Searching optimum equation of states of neutron stars with internal magnetic fields

Persistent ID (NDL): info:ndljp/pid/12911132

Material type: 博士論文

Author: 渡邊, 千夏

Publisher: 埼玉大学大学院理工学研究科

Publication date: 2022

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Note (General)：: type:textOn August 17 in 2017, a gravitational wave signal from a binary neutron star spiral was observed at various wavelengths (GW170817). Now, obse...

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Material Type: 博士論文
Title: Searching optimum equation of states of neutron stars with internal magnetic fields
Author/Editor: 渡邊, 千夏
Author Heading: 渡邊, 千夏
Publication, Distribution, etc.: 埼玉大学大学院理工学研究科
Publication Date: 2022
Publication Date (W3CDTF): 2022
Alternative Title: 内部磁場を持つ中性子星における最適な状態方程式の探索
Degree grantor/type: 埼玉大学
Date Granted: 2022-03-24
Date Granted (W3CDTF): 2022-03-24
Dissertation Number: 甲第1237号
Degree Type: 博士(理学)
Text Language Code: eng
Target Audience: 一般
Note (General): type:text
On August 17 in 2017, a gravitational wave signal from a binary neutron star spiral was observed at various wavelengths (GW170817). Now, observation of the gravitational waves together with ordinary light and X-rays from pulsars and magnetars (neutron stars with magnetic field strength of B ～ 10¹⁵ G) are being searched for throughout the world. Gravitational waves together with electromagnetic sources have opened an era of multi-messenger astrophysics, which provides a powerful means for the precise information on neutron stars and magnetars. Recently, neutron star PSR J1614―2230 making a binary system with a white dwarf has been discovered to have the mass of 1.97 ± 0.04M⨀. In 2013, mass of the neutron star PSR J0348+0432 was measured as 2.01 ± 0.04M⨀. Furthermore, in 2019, PSR J0740+6620 was observed by NICER and XMM―Newton and mass was measured as 2.072+0.067-0.066M⨀. Existence of neutron stars with mass around twice the solar mass has been now established. Such very heavy neutron stars give strong constraints on equations of state (EoS) for nuclear matter. In this thesis, mass and radius of a neutron star are calculated for twelve EoSs based on the relativistic mean field (RMF) theory, and mass-radius relations (MR relations) are obtained with or without strong internal magnetic fields. For different choices of the observed constraints, we investigate which EoS is optimum in describing the structure of a neutron star. As the first constraints for EoSs, the observed maximum mass of 2.072M⨀ (PSR J0740+6620), the upper limit radius of 13.76 km at 1.4M⨀, and radius 12.39+1.30-0.98 km at 2.072M⨀ are considered. Here two EoSs with strong internal magnetic fields meet the requirements of observations. As the second constraints for EoSs, the observed masses and radii of two pulsars are considered for the following neutron stars: PSR J0030+0451 (R = 13.02+1.24-1.06 km at M = 1.44+0.15-0.14M⨀) and PSR J0740+6620. Here three EoSs with strong internal magnetic fields meet the requirements of observations. Furthermore, in this thesis, to search for a proper EoS with strong internal magnetic fields, we have made an attempt to vary the strength B0 at the center, the strength Bs at the surface, and two other shape parameters of the internal magnetic field, which is a smooth function of the baryon number density. Consequently, mass and radius of a neutron star take various values. We investigate which EoS is optimum in the sense that mass and radius determined by a certain EoS are within the proper range of the observed masses and radii.
1 Introduction 51.1 Neutron stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Problems concerning neutron stars . . . . . . . . . . . . . . . . . . . . . . 61.3 What are done in this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Nuclear physics and nuclear matter 82.1 Nuclear physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Nuclear matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Neutron star with quark matter . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 MIT Bag model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Observation 173.1 Rotating Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Magnetic fields in Neutron Star . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.1 Gravitational wave observation . . . . . . . . . . . . . . . . . . . . 21 3.3.2 Gravitational waves from GW170817 . . . . . . . . . . . . . . . . . 223.4 Mass and Radius of Neutron star . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.1 Masses around 2 M⨀ . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.2 Radius of neutron star . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.3 Both mass and radius observation of Neutron star . . . . . . . . . 29 4 Formalism 304.1 Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 RMF Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4 Baym-Pethick-Sutherland (BPS) EoS . . . . . . . . . . . . . . . . . . . . . 344.5 Tolman Oppenheimer-Volkoff equation . . . . . . . . . . . . . . . . . . . . 344.6 Hartle Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.7 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.7.1 EoS of hadronic matter with magnetic fields . . . . . . . . . . . . . 37 4.7.2 Landau diamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . 374.8 Eccentricity of neutron star . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Results 395.1 MR relations of EoSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2 MR relation of EoS with rotation . . . . . . . . . . . . . . . . . . . . . . . 415.3 MR relations of EoSs with internal magnetic fields . . . . . . . . . . . . . 435.4 MR relation of EoS with rotation and magnetic fields . . . . . . . . . . . 486 Discussion 526.1 Two-solar-mass problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.2 Radius at 1.4 M⨀ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.3 Radius at 2.072 M⨀ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.4 Constraining masses and radii from two observed pulsars . . . . . . . . . 556.5 Comparison of the case with/without hyperons with magnetic fields . . . 566.6 Magnetic fields with different forms . . . . . . . . . . . . . . . . . . . . . 57 6.6.1 Change of α and γ in magnetic fields . . . . . . . . . . . . . . . . 57 6.6.2 Searching optimum α and γ in magnetic fields for each EoS . . . 626.7 Particle populations of neutron star with magnetic fields . . . . . . . . . . 687 Summary 727.1 Searching EoS in rotating magnetized neutron star . . . . . . . . . . . . . 727.2 Searching α and γ of magnetic fields . . . . . . . . . . . . . . . . . . . . . 737.3 Summary of summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Appendices 83A Relativistic mean field 84 A.1 RMF without and with magnetic fields . . . . . . . . . . . . . . . . . . . . 84B Landau level 88 B.1 Zero temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 B.2 BPS with magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 89C TOV equation 91 C.1 Derivation of TOV equation . . . . . . . . . . . . . . . . . . . . . . . . . . 91D Units 94 D.1 Gravitational unit and Natural unit . . . . . . . . . . . . . . . . . . . . . 94 D.1.1 Gravitational unit . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 D.1.2 Natural unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 E Hartle equations 96F Energy levels in a strong magnetic field 100G Original results by changing α and γ for neutron star with magnetic fields (Bs = 10¹² G) 103H Original resutls by changing α and γ for neutron star with magnetic fields (Bs = 10¹⁵ G) 128
指導教員 : 吉永尚孝教授
DOI: 10.24561/00019782
https://doi.org/10.24561/00019782
Persistent ID (NDL): info:ndljp/pid/12911132
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Date Accepted (W3CDTF): 2023-07-08T03:42:30+09:00
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Periodical Title (URI): http://dx.doi.org/10.24561/00019782
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