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开展强磁场环境下中子星物质性质的研究对约束中子星物态方程, 揭示星体内部磁场分布形式等有重要意义. 本文基于相对论平均场理论利用GL91参数组研究了处于β平衡条件下传统中子星物质在强磁场作用下的主要宏观性质. 结果表明, 强磁场的引入使传统中子星物态方程变硬, 星体质量上限由2.111 M⊙增大到3.081 M⊙, 相同质量星体对应的半径变大使星体变得不那么致密; 强磁场对传统中子星表面引力红移有抑制作用, 对转动惯量有促进作用. 此外, 给出了目前已观测到的四颗大质量脉冲星—PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135, 以及双星合并事件GW190814中质量在2.50 M⊙—2.67 M⊙的致密星体表面引力红移和转动惯量的理论值范围. 结果表明, 随着中子星内部磁场的增强, 这五颗星的表面引力红移值范围变窄, 而转动惯量的范围变宽.Research on the properties of neutron stars with strong magnetic fields is of great significance in constraining the equation of state and revealing the real distribution of magnetic fields in neutron stars. The main macroscopic properties of the traditional neutron star matter under β equilibrium condition are studied within the relativistic mean field theory through using the GL91 parameter set by considering the strong magnetic field. It is found that the onset of the strong magnetic field leads to the stiffened equation of state of the traditional neutron star matter. The maximum mass of the traditional neutron star grows from 2.111 M⊙ to 3.081 M⊙, the radius of the fixed mass traditional neutron star grows larger with the increase of internal magnetic field, which makes traditional neutron star become less dense. The strong magnetic field can also reduce the surface gravitational redshift and strengthen the moment of inertia of the traditional neutron star matter. In addition, the theoretical ranges of the surface gravitational redshift and the moment of inertia for the four massive PSRs J1614-2230, J0348+0432, J0740+6620 and J2215-5135, and the 2.50 M⊙ − 2.67 M⊙ compact object in the binary merger event GW190814 are also given. The results show that the ranges of the surface redshift become narrower, while the scopes of the moment of inertia widen as the magnetizing field increases in the five stars.
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Keywords:
- neutron star /
- strong magnetic field /
- gravitational redshift /
- moment of inertia
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[2] Shao D H, Tang S P, Jiang J L, et al. 2020 Phys. Rev. D 102 063006Google Scholar
[3] Zhao X F 2020 Chin. J. Phys. 63 240Google Scholar
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[5] 陈家麟, 季沛勇 2013 上海大学学报(自然科学版) 19 176Google Scholar
Chen J L, Ji P Y 2013 Journal of Shanghai University (Natural science Edition) 19 176Google Scholar
[6] 彭芳, 彭秋和, 张丰收 2001 天文学报 42 1Google Scholar
Peng F, Peng Q H, Zhang F S 2001 Acta Astronomica Sinica 42 1Google Scholar
[7] 赵先锋, 张华 2010 四川大学学报(自然科学版) 4 28Google Scholar
Zhao X F, Zhang H 2010 Journal of Sichuan University (Natural Science Edition) 4 28Google Scholar
[8] Zhao X F 2020 Chin. J. Physics 63 240
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[10] Sen D 2021 J. Phys. G 48 025201Google Scholar
[11] Wang W, Tang Y M, Tuo Y L 2021 J. High. Energy Astrophys. 30 1Google Scholar
[12] Kouvelioton C 1998 Nature 393 253Google Scholar
[13] Kaspi V M 2003 Astrophys. J. 588 93Google Scholar
[14] Shapiro S L 1983 Black Holes, White Dwarfs and neutron Stars (New York: Wiley - Insterscience) pp277−282
[15] Lai D, Shapiro S L 1991 Astrophys. J. 383 745Google Scholar
[16] 孙晓辉, 韩金林 2002 天文学进展 20 130Google Scholar
Sun X H, Han J L 2002 Prog. Astron. 20 130Google Scholar
[17] Chakrabarty S, Debades B, Subrata P 1997 Phys. Rev. Lett. 78 2898Google Scholar
[18] Broderick A, Prakash M, Lattimer J M 2000 Astrophys. J. 537 351Google Scholar
[19] Broderick A E, Prakash M, Lattimer J M 2002 Phys. Lett. B 531 167Google Scholar
[20] Bednarek I, Brzezina A, Manka R 2003 Nucl. Phys. A 24 245Google Scholar
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[22] 张洁, 刘门全, 魏丙涛, 罗志全 2008 物理学报 57 5448Google Scholar
Zhang J, Liu M Q, Wei B T, Luo Z Q 2008 Acta Phys. Sin. 57 5448Google Scholar
[23] Dong J M, Lombardo U, Zuo W 2013 Nucl. Phys. A 898 32Google Scholar
[24] Dong J M, Zuo W, Gu J Z 2016 Sci. China Phys. Mech. 59 642003Google Scholar
[25] 鲍世绍, 胡金牛, 申虹 2018 科学通报 63 828Google Scholar
Bao S S, Hu J N, Shen H 2018 Chin. Sci. Bull. 63 828Google Scholar
[26] Boguta J, Bodmer A R 1977 Nucl. Phys. 292 413Google Scholar
[27] Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414Google Scholar
[28] Glendenning N K 1992 Phys. Rev. D 46 1274Google Scholar
[29] 朗道 著 (周奇 译)1 963 连续媒介电动力学 (北京: 人民教育出版社) 第179—182页
Landau L D, Lifshitz E M, Pitaevskii L P (translated by Zhou Q) 1963 Electrodynamics of Continuous Media (Beijing: People’s Education Press) pp179−182 (in Chinese)
[30] Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 55 374Google Scholar
[31] Tolman R C 1939 Phys. Rev. 55 364Google Scholar
[32] Worley A, Krastev P G, Li B A 2008 Astronphys. J. 685 390Google Scholar
[33] Lattimer J M, Schutz B F 2005 Astrophys. J. 629 979Google Scholar
[34] Glendenning N K 1997 Compact Stars: Nuclear Physics, Particle Physics, and General Relativity (New York: Springer-Verlag) pp75−78
[35] Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys. Rev. Lett. 79 2176Google Scholar
[36] Wiringa R B, Fiks V, Fabroeini A 1988 Phys. Rev. 38 1010Google Scholar
[37] Manchester R N 2004 Science 304 542Google Scholar
[38] Gao Z F, Shan H, Wang H 2021 Astron. Nachr. 342 369Google Scholar
[39] Krotscheck E, Kundt W 1978 Commun. Math. Phys. 60 171Google Scholar
[40] Demorest P B, Pennucci T, Ransom S M 2010 Nature 467 1081Google Scholar
[41] Fonseca E, Pennucci T T, Ellis J A 2016 Astrophys. J. 832 167Google Scholar
[42] Antoniadis J, Freire, P C C, Wex N 2013 Science 340 448Google Scholar
[43] Cromartie H T, Fonseca E, Ransom S M 2020 Nat. Astron. 4 72Google Scholar
[44] Kandel D, Romani R W 2020 Astrophys. J. 892 101Google Scholar
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[46] Fattoyev F J, Horowitz C J, Piekarewicz J 2020 Phys. Rev. C 102 065805Google Scholar
[47] Liang E P 1986 Astrophys. J. 304 682Google Scholar
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图 1 不同磁场强度下(α = 0, 20, 40, 60)中子星物质的(a)压强-核子密度、(b)质量-半径关系. 本文中, 黑红绿蓝四条线表示α = 0, 20, 40, 60四种情况; 不同颜色条纹区域分别表示PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135以及GW190814中致密星的质量测量值范围; 橙色误差棒表示NICER公布的PSR J0030+0415的质量-半径测量值对中子星质量-半径关系的约束. 各曲线上黑色圆点表示中子星最大质量所处位置, 三角形点表示最大半径所处位置
Fig. 1. Relationship of (a) the pressure - density and (b) the mass - radius in neutron star (NS) matter. In the paper the black, red, green, and blue lines represent the four cases of α = 0, 20, 40 and 60, respectively. The different colored areas stand for the recent constraints inferred from PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135 and GW190814 respectively. The orange error bar represents the constraints on the mass-radius limits of PSR J0030+0451 obtained from NICER observations. The dots and the triangle points show the maximum masses and radii of NSs for the four cases, respectively.
表 1 不同磁场强度下(α = 0, 20, 40, 60), 中子星最大质量及其对应半径和中心密度, 最大半径及其对应质量和中心密度
Table 1. Table 1. Values of the maximum NS masses Mmax and the corresponding radii R as well as the center densities ρc/ρ0, values of the maximum NS radii Rmax and the corresponding masses M as well as the center densities ρc/ρ0 with α = 0, 20, 40, 60 in npeμ matter.
α 中子星最大质量处 中子星最大半径处 M /M⊙ R /km ρc/ρ0 M /M⊙ R/km ρc/ρ0 0 2.111 11.648 7.013 0.971 14.014 2.102 20 2.574 12.496 3.977 1.520 14.306 2.227 40 2.877 13.601 2.960 2.066 15.060 2.031 60 3.081 14.375 2.478 2.415 15.765 1.734 表 2 不同磁场强度下(α = 0, 20, 40, 60), PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135以及GW190814中致密星的半径、转动惯量、引力红移理论值范围
Table 2. Ranges of the theoretical values for the radius, the moment of inertia and the gravitational redshift corresponding to PSRS J1614-2230, J0348+0432, J0740+6620, J2215-5135 and the compact star in GW190814 with α = 0, 20, 40, 60.
Source α R/km I/M⊙·km2 Z PSR J1614-2230 0 [13.067, 13.158] [131.615, 133.926] [0.317, 0.329] 20 [14.179, 14.220] [148.276, 152.485] [0.283, 0.291] 40 [15.037, 15.048] [161.795, 166.371] [0.261, 0.269] 60 [15.450, 15.670] [172.197, 175.693] [0.244, 0.253] PSR J0348-0432 0 [12.548, 12.954] [135.781, 138.653] [0.348, 0.388] 20 [14.108, 14.179] [155.490, 164.997] [0.305, 0.323] 40 [15.048, 15.068] [171.237, 182.428] [0.277, 0.291] 60 [15.690, 15.722] [182.428, 195.897] [0.260, 0.276] PSR J0740+6620 0 [11.648, 12.965] [119.641, 138.653] [0.344, 0.462] 20 [13.782, 14.170] [155.490, 194.213] [0.300, 0.416] 40 [14.976, 15.060] [171.237, 220.062] [0.273, 0.361] 60 [15.670, 15.783] [182.428, 238.087] [0.259, 0.334] PSR J2215-5135 0 — — — 20 [13.679, 13.986] [180.150, 198.670] [0.362, 0.429] 40 [14.987, 15.037] [199.859, 226.797] [0.325, 0.371] 60 [15.742, 15.783] [215.606, 244.822] [0.300, 0.343] GW190814 0 — — — 20 [12.496, 13.291] [203.820, 206.593] [0.496, 0.591] 40 [14.670, 14.905] [242.544, 264.431] [0.407, 0.470] 60 [15.670, 15.752] [262.153, 288.002] [0.370, 0.418] -
[1] Riley T E, Watts A L, Bogdanov S, et al. 2019 Astrophys. J. Lett. 887 21Google Scholar
[2] Shao D H, Tang S P, Jiang J L, et al. 2020 Phys. Rev. D 102 063006Google Scholar
[3] Zhao X F 2020 Chin. J. Phys. 63 240Google Scholar
[4] 喻传赞 1980 科学通报 16 50Google Scholar
Yu C Z 1980 Chin. Sci. Bull. 16 50Google Scholar
[5] 陈家麟, 季沛勇 2013 上海大学学报(自然科学版) 19 176Google Scholar
Chen J L, Ji P Y 2013 Journal of Shanghai University (Natural science Edition) 19 176Google Scholar
[6] 彭芳, 彭秋和, 张丰收 2001 天文学报 42 1Google Scholar
Peng F, Peng Q H, Zhang F S 2001 Acta Astronomica Sinica 42 1Google Scholar
[7] 赵先锋, 张华 2010 四川大学学报(自然科学版) 4 28Google Scholar
Zhao X F, Zhang H 2010 Journal of Sichuan University (Natural Science Edition) 4 28Google Scholar
[8] Zhao X F 2020 Chin. J. Physics 63 240
[9] Lim Y, Holt J W, Stahulak R J 2019 Phys. Rev. C 3 035802Google Scholar
[10] Sen D 2021 J. Phys. G 48 025201Google Scholar
[11] Wang W, Tang Y M, Tuo Y L 2021 J. High. Energy Astrophys. 30 1Google Scholar
[12] Kouvelioton C 1998 Nature 393 253Google Scholar
[13] Kaspi V M 2003 Astrophys. J. 588 93Google Scholar
[14] Shapiro S L 1983 Black Holes, White Dwarfs and neutron Stars (New York: Wiley - Insterscience) pp277−282
[15] Lai D, Shapiro S L 1991 Astrophys. J. 383 745Google Scholar
[16] 孙晓辉, 韩金林 2002 天文学进展 20 130Google Scholar
Sun X H, Han J L 2002 Prog. Astron. 20 130Google Scholar
[17] Chakrabarty S, Debades B, Subrata P 1997 Phys. Rev. Lett. 78 2898Google Scholar
[18] Broderick A, Prakash M, Lattimer J M 2000 Astrophys. J. 537 351Google Scholar
[19] Broderick A E, Prakash M, Lattimer J M 2002 Phys. Lett. B 531 167Google Scholar
[20] Bednarek I, Brzezina A, Manka R 2003 Nucl. Phys. A 24 245Google Scholar
[21] Mao G J, Akira 2003 Chin. J. Astron. Astrophys. 3 359Google Scholar
[22] 张洁, 刘门全, 魏丙涛, 罗志全 2008 物理学报 57 5448Google Scholar
Zhang J, Liu M Q, Wei B T, Luo Z Q 2008 Acta Phys. Sin. 57 5448Google Scholar
[23] Dong J M, Lombardo U, Zuo W 2013 Nucl. Phys. A 898 32Google Scholar
[24] Dong J M, Zuo W, Gu J Z 2016 Sci. China Phys. Mech. 59 642003Google Scholar
[25] 鲍世绍, 胡金牛, 申虹 2018 科学通报 63 828Google Scholar
Bao S S, Hu J N, Shen H 2018 Chin. Sci. Bull. 63 828Google Scholar
[26] Boguta J, Bodmer A R 1977 Nucl. Phys. 292 413Google Scholar
[27] Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414Google Scholar
[28] Glendenning N K 1992 Phys. Rev. D 46 1274Google Scholar
[29] 朗道 著 (周奇 译)1 963 连续媒介电动力学 (北京: 人民教育出版社) 第179—182页
Landau L D, Lifshitz E M, Pitaevskii L P (translated by Zhou Q) 1963 Electrodynamics of Continuous Media (Beijing: People’s Education Press) pp179−182 (in Chinese)
[30] Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 55 374Google Scholar
[31] Tolman R C 1939 Phys. Rev. 55 364Google Scholar
[32] Worley A, Krastev P G, Li B A 2008 Astronphys. J. 685 390Google Scholar
[33] Lattimer J M, Schutz B F 2005 Astrophys. J. 629 979Google Scholar
[34] Glendenning N K 1997 Compact Stars: Nuclear Physics, Particle Physics, and General Relativity (New York: Springer-Verlag) pp75−78
[35] Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys. Rev. Lett. 79 2176Google Scholar
[36] Wiringa R B, Fiks V, Fabroeini A 1988 Phys. Rev. 38 1010Google Scholar
[37] Manchester R N 2004 Science 304 542Google Scholar
[38] Gao Z F, Shan H, Wang H 2021 Astron. Nachr. 342 369Google Scholar
[39] Krotscheck E, Kundt W 1978 Commun. Math. Phys. 60 171Google Scholar
[40] Demorest P B, Pennucci T, Ransom S M 2010 Nature 467 1081Google Scholar
[41] Fonseca E, Pennucci T T, Ellis J A 2016 Astrophys. J. 832 167Google Scholar
[42] Antoniadis J, Freire, P C C, Wex N 2013 Science 340 448Google Scholar
[43] Cromartie H T, Fonseca E, Ransom S M 2020 Nat. Astron. 4 72Google Scholar
[44] Kandel D, Romani R W 2020 Astrophys. J. 892 101Google Scholar
[45] Godzieba D A, Radice D, Bernuzzi S 2021 Astrophys. J. 908 122Google Scholar
[46] Fattoyev F J, Horowitz C J, Piekarewicz J 2020 Phys. Rev. C 102 065805Google Scholar
[47] Liang E P 1986 Astrophys. J. 304 682Google Scholar
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