该模型下的参数信息.

$图 4 外推得到的源3C 66A, 1ES 1218+304, PKS 1424+240和PG 1553+113的宽能量段伽马射线谱能量分布图, 可以看出, 采用内禀谱函数加EBL吸收的谱模型能较好地描述能谱的实验观测数据. 其中低能段为Fermi-LAT 4FGL的实验数据(蓝色菱形), VHE能段为VERITAS的实验数据(黄色圆圈代表低态, 黄色圆点代表不同耀发态的数据). 三种不同的红色虚线分别代表不同的谱函数模型, 实线代表Fermi-LAT采用的谱函数. 纵坐标代表观测的流强, 其中包含了EBL的吸收效应\r\nFig. 4. Gamma-ray spectral energy distribution for the sources 3C 66A, 1ES 1218+304, PKS 1424+240, and PG 1553+113 obtained over a wide energy range by extrapolation. The resulting data show that the spectral models using the intrinsic spectral function and EBL absorption fit the experimental data well. The Fermi-LAT 4FGL data is represented by blue diamonds in the low-energy band, while in the VHE band the VERITAS data is depicted by yellow circles for the low state and yellow dots for the different flaring states. Three different red dashed lines represent different spectral function models, while the solid line represents the Fermi-LAT preferred function. The y-axis represents the flux, which includes the absorption effect of EBL$

图 4 外推得到的源3C 66A, 1ES 1218+304, PKS 1424+240和PG 1553+113的宽能量段伽马射线谱能量分布图, 可以看出, 采用内禀谱函数加EBL吸收的谱模型能较好地描述能谱的实验观测数据. 其中低能段为Fermi-LAT 4FGL的实验数据(蓝色菱形), VHE能段为VERITAS的实验数据(黄色圆圈代表低态, 黄色圆点代表不同耀发态的数据). 三种不同的红色虚线分别代表不同的谱函数模型, 实线代表Fermi-LAT采用的谱函数. 纵坐标代表观测的流强, 其中包含了EBL的吸收效应

Fig. 4. Gamma-ray spectral energy distribution for the sources 3C 66A, 1ES 1218+304, PKS 1424+240, and PG 1553+113 obtained over a wide energy range by extrapolation. The resulting data show that the spectral models using the intrinsic spectral function and EBL absorption fit the experimental data well. The Fermi-LAT 4FGL data is represented by blue diamonds in the low-energy band, while in the VHE band the VERITAS data is depicted by yellow circles for the low state and yellow dots for the different flaring states. Three different red dashed lines represent different spectral function models, while the solid line represents the Fermi-LAT preferred function. The y-axis represents the flux, which includes the absorption effect of EBL

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表 2 HADAR视场内4个AGN源的性质参数, 谱的模型参数从4LAC/4FGL导出. 表中从左到右分别为: 4FGL源名称、源对应体、AGN类型、SED分类、红移、模型, 该谱模型下的能量参考值、对应在能量

$E_0$

处的微分流强、谱指数Γ和曲率参数β

$E_0$

, differential flux at

$E_0$

with the fit model, spectral index Γ, curvature parameter β

4FGL Name	Counterpart	Type	Class	Redshift	Model	E₀/GeV	F₀ /(TeV^–1·cm^–2·s^–1)	Γ	β
J0222.6+4301	3C 66A	BLL	ISP	0.444	LP	1.197	1.03 × 10^–5	1.89	0.04
J1221.3+3010	1ES 1218+304	BLL	EHSP	0.184	PL	4.501	1.83 × 10^–7	1.71	—
J1427.0+2348	PKS 1424+240	BLL	HSP	0.604	LP	1.205	7.03 × 10^–6	1.71	0.06
J1555.7+1111	PG 1553+113	BLL	HSP	0.360	LP	1.802	3.84 × 10^–6	1.54	0.07

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| 显示表格

对于VHE数据低态和耀发态的确定, 由于同一个耀变体在不同时间段会观测到不同的流强, 因此, 对实验给出的不同VHE能谱数据点, 可以采用积分的形式来确定谱的低态或耀发态. 具体做法是将每一个VHE源观测的不同能谱数据与外推的Fermi-LAT能谱函数进行最小二乘拟合, 根据拟合出的谱微分曲线与能量进行积分, 以得到不同VHE谱时积分流强的大小, 根据积分流强的大小确定耀变体的不同形态, 最小的确定为低态, 其余为耀发态.

4. 河外源的预期能谱

根据3.3节所述的能谱外推方法, 本节将对所有Fermi-LAT 4LAC-DR3源表数据进行能谱外推. 考虑到计算EBL的吸收效应需要红移参数, 选取了在HADAR视场内且有红移记录的源, 共992个源(高银纬958个, 低银纬34个), 其中包括492个BL Lacs, 376个FSRQs, 88个BCUs和36个Nonblazar AGN. 外推得到的观测能谱如图5所示, 图中蓝色实线为BL Lacs, 红色虚线为FSRQs, 绿色实线为BCUs, 黑色实线为Nonblazar AGN, 其中EBL采用了Domínguez模型. 为了直观地展示HADAR对这些源的观测能力, 将这些源的能谱与HADAR运行1 a的灵敏度曲线进行了比较, 可以看出HADAR预期观测到的河外源主要为BL Lacs和Nonblazar AGN, FSRQs和BCUs数量很少. 这与这些源的能谱指数与红移特点有关, 因为BL Lacs的能谱指数比FSRQs的能谱指数偏硬, 且红移偏小, 与预期一致.

$图 5 河外源的预期能谱图, 图中蓝色实线为BL Lacs, 红色虚线为FSRQs, 绿色实线为BCUs, 黑色虚线为Nonblazar AGN, 黑色实线为HADAR运行1 a的灵敏度曲线\r\nFig. 5. Expected energy spectrum for extragalactic sources. The blue solid line represents BL Lacs, the red dashed line represents FSRQs, the green solid line represents BCUs, the black dashed line represents Nonblazar AGN, and the black solid line indicates the sensitivity of HADAR operating for 1 a$

图 5 河外源的预期能谱图, 图中蓝色实线为BL Lacs, 红色虚线为FSRQs, 绿色实线为BCUs, 黑色虚线为Nonblazar AGN, 黑色实线为HADAR运行1 a的灵敏度曲线

Fig. 5. Expected energy spectrum for extragalactic sources. The blue solid line represents BL Lacs, the red dashed line represents FSRQs, the green solid line represents BCUs, the black dashed line represents Nonblazar AGN, and the black solid line indicates the sensitivity of HADAR operating for 1 a

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5. HADAR对伽马射线源的观测显著性预期

5.1 模拟方法

HADAR作为地面阵列望远镜实验, 可以扫描其视场内的伽马射线源, 由于每个源在HADAR天空视场内所处的位置不同, 随着地球的运动会形成一条源的轨迹. 因此, 对源显著性的观测, 就是正确估计每个源在不同天顶角处的背景数(宇宙线本底)和伽马射线信号数. 本文采用基于等天顶角的全天区扫描分析方法进行显著性估计, 该方法的具体介绍可以参看文献[22,23,42], 这里给出大体计算步骤.

1)合理估计HADAR对Fermi-LAT源的观测时间. 由于HADAR只能在晴朗无月夜进行切伦科夫光的观测, 因此必须正确计算每个源的每天有效观测时间, 每天有效观测时间累加后为一年的有效观测时间.

2)建立天球坐标系和地平坐标系, 分别细分成单元格, 利用处在同一天顶角但不同方位角上单元格的背景事例来正确估计宇宙线本底.

3)根据Fermi-LAT源的能谱信息, 计算伽马射线事例的超出, 来计算源的统计显著性. 其中, 宇宙线背景事例数的计算表达式为

$\begin{align} N_{\rm CR}(t, \theta, \phi) = \eta_{\rm CR}\int_{E}N_{\rm CR}(E)A_{\rm CR}(\theta, E){\varOmega}{\rm{d}}E{\text{δ}}t.\end{align}$

(6)

伽马射线事例的计算可表示为

$\begin{split} &N_{\gamma}(t, \theta, \phi) \\ =\;& \eta_{\gamma}\int_{E}N_{\gamma}(E){\rm{e}}^{-\tau(E,z)}A_{\gamma}(\theta, E){\rm{d}}E{\text{δ}}t{\varepsilon_{\gamma}}(\varOmega), \end{split}$

(7)

式中, $A_{{\rm{CR}}}(\theta, E)$ 和 $A_{\gamma}(\theta, E)$ 分别是对入射角度为θ、能量为E的宇宙线和伽马事例的微分有效面积, $N_{\rm CR}(E)$ 是宇宙线能谱, $N_{\gamma}(E)$ 是Fermi-LAT源的能谱, Ω是阵列角分辨所对应的立体角大小, $\varepsilon_{\gamma}(\varOmega)$ 取68%, $\eta_{{\rm{CR}}}$ 是通过伽马/质子鉴别后宇宙线的存活率, $\eta_{\gamma}$ 是通过伽马/质子鉴别后伽马事例的存活率, ${\text{δ}}t$ 是观测时间的采样时间间隔. 在计算河内源时不需要考虑衰减因子 ${\rm{e}}^{-\tau(E, z)}$ .

5.2 结果

表3列出了基于Fermi-LAT 4FGL-DR3和4LAC-DR3源表, HADAR分别运行1 a和5 a预期观测到的银河系内和银河系外伽马射线源的数量. HADAR运行1 a预期有39个银河系外的伽马射线源以大于5倍的显著性标准偏差被观测到, 其中大部分为BL Lacs类型. 39个源中有34个为BL Lacs类型, 2个为FSRQs类型(CTA 102, 3C 454.3), 3个为非耀变体类型的AGN (分别为射电星系NGC 1275, M87和B2 1447+27). 未观测到星暴星系和一般星系类型的源. 有45个银河系内的伽马射线源可被观测到, 其中34个为脉冲星类型, 10个为脉冲星风星云和超新星遗迹, 1个为恒星形成区. 另外还有3个未知类型的源和6个未关联类型的源(unassociated sources)预期被观测到. 表4和表5分别列出了每个河外源和河内源的详细信息, 两维的显著性天图如图6所示, 下面重点对河外源的观测做一些讨论.

表 3 HADAR预期观测到的Fermi-LAT源的种类和数目

Table 3. Types and numbers of Fermi-LAT sources that HADAR is expected to detect

4FGL-DR3 source classes	Number of sources in 4FGL-DR3	Number of sources in HADAR FOV	Expected to be observed by HADAR in 1 a	Expected to be observed by HADAR in 5 a
Young / Millisecond pulsars	292	106	34	52
PWNe, SNR	63	22	10	13
SNR / PWNe	114	26	0	1
Globular cluster	35	5	0	0
Star-forming region	5	2	1	1
High-mass Binary, Low-mass Binary, Binary, Nova	30	6	0	0
BL Lacs	1458	492	34	66
FSRQs	792	376	2	5
Blazar candidate of uncertain type	1493	88	0	2
Nonblazar AGN (RDG, AGN, SSRQ, CSS, NLSY1, SEY)	71	36	3	8
Starburst galaxy	8	3	0	0
Normal galaxy	6	3	0	0
Unkown	134	48	3	7
Unassociated	2157	592	6	25
Total	6658	1805	93	180

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| 显示表格

表 4 HADAR视场内Fermi-LAT河外源的能谱参数及观测信息, 谱的参数从4LAC-DR3导出. 表中从左到右分别为: 4FGL源名称, 源对应体, 赤经, 赤纬, SED分类, 红移, 拟合模型, 该谱模型下的能量参考值, 对应在能量

$E_0$

处的微分流强, 谱指数Γ, 曲率参数β, 有效观测时间, 观测显著性

$E_0$

, differential flux at

$E_0$

with the fit model, spectral index Γ, curvature parameter β, live time and significance

4FGL name	Counterpart	R.A.	Dec.	Type	Redshift	Model	E₀/GeV	F₀/(TeV^–1·cm^–2·s^–1)	Γ	β	Time/h	S/σ
J0112.1+2245	S2 0109+22	18.03	22.75	BLL	0.265	LP	0.769	1.46 × 10^–5	1.99	0.060	277.8	9.05
J0211.2+1051	MG1J021114+1051	32.81	10.86	BLL	0.200	LP	0.922	7.51 × 10^–6	2.02	0.042	196.3	6.47
J0222.6+4302	3C 66A	35.67	43.04	BLL	0.444	LP	1.246	8.40 × 10^–6	1.89	0.046	264.2	17.9
J0319.8+4130	NGC 1275	49.96	41.51	RDG	0.018	LP	0.918	4.36 × 10^–5	2.05	0.069	271.9	54.6
J0521.7+2112	TXS 0518+211	80.44	21.21	bll	0.108	LP	1.541	4.64 × 10^–6	1.86	0.045	271.0	50.2
J0620.7+2643	RX J0620.6+2644	95.18	26.73	bll	0.134	PL	17.415	1.22 × 10^–9	1.55	—	290.3	5.1
J0648.7+1516	RX J0648.7+1516	102.19	15.28	bll	0.179	LP	3.248	1.22 × 10^–7	1.60	0.056	234.3	10.9
J0650.7+2503	1ES 0647+250	102.7	25.05	bll	0.203	LP	2.067	8.44 × 10^–7	1.65	0.041	286.0	32.9
J0738.1+1742	PKS 0735+17	114.54	17.71	bll	0.424	LP	1.623	2.25 × 10^–6	1.97	0.067	251.3	5.2
J0809.8+5218	1ES 0806+524	122.46	52.31	BLL	0.138	LP	1.342	1.91 × 10^–6	1.83	0.023	193.9	15.1
J0915.9+2933	Ton 0396	138.99	29.55	bll	0.190	LP	1.390	9.28 × 10^–7	1.74	0.081	294.7	7.4
J1015.0+4926	1H 1013+498	153.77	49.43	bll	0.212	LP	1.044	6.00 × 10^–6	1.75	0.044	220.0	27.9
J1058.6+5627	TXS 1055+567	164.67	56.46	BLL	0.143	LP	1.102	2.38 × 10^–6	1.86	0.050	149.4	6.1
J1104.4+3812	Mkn 421	166.12	38.21	BLL	0.030	PLEC	1.258	1.79 × 10^–5	1.74	—	284.9	519.6
J1117.0+2013	RBS 0958	169.27	20.23	bll	0.139	PL	1.964	3.12 × 10^–7	1.95	—	266.1	5.0
J1120.8+4212	RBS 0970	170.20	42.20	bll	0.124	LP	2.416	2.11 × 10^–7	1.55	0.046	268.6	23.9
J1150.6+4154	RBS 1040	177.66	41.91	bll	0.320	LP	1.949	4.71 × 10^–7	1.55	0.135	270.0	7.2
J1217.9+3007	B2 1215+30	184.48	30.12	BLL	0.130	LP	1.248	5.77 × 10^–6	1.87	0.043	295.1	37.7
J1221.3+3010	PG 1218+304	185.34	30.17	bll	0.184	LP	2.590	5.27 × 10^–7	1.65	0.029	295.2	37.4
J1221.5+2814	W Comae	185.38	28.24	bll	0.102	LP	0.781	6.00 × 10^–6	2.11	0.024	293.1	5.5
J1230.2+2517	ON 246	187.56	25.30	bll	0.135	LP	0.800	6.66 × 10^–6	2.02	0.056	286.7	5.8
J1230.8+1223	M 87	187.71	12.39	rdg	0.004	LP	1.124	1.30 × 10^–6	2.00	0.036	210.5	5.3
J1417.9+2543	1E 1415.6+2557	214.49	25.72	bll	0.237	LP	8.155	6.13 × 10^–9	1.28	0.138	287.9	5.1
J1427.0+2348	PKS 1424+240	216.76	23.80	BLL	0.604	LP	1.254	5.70 × 10^–6	1.71	0.057	281.8	21.7
J1428.5+4240	H 1426+428	217.13	42.68	bll	0.129	PL	5.135	2.69 × 10^–8	1.65	—	266.1	10.3
J1449.5+2746	B2 1447+27	222.40	27.77	rdg	0.031	PL	14.614	5.37 × 10^–10	1.46	—	292.4	6.8
J1555.7+1111	PG 1553+113	238.93	11.19	BLL	0.360	LP	3.802	1.16 × 10^–6	1.57	0.095	199.5	56.4
J1653.8+3945	Mkn 501	253.47	39.76	BLL	0.033	LP	1.508	3.78 × 10^–6	1.75	0.018	279.5	125.1
J1725.0+1152	1H 1720+117	261.27	11.87	bll	0.180	LP	2.216	7.55 × 10^–7	1.76	0.056	205.9	14.5
J1728.3+5013	I Zw 187	262.08	50.23	bll	0.055	PL	2.983	1.82 × 10^–7	1.79	—	213.2	21.1
J1838.8+4802	GB6J1838+4802	279.71	48.04	bll	0.300	LP	1.631	8.39 × 10^–7	1.78	0.040	231.3	6.7
J1904.1+3627	MG2J190411+3627	286.03	36.45	bll	0.078	PL	5.074	2.01 × 10^–8	1.80	—	289.7	5.8
J2116.2+3339	B2 2114+33	319.06	33.66	bll	0.350	LP	1.653	1.10 × 10^–6	1.75	0.095	294.4	7.1
J2202.7+4216	BL Lac	330.69	42.28	BLL	0.069	LP	0.871	4.07 × 10^–5	2.12	0.059	268.2	27.4
J2232.6+1143	CTA 102	338.15	11.73	FSRQ	1.037	PLEC	1.082	4.34 × 10^–5	2.27	—	204.5	5.9
J2250.0+3825	B3 2247+381	342.51	38.42	bll	0.119	PL	5.338	2.55 × 10^–8	1.74	—	284.2	7.9
J2253.9+1609	3C 454.3	343.50	16.15	FSRQ	0.859	PLEC	0.892	1.32 × 10^–4	2.38	—	240.7	10.9
J2323.8+4210	1ES 2321+419	350.97	42.18	bll	0.059	LP	1.857	5.31 × 10^–7	1.80	0.068	268.7	11.0
J2347.0+5141	1ES 2344+514	356.77	51.70	bll	0.044	LP	1.911	7.15 × 10^–7	1.74	0.039	199.8	29.2

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表 5 HADAR视场内Fermi-LAT河内源的能谱参数及观测信息, 谱的参数从4FGL-DR3导出. 表中从左到右分别为: 4FGL源名称, 源对应体, 赤经, 赤纬, SED分类, 拟合模型, 该谱模型下的能量参考值, 对应在能量

$E_0$

处的微分流强, 谱指数Γ, 曲率参数β, 有效观测时间, 观测显著性

$E_0$

, differential flux at

$E_0$

with the fit model, spectral index Γ, curvature parameter β, live time and significance

4FGL Name	Counterpart	R.A.	Dec.	Type	Model	$E_0$ /GeV	F₀/(TeV^–1·cm^–2·s^–1)	Γ	β	Time/h	S/σ
J0030.4+0451	PSR J0030+0451	7.61	4.86	MSP	PLEC	1.360	7.36 × 10^–6	2.08	—	130.1	40.6
J0102.8+4839	PSR J0102+4839	15.71	48.66	MSP	PLEC	1.378	1.42 × 10^–6	2.18	—	226.4	6.0
J0106.4+4855	PSR J0106+4855	16.61	48.93	PSR	PLEC	1.578	1.66 × 10^–6	2.11	—	224.2	14.2
J0218.1+4232	PSR J0218+4232	34.53	42.55	MSP	PLEC	0.820	1.20 × 10^–5	2.35	—	266.8	6.2
J0220.1+1155	—	35.04	11.92	—	PL	16.622	3.98 × 10^–10	1.57	—	206.2	5.6
J0340.3+4130	PSR J0340+4130	55.10	41.51	MSP	PLEC	1.659	1.38 × 10^–6	2.03	—	271.9	24.6
J0357.8+3204	PSR J0357+3205	59.46	32.08	PSR	PLEC	1.104	1.26 × 10^–5	2.30	—	295.5	19.3
J0425.6+5522e	SNR G150.3+04.5	66.42	55.37	SNR	LP	7.240	1.19 × 10^–7	1.64	0.047	161.8	123.6
J0534.5+2201i	Crab Nebula	83.63	22.02	PWN	LP	10.000	5.50 × 10^–7	1.75	0.080	274.7	639.6
J0540.3+2756e	Sim 147	85.10	27.94	SNR	LP	1.192	5.50 × 10^–6	2.07	0.081	292.7	11.1
J0554.1+3107	PSR J0554+3107	88.55	31.12	PSR	PLEC	1.066	4.06 × 10^–6	2.34	—	295.5	5.1
J0605.1+3757	PSR J0605+3757	91.28	37.96	MSP	PLEC	1.507	7.88 × 10^–7	2.18	—	285.7	5.3
J0617.2+2234e	IC 443	94.31	22.58	SNR	LP	4.551	2.58 × 10^–6	2.28	0.123	277.1	37.6
J0620.9+2201	—	95.23	22.02	—	PL	20.913	6.45 × 10^–10	1.61	—	274.7	5.7
J0631.5+1036	PSR J0631+1036	97.88	10.60	PSR	PLEC	1.540	2.52 × 10^–6	2.20	—	193.8	11.1
J0631.8+0645	PSR J0631+0646	97.96	6.76	PSR	PLEC	2.258	7.60 × 10^–7	2.22	—	152.9	5.9
J0633.7+0632	PSR J0633+0632	98.44	6.54	PSR	PLEC	1.527	8.13 × 10^–6	2.22	—	150.4	26.3
J0633.9+1746	PSR J0633+1746	98.48	17.77	PSR	PLEC	1.670	3.19 × 10^–4	2.10	—	251.7	575.7
J0650.6+2055	NVSS J065035+205556	102.66	20.93	unk	LP	3.643	4.42 × 10^–8	1.63	0.096	269.6	9.5
J0751.2+1808	PSR J0751+1807	117.80	18.14	MSP	PLEC	1.643	9.45 × 10^–7	2.06	—	254.1	13.1
J1312.7+0050	PSR J1312+0051	198.19	0.84	MSP	PLEC	1.301	2.01 × 10^–6	2.15	—	76.3	5.7
J1554.2+2008	—	238.55	20.15	—	PL	4.619	1.14 × 10^–8	1.82	—	265.6	5.0
J1816.5+4510	PSR J1816+4510	274.15	45.17	MSP	PLEC	1.171	1.48 × 10^–6	2.14	—	251.6	6.1
J1836.2+5925	PSR J1836+5925	279.06	59.43	PSR	PLEC	1.428	6.64 × 10^–5	2.07	—	112.6	388.8
J1846.3+0919	PSR J1846+0919	281.60	9.33	PSR	PLEC	1.458	3.78 × 10^–6	2.19	—	181.0	14.9
J1854.5+2050	—	283.64	20.84	—	PL	103.233	2.68 × 10^–11	1.01	—	269.2	34.8
J1857.7+0246e	HESS J1857+026	284.45	2.77	PWN	PL	6.063	2.25 × 10^–7	2.13	—	103.1	19.5
J1907.9+0602	PSR J1907+0602	286.98	6.04	PSR	PLEC	1.898	1.39 × 10^–5	2.37	—	144.4	31.3
J1910.8+2856	NVSS J191052+285621	287.72	28.94	unk	PL	7.243	6.08 × 10^–9	1.80	—	294.1	7.1
J1911.0+0905	W 49B	287.76	9.09	snr	LP	4.552	7.74 × 10^–7	2.28	0.112	178.6	8.5
J1918.0+0331	NVSS J191803+033032	289.51	3.52	unk	PL	12.647	2.39 × 10^–9	1.72	—	113.0	6.2
J1923.2+1408e	W 51C	290.82	14.14	SNR	LP	2.768	5.08 × 10^–6	2.21	0.109	225.4	25.9
J1924.3+1628	—	291.10	16.48	—	PL	22.893	7.99 × 10^–10	1.76	—	243.1	7.7
J1952.9+3252	PSR J1952+3252	298.25	32.88	PSR	PLEC	1.618	9.92 × 10^–6	2.29	—	295.1	39.3
J1954.3+2836	PSR J1954+2836	298.59	28.60	PSR	PLEC	1.519	8.08 × 10^–6	2.32	—	293.7	23.1
J1958.7+2846	PSR J1958+2846	299.68	28.77	PSR	PLEC	1.356	1.13 × 10^–5	2.35	—	293.9	21.1
J2017.4+0602	PSR J2017+0603	304.35	6.05	MSP	PLEC	1.800	2.20 × 10^–6	1.98	—	144.6	43.2
J2017.9+3625	PSR J2017+3625	304.49	36.43	PSR	PLEC	1.467	6.99 × 10^–6	2.53	—	289.8	5.7
J2021.0+4031e	gamma Cygni	305.27	40.52	SNR	LP	7.758	2.07 × 10^–7	1.88	0.060	276.4	95.9
J2021.1+3651	PSR J2021+3651	305.28	36.86	PSR	PLEC	1.842	2.62 × 10^–5	2.32	—	288.8	114.0
J2028.3+3331	PSR J2028+3332	307.08	33.53	PSR	PLEC	1.467	6.57 × 10^–6	2.32	—	294.6	17.5
J2028.6+4110e	Cygnus X	307.17	41.17	SFR	LP	2.036	2.90 × 10^–5	2.04	0.033	273.5	368.3
J2030.0+3641	PSR J2030+3641	307.51	36.69	PSR	PLEC	1.650	3.92 × 10^–6	2.33	—	289.2	12.6
J2030.9+4416	PSR J2030+4415	307.73	44.27	PSR	PLEC	1.284	6.77 × 10^–6	2.47	—	257.2	5.4
J2032.2+4127	PSR J2032+4127	308.06	41.46	PSR	PLEC	2.918	3.31 × 10^–6	2.26	—	272.2	47.2
J2035.0+3632	PSR J2034+3632	308.76	36.54	MSP	PLEC	2.456	5.99 × 10^–7	2.17	—	289.5	11.3
J2043.3+1711	PSR J2043+1711	310.84	17.19	MSP	PLEC	1.222	3.47 × 10^–6	2.10	—	247.9	20.9
J2055.8+2540	PSR J2055+2539	313.96	25.67	PSR	PLEC	1.279	8.39 × 10^–6	2.18	—	287.7	26.6
J2111.4+4606	PSR J2111+4606	317.86	46.10	PSR	PLEC	1.305	4.84 × 10^–6	2.26	—	245.4	11.9
J2214.6+3000	PSR J2214+3000	333.67	30.01	MSP	PLEC	1.090	5.97 × 10^–6	2.06	—	295.1	28.8
J2301.9+5855e	CTB 109	345.49	58.92	SNR	LP	3.461	1.57 × 10^–7	1.91	0.054	119.2	6.8
J2302.7+4443	PSR J2302+4442	345.69	44.72	MSP	PLEC	2.049	2.04 × 10^–6	2.02	—	254.5	55.8
J2304.0+5406e	—	346.01	54.11	—	LP	14.034	1.58 × 10^–8	1.76	0.127	175.6	18.0
J2323.4+5849	Cas A	350.86	58.82	snr	LP	2.232	1.38 × 10^–6	1.87	0.076	120.5	20.9

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$图 6 赤道坐标系(J2000 坐标)下HADAR对Fermi-LAT源的观测显著性预期天图, 上面标注为河外源, 下面标注为河内源及未知类型和未关联的源, 显著性显示范围为–3—15\r\nFig. 6. Expected significance sky map of HADAR observations with respect to Fermi-LAT sources in the equatorial coordinates (J2000 epoch). The map is annotated with extragalactic sources above, and with galactic sources, unknown sources, and unassociated sources below. Significance levels are displayed in the range of –3 to 15$

图 6 赤道坐标系(J2000 坐标)下HADAR对Fermi-LAT源的观测显著性预期天图, 上面标注为河外源, 下面标注为河内源及未知类型和未关联的源, 显著性显示范围为–3—15

Fig. 6. Expected significance sky map of HADAR observations with respect to Fermi-LAT sources in the equatorial coordinates (J2000 epoch). The map is annotated with extragalactic sources above, and with galactic sources, unknown sources, and unassociated sources below. Significance levels are displayed in the range of –3 to 15

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5.2.1 耀变体

根据AGN统一模型, 不同类型的AGN其物理本质是一样的, 由于对AGN观测角度的不同(正对或偏离喷流方向)导致产生不同类型的AGN类型^[11]. 耀变体是一类喷流与视线夹角较小的AGN, 因此存在多普勒放大因子. 对耀变体的观测, 在VHE能段已经探测到80个耀变体¹, 其中大部分类型是HBL, FSRQ的观测主要依靠IACTs实验, 目前为止仅有9个FSRQs被观测到. 耀变体的一个重要观测特征是在不同时间尺度具有明显的流强变化, 现代IACTs实验的灵敏度可以观测到百分之几甚至小于1%的Crab流强, 因此一些流强较弱的源也已经被观测到, 比如RBS0413^[43], 1ES 0414+009^[44]和1ES 1312-423^[45]等. 耀变体的光变周期从几分钟到几年不等, 对较长时间尺度(天或小时)的耀变现象可以通过传统的激波加速理论来解释, 然而对快速光变(分钟量级或更小), 经典理论已不再适合, 尤其是在FSRQs观测到的短光变VHE能段的耀变, 比如在PKS 1222+21, MAGIC观测到约10 min光变的耀变^[46].

耀变体SED一般具有非热辐射的双峰结构, 低能峰主要是由喷流中相对论电子的同步辐射产生的, 第二个峰的起源一直存在争论, 可能是轻子起源、强子起源或两者的混合模型. 大部分耀变体能谱都可以用单区轻子模型(one-zone synchrotron self-compton, SSC)解释, 但是也有一些观测发现, 某些源无法用SSC模型解释, 例如1ES 1101-232^[47]和1ES 0229+200^[48], 谱指数偏硬(Γ < 1.5), 逆康普顿散射峰在几个TeV处. 对这些源能谱机制的解释还需要更多多波段的联合观测. HADAR运行1 a预期能观测到36个耀变体, 包括34个BL Lacs和2个FSRQs. 结合HADAR在观测AGN方面的优势, 通过对耀变体的光变及能谱观测, 将有助于进一步研究耀变体的伽马辐射起源及粒子加速机制.

5.2.2 射电星系

现在已经证实邻近的射电星系也是一种伽马射线源, 然而射电星系产生伽马射线的辐射机制还不是完全清楚. 射电星系提供了AGN中产生伽马射线辐射区域的重要信息, 伽马射线很可能产生于核区附近或喷流的结点处, 射电瓣也是可能的候选位置. Fermi-LAT已观测到GeV能段的射电星系有46个^[36], 在甚高能段到目前为止仅有6个射电星系的VHE伽马辐射被探测到, 分别是PKS 0625-35, M87, NGC 1275, Cen A, IC 310和3C 264, 大部分源的耀变周期是不确定的. 通过对射电星系IC 310和Cen A的观测, 已经证实在这些星系产生的伽马射线辐射很可能起源于黑洞附近. 其中, MAGIC于2014年在IC 310观测到连续两个5 min时间尺度的快速光变^[49], 该结果进一步限制了喷流内部辐射区域的大小, 认为该辐射区域可能比中心黑洞的引力半径更小. 在这种情况下, 活动星系喷流的标准辐射模型不再适用, 一种解释是辐射可能与相对论粒子穿过位于射电喷流位置磁层时的电场加速有关^[49]. 对Cen A的观测, H.E.S.S.在2020年探测到了大尺度喷流结构的TeV辐射^[50]. 这些观测证实了在活动星系核大尺度喷流上存在被加速到极端高能的粒子. 对M87的观测, VERITAS在2009年观测到伴随射电流强变化的强烈VHE伽马射线耀变, 证实了带电粒子在黑洞附近被加速到VHE能量^[51].

这些射电星系在静态期时TeV能段的流强大小约为20 mCrab, 根据预期, 有3个射电星系NGC 1275, M87和B2 1447+27可以被HADAR观测到, 具体信息见表4. 通过HADAR实验对这些射电星系的长期观测, 有助于我们了解其光变特征, 更好地理解射电星系产生伽马射线的辐射机制, 同时了解射电星系的伽马辐射在整个活动星系伽马辐射中所占的比例. 随着HADAR的长时间运行, 预计也可能有更多的射电星系伽马射线辐射被探测到.

5.2.3 星暴星系

星暴星系是一个大质量恒星形成率高的快速暴发区, 宇宙线能量密度远高于普通星系. 宇宙线质子和周围星际物质相互作用产生伽马射线. 现有观测数据显示伽马射线的辐射机制更倾向于强子起源. 对星暴星系的伽马射线观测对研究宇宙线强子的非热辐射过程以及恒星形成过程具有重要意义, 比如可以通过伽马射线的光度研究星系的宇宙线能量密度, 在高恒星形成率的极端条件下研究宇宙线的起源等. 两个近邻的星暴星系NGC253和M82已经在HE和VHE能段被探测到, 其中NGC253最早被H.E.S.S.观测到^[52], 之后H.E.S.S.和Fermi-LAT进行了联合观测分析, 得出其能谱可用一个幂律谱描述, 倾向于强子模型^[53]. M82的伽马射线辐射最早被VERITAS以4.8σ显著性观测到^[54], 后来也被Fermi-LAT在HE能段观测到^[55]. NGC253和M82都展示了较弱的辐射水平, 分别为3和9 mCrab流强水平, 这两个源基本上是星暴星系中最亮的两个伽马射线星系. 除这两个源外, Fermi-LAT还观测到NGC1068和NGC4945星暴星系, 这些源都没有显著光变, 能谱可以用幂律谱很好地描述(Γ $\sim$ 2.2). 位于HADAR视场内的星暴星系有3个, 分别是NGC 3424, Arp 299和Arp 220, 但是由于流强水平较弱, 没有预期到有显著的伽马射线辐射可以被HADAR探测到.

5.2.4 未关联源的分类类型讨论

在4FGL-DR3源表中还存在2157个未关联的源, 这些源由于没有其他波段的对应体, 其类型往往不能确定. 根据文献[33], 不同已知类型源的能谱分布呈现不同特征, 因此可以从已知源的光谱指数、光变指数和谱曲率等方面的能谱特征对未关联源进行分类讨论.

从未关联源的谱指数随银纬的变化可以看出, 低银纬源( $\left|b\right|$ < 10°)的谱指数普遍软于高银纬源. 对高银纬未关联源, 考虑到BCUs的谱指数分布特点, 高银纬源的谱指数分布与BCUs的谱指数分布类似, 因此可以得出高银纬未关联源大部分属于耀变体类型. 如果进一步考虑这些源的统计显著性特点, 发现大部分高统计显著性的源倾向于毫秒脉冲星(millisecond pulsars, MSP)类型, 而低统计显著性的源倾向于BCU类型^[33].

对低银纬未关联源, 从源的数目随银纬的分布来看, 靠近银道面的未关联源具有一个显著的簇状分布, 分布宽度较窄, 与年轻脉冲星分布类似, 且谱的曲率参数β也与脉冲星相似, 因此低银纬未关联源倾向于脉冲星类型. 但是这些源也存在一些区别于脉冲星的特征, 比如整体银纬分布宽于脉冲星分布、处于低银纬源的数目明显多于脉冲星却未被其他波段实验探测到等. 因此还需要对这些未关联源做进一步探测和研究. 在HADAR视场内的未关联源有592个, 在利用HADAR对这些未关联源进行观测预期时, 我们并未考虑EBL的吸收效应, 预期可以观测到6个未关联的源.

6. 结　论

随着地面和空间伽马射线实验的发展, 近二十几年来, 大量伽马射线源已经被观测到, 包括低能和高能段, 河内和河外源. 这些源的发现和观测增加了我们对伽马射线天文物理机制的理解, 包括脉冲星辐射机制、AGN的喷流辐射机制等. HADAR实验创新性地采用纯水作为介质构造半球型透镜成为广角的切伦科夫望远镜, 以实现低阈能、高灵敏度和大视场的优势, 具有传统IACTs实验所不具备的大视场优势, 因此将成为伽马天文爆发源和时变源的理想搜寻探测器和全天伽马源的观测仪器.

本文基于Fermi-LAT的最新4FGL-DR3和4LAC-DR3源表, 对HADAR实验对这些源的观测能力进行了详细研究. 对银河系外的源, 将这些源HE能段的能谱外推至VHE能段, 同时加入EBL的吸收效应, 通过与现有VHE实验数据对比, 证明该外推方法可行. 通过对这些源的显著性进行模拟, HADAR运行一年预期共有93个伽马射线源以大于5倍的显著性标准偏差被观测到, 包括45个银河系内的源, 39个银河系外的源, 3个未知类型的源和6个未关联的源.

HADAR可以对其视场内的源进行连续监测, 随着实验的运行, 将提高对已有伽马射线源的观测显著性, 同时也会增加探测新源的可能性. 对这些源的长期观测将为我们提供丰富的能谱数据, 以研究伽马射线源的能谱特点、光变特点及物理产生机制等. 除了对伽马射线天体源本身性质的研究外, HADAR的长期观测也将对基础物理的研究, 比如EBL的研究、量子引力效应及搜寻暗物质等发挥重要作用.

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图 1 HADAR阵列示意图　(a)阵列分布图; (b)单个水透镜详细结构图^[21]

Figure 1. Schematic of HADAR: (a) Layout of the HADAR experiment; (b) detailed design of a water-lens telescope^[21].

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图 2 HADAR及其他伽马射线实验的灵敏度曲线对比图^[23]

Figure 2. Comparisons of the sensitivity of HADAR with other γ-ray instruments^[23]

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Figure 3. Attenuation ${\rm{e}}^{-\tau}$ of gamma-rays versus gamma-ray energy, for sources at z = 0.03, 0.1, 0.25, 0.5 and 1.0. Results are compared for Wilkinson microwave anisotropy probe 5-year (WMAP5, solid) and WMAP5 + fixed (dash-dotted violet) models, as well as the model of Domínguez^[38] (dash-dotted red). Increasing distance causes absorption features to increase in magnitude and appear at lower energies. A plateau can be seen between 1–10 TeV at low redshift^[37]

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Figure 4. Gamma-ray spectral energy distribution for the sources 3C 66A, 1ES 1218+304, PKS 1424+240, and PG 1553+113 obtained over a wide energy range by extrapolation. The resulting data show that the spectral models using the intrinsic spectral function and EBL absorption fit the experimental data well. The Fermi-LAT 4FGL data is represented by blue diamonds in the low-energy band, while in the VHE band the VERITAS data is depicted by yellow circles for the low state and yellow dots for the different flaring states. Three different red dashed lines represent different spectral function models, while the solid line represents the Fermi-LAT preferred function. The y-axis represents the flux, which includes the absorption effect of EBL

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图 5 河外源的预期能谱图, 图中蓝色实线为BL Lacs, 红色虚线为FSRQs, 绿色实线为BCUs, 黑色虚线为Nonblazar AGN, 黑色实线为HADAR运行1 a的灵敏度曲线

Figure 5. Expected energy spectrum for extragalactic sources. The blue solid line represents BL Lacs, the red dashed line represents FSRQs, the green solid line represents BCUs, the black dashed line represents Nonblazar AGN, and the black solid line indicates the sensitivity of HADAR operating for 1 a

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Figure 6. Expected significance sky map of HADAR observations with respect to Fermi-LAT sources in the equatorial coordinates (J2000 epoch). The map is annotated with extragalactic sources above, and with galactic sources, unknown sources, and unassociated sources below. Significance levels are displayed in the range of –3 to 15

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表 1 HADAR及其他IACT和EAS实验的性能对比, 表中列出了各实验的名称、覆盖天区、视场、能量阈值、角分辨、观测点源的灵敏度和参考文献

Experiment	Hemisphere/(N, S)	FOV/sr	Energy threshold	Angular resolution/(°)	Sensitivity/Crab	Ref.
Fermi-LAT 2FHL	space	2.7	10 GeV–2 TeV	0.1°(30 GeV)	3%–4%	[24]
LHAASO-WCDA	N	1.5	100 GeV–30 TeV	0.4°(2 TeV)	< 10%	[29]
HAWC	N	1.5	100 sGeV–10 sTeV	~0.5°	5%–10%	[9]
H.E.S.S.	S	0.006	30 GeV–100 TeV	0.08°	0.4%–2.0%	[7]
MAGIC	N	0.003	50 GeV–10 TeV	~0.1°	~0.7%	[25]
CTA	N, S	0.0048–0.015	20 GeV–300 TeV	0.07°(1 TeV)	0.2%–0.4%	[4]
HADAR	N	0.84	10 GeV–10 TeV	0.4°(100 GeV)	1.3%–2.4%	[22]

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表 2 HADAR视场内4个AGN源的性质参数, 谱的模型参数从4LAC/4FGL导出. 表中从左到右分别为: 4FGL源名称、源对应体、AGN类型、SED分类、红移、模型, 该谱模型下的能量参考值、对应在能量 $E_0$ 处的微分流强、谱指数Γ和曲率参数β

Table 2. Property parameters for four AGN sources, where the spectral model parameters are based on 4LAC or 4FGL. Columns from left to right are as follows: 4FGL source name, counterpart, type, class, redshift, model, $E_0$ , differential flux at $E_0$ with the fit model, spectral index Γ, curvature parameter β

4FGL Name	Counterpart	Type	Class	Redshift	Model	E₀/GeV	F₀ /(TeV^–1·cm^–2·s^–1)	Γ	β
J0222.6+4301	3C 66A	BLL	ISP	0.444	LP	1.197	1.03 × 10^–5	1.89	0.04
J1221.3+3010	1ES 1218+304	BLL	EHSP	0.184	PL	4.501	1.83 × 10^–7	1.71	—
J1427.0+2348	PKS 1424+240	BLL	HSP	0.604	LP	1.205	7.03 × 10^–6	1.71	0.06
J1555.7+1111	PG 1553+113	BLL	HSP	0.360	LP	1.802	3.84 × 10^–6	1.54	0.07

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表 3 HADAR预期观测到的Fermi-LAT源的种类和数目

Table 3. Types and numbers of Fermi-LAT sources that HADAR is expected to detect

4FGL-DR3 source classes	Number of sources in 4FGL-DR3	Number of sources in HADAR FOV	Expected to be observed by HADAR in 1 a	Expected to be observed by HADAR in 5 a
Young / Millisecond pulsars	292	106	34	52
PWNe, SNR	63	22	10	13
SNR / PWNe	114	26	0	1
Globular cluster	35	5	0	0
Star-forming region	5	2	1	1
High-mass Binary, Low-mass Binary, Binary, Nova	30	6	0	0
BL Lacs	1458	492	34	66
FSRQs	792	376	2	5
Blazar candidate of uncertain type	1493	88	0	2
Nonblazar AGN (RDG, AGN, SSRQ, CSS, NLSY1, SEY)	71	36	3	8
Starburst galaxy	8	3	0	0
Normal galaxy	6	3	0	0
Unkown	134	48	3	7
Unassociated	2157	592	6	25
Total	6658	1805	93	180

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表 4 HADAR视场内Fermi-LAT河外源的能谱参数及观测信息, 谱的参数从4LAC-DR3导出. 表中从左到右分别为: 4FGL源名称, 源对应体, 赤经, 赤纬, SED分类, 红移, 拟合模型, 该谱模型下的能量参考值, 对应在能量 $E_0$ 处的微分流强, 谱指数Γ, 曲率参数β, 有效观测时间, 观测显著性

Table 4. Property parameters for extragalactic sources in HADAR FOV, where the spectral model parameters are derived from 4LAC-DR3. Columns from left to right are as follows: 4FGL source name, counterpart, right ascension, declination, class, redshift, model, $E_0$ , differential flux at $E_0$ with the fit model, spectral index Γ, curvature parameter β, live time and significance

4FGL name	Counterpart	R.A.	Dec.	Type	Redshift	Model	E₀/GeV	F₀/(TeV^–1·cm^–2·s^–1)	Γ	β	Time/h	S/σ
J0112.1+2245	S2 0109+22	18.03	22.75	BLL	0.265	LP	0.769	1.46 × 10^–5	1.99	0.060	277.8	9.05
J0211.2+1051	MG1J021114+1051	32.81	10.86	BLL	0.200	LP	0.922	7.51 × 10^–6	2.02	0.042	196.3	6.47
J0222.6+4302	3C 66A	35.67	43.04	BLL	0.444	LP	1.246	8.40 × 10^–6	1.89	0.046	264.2	17.9
J0319.8+4130	NGC 1275	49.96	41.51	RDG	0.018	LP	0.918	4.36 × 10^–5	2.05	0.069	271.9	54.6
J0521.7+2112	TXS 0518+211	80.44	21.21	bll	0.108	LP	1.541	4.64 × 10^–6	1.86	0.045	271.0	50.2
J0620.7+2643	RX J0620.6+2644	95.18	26.73	bll	0.134	PL	17.415	1.22 × 10^–9	1.55	—	290.3	5.1
J0648.7+1516	RX J0648.7+1516	102.19	15.28	bll	0.179	LP	3.248	1.22 × 10^–7	1.60	0.056	234.3	10.9
J0650.7+2503	1ES 0647+250	102.7	25.05	bll	0.203	LP	2.067	8.44 × 10^–7	1.65	0.041	286.0	32.9
J0738.1+1742	PKS 0735+17	114.54	17.71	bll	0.424	LP	1.623	2.25 × 10^–6	1.97	0.067	251.3	5.2
J0809.8+5218	1ES 0806+524	122.46	52.31	BLL	0.138	LP	1.342	1.91 × 10^–6	1.83	0.023	193.9	15.1
J0915.9+2933	Ton 0396	138.99	29.55	bll	0.190	LP	1.390	9.28 × 10^–7	1.74	0.081	294.7	7.4
J1015.0+4926	1H 1013+498	153.77	49.43	bll	0.212	LP	1.044	6.00 × 10^–6	1.75	0.044	220.0	27.9
J1058.6+5627	TXS 1055+567	164.67	56.46	BLL	0.143	LP	1.102	2.38 × 10^–6	1.86	0.050	149.4	6.1
J1104.4+3812	Mkn 421	166.12	38.21	BLL	0.030	PLEC	1.258	1.79 × 10^–5	1.74	—	284.9	519.6
J1117.0+2013	RBS 0958	169.27	20.23	bll	0.139	PL	1.964	3.12 × 10^–7	1.95	—	266.1	5.0
J1120.8+4212	RBS 0970	170.20	42.20	bll	0.124	LP	2.416	2.11 × 10^–7	1.55	0.046	268.6	23.9
J1150.6+4154	RBS 1040	177.66	41.91	bll	0.320	LP	1.949	4.71 × 10^–7	1.55	0.135	270.0	7.2
J1217.9+3007	B2 1215+30	184.48	30.12	BLL	0.130	LP	1.248	5.77 × 10^–6	1.87	0.043	295.1	37.7
J1221.3+3010	PG 1218+304	185.34	30.17	bll	0.184	LP	2.590	5.27 × 10^–7	1.65	0.029	295.2	37.4
J1221.5+2814	W Comae	185.38	28.24	bll	0.102	LP	0.781	6.00 × 10^–6	2.11	0.024	293.1	5.5
J1230.2+2517	ON 246	187.56	25.30	bll	0.135	LP	0.800	6.66 × 10^–6	2.02	0.056	286.7	5.8
J1230.8+1223	M 87	187.71	12.39	rdg	0.004	LP	1.124	1.30 × 10^–6	2.00	0.036	210.5	5.3
J1417.9+2543	1E 1415.6+2557	214.49	25.72	bll	0.237	LP	8.155	6.13 × 10^–9	1.28	0.138	287.9	5.1
J1427.0+2348	PKS 1424+240	216.76	23.80	BLL	0.604	LP	1.254	5.70 × 10^–6	1.71	0.057	281.8	21.7
J1428.5+4240	H 1426+428	217.13	42.68	bll	0.129	PL	5.135	2.69 × 10^–8	1.65	—	266.1	10.3
J1449.5+2746	B2 1447+27	222.40	27.77	rdg	0.031	PL	14.614	5.37 × 10^–10	1.46	—	292.4	6.8
J1555.7+1111	PG 1553+113	238.93	11.19	BLL	0.360	LP	3.802	1.16 × 10^–6	1.57	0.095	199.5	56.4
J1653.8+3945	Mkn 501	253.47	39.76	BLL	0.033	LP	1.508	3.78 × 10^–6	1.75	0.018	279.5	125.1
J1725.0+1152	1H 1720+117	261.27	11.87	bll	0.180	LP	2.216	7.55 × 10^–7	1.76	0.056	205.9	14.5
J1728.3+5013	I Zw 187	262.08	50.23	bll	0.055	PL	2.983	1.82 × 10^–7	1.79	—	213.2	21.1
J1838.8+4802	GB6J1838+4802	279.71	48.04	bll	0.300	LP	1.631	8.39 × 10^–7	1.78	0.040	231.3	6.7
J1904.1+3627	MG2J190411+3627	286.03	36.45	bll	0.078	PL	5.074	2.01 × 10^–8	1.80	—	289.7	5.8
J2116.2+3339	B2 2114+33	319.06	33.66	bll	0.350	LP	1.653	1.10 × 10^–6	1.75	0.095	294.4	7.1
J2202.7+4216	BL Lac	330.69	42.28	BLL	0.069	LP	0.871	4.07 × 10^–5	2.12	0.059	268.2	27.4
J2232.6+1143	CTA 102	338.15	11.73	FSRQ	1.037	PLEC	1.082	4.34 × 10^–5	2.27	—	204.5	5.9
J2250.0+3825	B3 2247+381	342.51	38.42	bll	0.119	PL	5.338	2.55 × 10^–8	1.74	—	284.2	7.9
J2253.9+1609	3C 454.3	343.50	16.15	FSRQ	0.859	PLEC	0.892	1.32 × 10^–4	2.38	—	240.7	10.9
J2323.8+4210	1ES 2321+419	350.97	42.18	bll	0.059	LP	1.857	5.31 × 10^–7	1.80	0.068	268.7	11.0
J2347.0+5141	1ES 2344+514	356.77	51.70	bll	0.044	LP	1.911	7.15 × 10^–7	1.74	0.039	199.8	29.2

DownLoad: CSV

表 5 HADAR视场内Fermi-LAT河内源的能谱参数及观测信息, 谱的参数从4FGL-DR3导出. 表中从左到右分别为: 4FGL源名称, 源对应体, 赤经, 赤纬, SED分类, 拟合模型, 该谱模型下的能量参考值, 对应在能量 $E_0$ 处的微分流强, 谱指数Γ, 曲率参数β, 有效观测时间, 观测显著性

Table 5. Property parameters for galactic sources in HADAR FOV, where the spectral model parameters are derived from 4FGL-DR3. Columns from left to right are as follows: 4FGL source name, counterpart, right ascension, declination, class, model, $E_0$ , differential flux at $E_0$ with the fit model, spectral index Γ, curvature parameter β, live time and significance

4FGL Name	Counterpart	R.A.	Dec.	Type	Model	$E_0$ /GeV	F₀/(TeV^–1·cm^–2·s^–1)	Γ	β	Time/h	S/σ
J0030.4+0451	PSR J0030+0451	7.61	4.86	MSP	PLEC	1.360	7.36 × 10^–6	2.08	—	130.1	40.6
J0102.8+4839	PSR J0102+4839	15.71	48.66	MSP	PLEC	1.378	1.42 × 10^–6	2.18	—	226.4	6.0
J0106.4+4855	PSR J0106+4855	16.61	48.93	PSR	PLEC	1.578	1.66 × 10^–6	2.11	—	224.2	14.2
J0218.1+4232	PSR J0218+4232	34.53	42.55	MSP	PLEC	0.820	1.20 × 10^–5	2.35	—	266.8	6.2
J0220.1+1155	—	35.04	11.92	—	PL	16.622	3.98 × 10^–10	1.57	—	206.2	5.6
J0340.3+4130	PSR J0340+4130	55.10	41.51	MSP	PLEC	1.659	1.38 × 10^–6	2.03	—	271.9	24.6
J0357.8+3204	PSR J0357+3205	59.46	32.08	PSR	PLEC	1.104	1.26 × 10^–5	2.30	—	295.5	19.3
J0425.6+5522e	SNR G150.3+04.5	66.42	55.37	SNR	LP	7.240	1.19 × 10^–7	1.64	0.047	161.8	123.6
J0534.5+2201i	Crab Nebula	83.63	22.02	PWN	LP	10.000	5.50 × 10^–7	1.75	0.080	274.7	639.6
J0540.3+2756e	Sim 147	85.10	27.94	SNR	LP	1.192	5.50 × 10^–6	2.07	0.081	292.7	11.1
J0554.1+3107	PSR J0554+3107	88.55	31.12	PSR	PLEC	1.066	4.06 × 10^–6	2.34	—	295.5	5.1
J0605.1+3757	PSR J0605+3757	91.28	37.96	MSP	PLEC	1.507	7.88 × 10^–7	2.18	—	285.7	5.3
J0617.2+2234e	IC 443	94.31	22.58	SNR	LP	4.551	2.58 × 10^–6	2.28	0.123	277.1	37.6
J0620.9+2201	—	95.23	22.02	—	PL	20.913	6.45 × 10^–10	1.61	—	274.7	5.7
J0631.5+1036	PSR J0631+1036	97.88	10.60	PSR	PLEC	1.540	2.52 × 10^–6	2.20	—	193.8	11.1
J0631.8+0645	PSR J0631+0646	97.96	6.76	PSR	PLEC	2.258	7.60 × 10^–7	2.22	—	152.9	5.9
J0633.7+0632	PSR J0633+0632	98.44	6.54	PSR	PLEC	1.527	8.13 × 10^–6	2.22	—	150.4	26.3
J0633.9+1746	PSR J0633+1746	98.48	17.77	PSR	PLEC	1.670	3.19 × 10^–4	2.10	—	251.7	575.7
J0650.6+2055	NVSS J065035+205556	102.66	20.93	unk	LP	3.643	4.42 × 10^–8	1.63	0.096	269.6	9.5
J0751.2+1808	PSR J0751+1807	117.80	18.14	MSP	PLEC	1.643	9.45 × 10^–7	2.06	—	254.1	13.1
J1312.7+0050	PSR J1312+0051	198.19	0.84	MSP	PLEC	1.301	2.01 × 10^–6	2.15	—	76.3	5.7
J1554.2+2008	—	238.55	20.15	—	PL	4.619	1.14 × 10^–8	1.82	—	265.6	5.0
J1816.5+4510	PSR J1816+4510	274.15	45.17	MSP	PLEC	1.171	1.48 × 10^–6	2.14	—	251.6	6.1
J1836.2+5925	PSR J1836+5925	279.06	59.43	PSR	PLEC	1.428	6.64 × 10^–5	2.07	—	112.6	388.8
J1846.3+0919	PSR J1846+0919	281.60	9.33	PSR	PLEC	1.458	3.78 × 10^–6	2.19	—	181.0	14.9
J1854.5+2050	—	283.64	20.84	—	PL	103.233	2.68 × 10^–11	1.01	—	269.2	34.8
J1857.7+0246e	HESS J1857+026	284.45	2.77	PWN	PL	6.063	2.25 × 10^–7	2.13	—	103.1	19.5
J1907.9+0602	PSR J1907+0602	286.98	6.04	PSR	PLEC	1.898	1.39 × 10^–5	2.37	—	144.4	31.3
J1910.8+2856	NVSS J191052+285621	287.72	28.94	unk	PL	7.243	6.08 × 10^–9	1.80	—	294.1	7.1
J1911.0+0905	W 49B	287.76	9.09	snr	LP	4.552	7.74 × 10^–7	2.28	0.112	178.6	8.5
J1918.0+0331	NVSS J191803+033032	289.51	3.52	unk	PL	12.647	2.39 × 10^–9	1.72	—	113.0	6.2
J1923.2+1408e	W 51C	290.82	14.14	SNR	LP	2.768	5.08 × 10^–6	2.21	0.109	225.4	25.9
J1924.3+1628	—	291.10	16.48	—	PL	22.893	7.99 × 10^–10	1.76	—	243.1	7.7
J1952.9+3252	PSR J1952+3252	298.25	32.88	PSR	PLEC	1.618	9.92 × 10^–6	2.29	—	295.1	39.3
J1954.3+2836	PSR J1954+2836	298.59	28.60	PSR	PLEC	1.519	8.08 × 10^–6	2.32	—	293.7	23.1
J1958.7+2846	PSR J1958+2846	299.68	28.77	PSR	PLEC	1.356	1.13 × 10^–5	2.35	—	293.9	21.1
J2017.4+0602	PSR J2017+0603	304.35	6.05	MSP	PLEC	1.800	2.20 × 10^–6	1.98	—	144.6	43.2
J2017.9+3625	PSR J2017+3625	304.49	36.43	PSR	PLEC	1.467	6.99 × 10^–6	2.53	—	289.8	5.7
J2021.0+4031e	gamma Cygni	305.27	40.52	SNR	LP	7.758	2.07 × 10^–7	1.88	0.060	276.4	95.9
J2021.1+3651	PSR J2021+3651	305.28	36.86	PSR	PLEC	1.842	2.62 × 10^–5	2.32	—	288.8	114.0
J2028.3+3331	PSR J2028+3332	307.08	33.53	PSR	PLEC	1.467	6.57 × 10^–6	2.32	—	294.6	17.5
J2028.6+4110e	Cygnus X	307.17	41.17	SFR	LP	2.036	2.90 × 10^–5	2.04	0.033	273.5	368.3
J2030.0+3641	PSR J2030+3641	307.51	36.69	PSR	PLEC	1.650	3.92 × 10^–6	2.33	—	289.2	12.6
J2030.9+4416	PSR J2030+4415	307.73	44.27	PSR	PLEC	1.284	6.77 × 10^–6	2.47	—	257.2	5.4
J2032.2+4127	PSR J2032+4127	308.06	41.46	PSR	PLEC	2.918	3.31 × 10^–6	2.26	—	272.2	47.2
J2035.0+3632	PSR J2034+3632	308.76	36.54	MSP	PLEC	2.456	5.99 × 10^–7	2.17	—	289.5	11.3
J2043.3+1711	PSR J2043+1711	310.84	17.19	MSP	PLEC	1.222	3.47 × 10^–6	2.10	—	247.9	20.9
J2055.8+2540	PSR J2055+2539	313.96	25.67	PSR	PLEC	1.279	8.39 × 10^–6	2.18	—	287.7	26.6
J2111.4+4606	PSR J2111+4606	317.86	46.10	PSR	PLEC	1.305	4.84 × 10^–6	2.26	—	245.4	11.9
J2214.6+3000	PSR J2214+3000	333.67	30.01	MSP	PLEC	1.090	5.97 × 10^–6	2.06	—	295.1	28.8
J2301.9+5855e	CTB 109	345.49	58.92	SNR	LP	3.461	1.57 × 10^–7	1.91	0.054	119.2	6.8
J2302.7+4443	PSR J2302+4442	345.69	44.72	MSP	PLEC	2.049	2.04 × 10^–6	2.02	—	254.5	55.8
J2304.0+5406e	—	346.01	54.11	—	LP	14.034	1.58 × 10^–8	1.76	0.127	175.6	18.0
J2323.4+5849	Cas A	350.86	58.82	snr	LP	2.232	1.38 × 10^–6	1.87	0.076	120.5	20.9

DownLoad: CSV

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