緻密脈衝雙星系統（cbMSP）是由快速旋轉的中子星（NS）和低質量的伴星所
組成的，且它們的軌道週期小於24小時。在本論文中，我們採用多信使方法研究這
類系統的兩個方面：
（i）我們報告了迄今為止觀測到的最緻密cbMSP系統， PSR J1653-0158，
的X射線和伽馬射線觀測結果，其軌道周期為75分鐘。我們擬合了XMM-
Newton和NuSTAR X射線光譜，並顯示可以通過在軌道內衝擊波加速的電子的
同步輻射來解釋它，以及由Fermi測量的伽馬射線是脈衝星磁層中電子和正電子的
曲率輻射。我們對cbMSP PSRJ1653-0158和PSRJ1311-3430進行了運動學分析，表
明這兩個系統可能起源於銀盤。
（ii）我們提出了一種利用多信使觀測資訊進行質量確定的方法。在這項研究
中，我們專注於一類cbMSP系統，其軌道周期小於1小時，可以被LISA探測到的引
力波源。通過結合從光學觀測獲得的雙星質量函數和從引力波觀測獲得的補充質量
函數，我們演示了如何對中子星質量進行改進的約束，並打破質量和軌道傾斜度的
簡並現象。

Compact millisecond pulsar binaries (cbMSP) are extreme systems that consist of
a fast spinning neutron star (NS) and a low mass companion star with short orbital
period less than 24 hours. We use an multi-messenger approach to study two aspects
of such systems in this thesis:
(i) We report X-ray and gamma-ray observations of the most compact cbMSP
record to date PSR J1653-0158, which orbital period is 75-minute. We fit the joint
XMM-Newton and NuSTAR X-ray spectrum and showed that it can be explained by
synchrotron radiation from electrons accelerated in the intra-binary shock, and the
gamma-rays measured by Fermi are curvature radiations from electrons and positrons
in the pulsar magnetosphere. Our kinematic analysis of the cbMSP PSR J1653{0158
and PSR J1311{3430 indicates that the two systems are likely to have originated from
the Galactic Disk.
(ii) We propose a mass determination method utilising multi-messenger observational
information. In this study we focus on a subset of cbMSP systems with
orbital periods shorter than 1 hour, that are gravitational wave sources detectable
by LISA. By combining the binary mass function obtained from optical observations
and a complementary mass function derived from gravitational wave observations, we
demonstrate how we can set improved constraints on the neutron star mass and break
the degeneracy in the mass and viewing inclination determination.

Contents
Declaration iv
Abstract v
Acknowledgements viii
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Evolution of cbMSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Instruments and data reduction 7
2.1 NuSTAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Fermi-LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 X-ray/
-ray observations of cbMSP J1653􀀀0158 11
3.1 Timing analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.1 X-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.2 Gamma-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Theoretical discussions of PSR J1653􀀀0158 . . . . . . . . . . . . . . . 14
3.4 Population and kinematics study of Tidarren . . . . . . . . . . . . . . . 18
4 Multi-messenger mass determination method for cbMSP 26
4.1 SNR threshold for cbMSP as gravitational-wave sources . . . . . . . . . 27
4.1.1 Multi-messenger identication . . . . . . . . . . . . . . . . . . . 30
4.2 Parameter estimation method . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Analytical estimates of NS's mass by two mass functions . . . . . . . . 38
4.4 The joint constraints on the NS's mass . . . . . . . . . . . . . . . . . . 41
4.5 Comments on the applicability of the method . . . . . . . . . . . . . . 46
4.5.1 Observational prospects . . . . . . . . . . . . . . . . . . . . . . 50
4.5.2 Assumptions and Error propagation . . . . . . . . . . . . . . . . 52
5 Summary 57
6 Future works 60

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