基于MIT袋模型的零温与强磁场下夸克物质与磁星的性质研究

初鹏程; 王姣姣; 刘玉珩; 刘鹤; 刘宏铭

doi:10.7498/aps.74.20250898

摘要
本文基于MIT袋模型计算了零温与强磁场下奇异夸克物质与色味锁夸克物质的热力学性质. 发现色味锁态下夸克物质的热力学性质受色味锁夸克物质的能隙常数、磁场强度影响很大, 特别是物态方程会随着能隙常数的增加而变硬, 压强随着磁场强度的增加而呈现明显的各向异性. 结果表明色味锁态下基于MIT袋模型的夸克星质量半径曲线可以通过多个目前实验估测的脉冲星质量-半径区域, 色味锁夸克星的最大质量会随着能隙常数的增加而增大. 强磁场下色味锁磁星的质量与磁星内部磁场强度与方向的分布关系紧密, 星体物质的多方指数会随着星体质量的增加而减小.

关键词:
色味锁态 /

夸克星 /

磁星
Abstract
In this work, we investigate the properties of the strange quark matter (SQM) and the color-flavor-locked (CFL) quark matter at zero temperature or under strong magnetic fields within MIT bag model. We find the thermodynamical properties of CFL quark matter is strongly influenced by the pairing energy gap Δ and the magnetic field. The sound velocity of CFL quark matter and the tidal deformability of CFL quark stars both increase with Δ, while the central baryon density of the maximum star mass in CFL state decreasing with Δ. Especially, the equation of state (EOS) of the CFL quark matter becomes stiffer with the increment of Δ, and the pressure becomes anisotropic when considering the magnetic fields in CFL quark matter. Our results indicate that the mass-radius lines of the CFL quark matter within MIT bag model can describe the recent observations of pulsars, and the maximum star mass of CFL quark matter increases with Δ. Moreover, the results indicate that the star mass of CFL quark matter depends on the magnetic field strength and orientation distributions inside the magnetars, and the polytropic index of CFL quark matter decreases with the star mass.

Keywords:
color-flavor-locked phase /

quark star /

magnetar
文章全文

施引文献
图 1 零温情况下基于MIT袋模型的奇异夸克物质与色味锁夸克物质的每核子能量与相应的压强随重子数密度变化关系

Fig. 1. The energy per baryon and corresponding pressure as functions of baryon densityof SQM and CFL quark matter within MIT bag model.

下载: 全尺寸图片幻灯片

图 2 奇异夸克物质与色味锁夸克物质的声速平方随重子数密度的变化

Fig. 2. The sound velocity square of SQM and CFL quark matter as functions of baryon density.

下载: 全尺寸图片幻灯片

图 3 奇异夸克物质与CFL夸克物质的多方指数随重子数密度变化关系

Fig. 3. The polytropic index of SQM and CFL quark matter as a function of $ n_B $.

下载: 全尺寸图片幻灯片

图 4 夸克星最大质量随能隙常数的变化规律

Fig. 4. The maximum mass of quark stars as a function of Δ

下载: 全尺寸图片幻灯片

图 5 色味锁夸克星引力波潮汐形变随能隙常数的变化规律

Fig. 5. Tidal deformability of the CFL quark stars as a function of Δ.

下载: 全尺寸图片幻灯片

图 6 不同袋常数下色味锁夸克星最大质量所对应的中心密度随着Δ的变化

Fig. 6. The central density of the maximum mass of CFL quark stars as a functions of Δ with different bag constant.

下载: 全尺寸图片幻灯片

图 7 奇异夸克星与色味锁夸克星在不同Δ的质量半径关系

Fig. 7. Mass-radius lines of strange quark stars and CFL quark stars with different Δ.

下载: 全尺寸图片幻灯片

图 8 强磁场下MCFL夸克物质的每核子能量与压强随重子数密度变化关系

Fig. 8. The energy per baryon and pressure as functions of $ n_B $ under strong magnetic fields.

下载: 全尺寸图片幻灯片

图 9 基于MIT袋模型下的MCFL磁星的质量半径关系

Fig. 9. Mass-radius relation of MCFL magnetars within MIT bag model.

下载: 全尺寸图片幻灯片

图 10 横向磁场与径向磁场下, MCFL态夸克物质的多方指数随重子数密度的变化关系

Fig. 10. The polytropic index as a function of baryon number density with transverse magnetic field and longitudinal magnetic field.

下载: 全尺寸图片幻灯片

map

[1]	Glendenning N K 2000 Compact Stars (2 nd edition) (New York: Spinger-Verlag, Inc.)
[2]	Weber F 1999 Pulsars as Astrophyical Laboratories for Nuclear and Particle Physics (London: IOP Publishing Ltd)
[3]	Lattimer J M and Prakash M 2004 Science 304 536 Google Scholar
[4]	Steiner A W, Prakash M, Lattimer J M, Ellis P J 2005 Phys. Rep. 410 325
[5]	Demorest P 2010 Nature 46 7
[6]	Antoniadis J 2013 Science 340 6131
[7]	Shahbaz T, Casares J 2018 Astrophys. Journal 859 54
[8]	Thankful H, Cromartie 2020 Nat. Astron. Lett. 4 72
[9]	Fonseca E, Cromartie H T, Pennucci T T et al 2021 Astrophys. J. Lett. 915 L12
[10]	Miller M C, Lamb F K, Dittmann A J et al 2021 Astrophys. J. Lett. 918 L28 Google Scholar
[11]	Miller M C, Lamb F K, Dittmann A J al. 2019 Astrophys. J. Lett. 887 L24
[12]	Nattila J, Lamb F K, Dittmann A J et al 2017 A&A 3 8
[13]	Doroshenko V 2022 Nature Astronomy 6 1444 Google Scholar
[14]	Abbott R. 2020 Astrophys. J. Lett. 896 L44 Google Scholar
[15]	Ivanenko D, Kurdgelaidze D F 1969 Lett. Nuovo Cimento 2 13 Google Scholar
[16]	Itoh N 1970 Prog. Theor. Phys. 44 291 Google Scholar
[17]	Bodmer A R 1971 Phys. Rev. D 4 1601 Google Scholar
[18]	Witten E 1984 Phys. Rev. D 30 272
[19]	Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379
[20]	Holdom B 2018 Phys. Rev. L 120 22001 Google Scholar
[21]	Zhang C and Mann R B 2021 Phys. Rev. D 103 063018 Google Scholar
[22]	Li C M et al 1984 Phys. Rev. D 30 2379 Google Scholar
[23]	Yuan L W, Li A, Miao Z Q, Zuo B J, and Bai Z 1984 Phys. Rev. D 105 123004
[24]	Alcock C, Farh E, Olinto A 1986 Astrophy. J. 310 261 Google Scholar
[25]	Weber F 2005 Prog. Part. Nucl. Phys. 54 193 Google Scholar
[26]	Bombaci I, Parenti I, Vidana I 2004 Astrophy. J. 614 314 Google Scholar
[27]	Staff J, Ouyed R, Bagchi M 2007 Astrophy. J. 667 340 Google Scholar
[28]	Herzog T M, RÖpke F K 2011 Phys. Rev. D 84 083002 Google Scholar
[29]	Stephanov M A, Rajagopal K, Shuryak E V 1998 Phys. Rev. Lett. 81 4816 Google Scholar
[30]	Terazawa H 1979 INS-Report (Tokyo: Univ. of Tokyo) 336
[31]	Alford M, Reddy S 2003 Phys. Rev. D 67 074024 Google Scholar
[32]	Alford M, Jotwani P, Kouvaris C, Kundu J, Rajagopal K 2005 Phys. Rev. D 71 114011 Google Scholar
[33]	Baldo M 2003 Phys. Lett. B 562 153 Google Scholar
[34]	Ippolito N D, Ruggieri M, Rischke D H, Sedrakian A, Weber F 2008 Phys. Rev. D 77 023004 Google Scholar
[35]	Lai X Y, Xu R X 2011 Research Astron. Astrophys. 11 687 Google Scholar
[36]	Avellar M G B de, Horvath J E, Paulucci L 2011 Phys. Rev. D 84 043004 Google Scholar
[37]	Bonanno L, Sedrakian A 2012 A&A 3 8
[38]	Chu P C, Wang B, Jia Y Y, Dong Y M, Wang S M, Li X H, Zhang L, Zhang X M, Ma H Y 2016 Phys. Rev. D 94 123014 Google Scholar
[39]	Chu P C, Li X H, Wang B, Dong Y M, Jia Y Y, Wang S M, Ma H Y 2017 Eur. Phys. J. C 77 512 Google Scholar
[40]	Chu P C, Zhou Y, Chen C, Li X H, Ma H Y 2020 J. Phys. G: Nucl. Part. Phys. 47 085201 Google Scholar
[41]	Bailin D and Love A 1984 Phys. Rept. 10 7
[42]	Alford M G, Rajagopal K, Reddy S and Wilczek F 2001 Phys. Rev. D 6 4
[43]	Shovkovy I A 2005 Found. Phys. 3 5
[44]	Rajagopal K and Wilczek F 2001 Phys. Rev. L 86 3492 Google Scholar
[45]	Alford M G, Rajagopal K, Schaefer T and Schmitt A 2008 Rev. Mod. Phys. 8 0
[46]	Lugones G and Horvath J E 2003 Astron. Astrophys. 40 3
[47]	Horvath J E and Lugones G 2004 Astron. Astrophys. 42 2
[48]	Li X H, Gao Z F, Li X D, Xu Y, Wang P, WangN, Peng Q H 2016 Int. J. Mod. Phys. D 2 5
[49]	Gao Z F, Wang N, Shan H, L i, X D, Wang W 2017 Astrophys. J. 849 19 Google Scholar
[50]	Deng Z L, Gao Z F, Li X D, Shao Y 2020 Astrophys. J. 892 4 Google Scholar
[51]	Yan F Z, Gao Z F, Yang W S, Dong A J 2021 Astron. Nachr. 342 249 Google Scholar
[52]	Wang H, Gao Z F, Jia H Y, Wang N, Li X 2020 Universe 6 63 Google Scholar
[53]	Li B P, Gao Z F 2023 Astron. Nachr. 34 4
[54]	Li B P, Ma W Q, Gao Z F 2024 Astron. Nachr. 34 5
[55]	Deng Z L, Li X D, Gao Z F, Shao Y 2021 Astrophys. J. 909 174 Google Scholar
[56]	G ao, Z F, Omar N, Shi X C, Wang N 2019 Astron. Nachr. 340 1030 Google Scholar
[57]	Lander, S K 2023 Astrophys.J. 94 7
[58]	L Woltjer 1964 Astrophys. J. 140 1309 Google Scholar
[59]	Mihara T A 1990 Nature 346 250 Google Scholar
[60]	Chanmugam G 1992 Annu. Rev. Astron. Astrophys. 30 143 Google Scholar
[61]	Lai D, Shapiro S L 1991 Astrophys. J. 383 745 Google Scholar
[62]	Ferrer E J, Incera V, Keith J P, Portillo I, Springsteen P L 2010 Phys. Rev. C 82 065802
[63]	Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys Rev. Lett. 79 2176 Google Scholar
[64]	Bandyopadhyay D, Pal S, Chakrabarty S 1998 J. Phys. G: Nucl. Part. Phys. 24 1647 Google Scholar
[65]	Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 79 035807 Google Scholar
[66]	Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 80 065805 Google Scholar
[67]	Ryu C Y, Kim K S, Cheoun Myung-Ki 2010 Phys. Rev. C 82 025804 Google Scholar
[68]	Ryu C Y, Cheoun Myung-Ki, Kajino T, Maruyama T, Mathews Grant J 2012 Astroparticle Physics 38 25 Google Scholar
[69]	Gao Z F, Li B P, de Andrade, Garcia L C, 2025, Eur. Phys. J. C 85(4) 433
[70]	Fu G Z, Xing C C, Wang N 2020 Eur. Phys. J. C 80 582 Google Scholar
[71]	Li B P, Gao Z F, Ma W Q, Cheng Q 2025 Front. Astron. Space Sci. 12 1625459 Google Scholar
[72]	Ma W Q, Gao Z F, Li B P, Niu C H, Yao J M, Wang F Y 2025 Astrophys.J. 98 1
[73]	Wang Z, Wen Z G, Yuan J P et al 2025 Astrophys.J. 98 7
[74]	Wen Z G, Yan W M, Yuan J P et al 2020 Astrophys.J. 904 72 Google Scholar
[75]	Wen Z G, Yuan J P, Wang N et al 2022 Astrophys.J. 928 71 Google Scholar
[76]	Schertler K, Greiner C, Thoma M H, Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659 Google Scholar
[77]	Pisarski R D 1989 Nucl. Phys. A 498 423 Google Scholar
[78]	Wen X J 2009 J. Phys. G: Nucl. Part. Phys. 36 025011 Google Scholar
[79]	Zhang Z, Chu P C, Li X H, Liu H, Zhang X M 2021 Phys. Rev. D 103 103021 Google Scholar
[80]	Chu P C, Chen L W 2014 Astrophys. J. 780 135
[81]	Chu P C 2018 Phys. Lett. B 778 447 Google Scholar
[82]	Chu P C, Chen L W 2017 Phys. Rev. D 96 103001 Google Scholar
[83]	Chodos A, Jaffe R L, Ohnson K, Thorn C B, Weisskopf V F 1974 Phys. Rev. D 9 3471 Google Scholar
[84]	Alford M, Braby M, Paris M, Reddy S 2005 Astrophy. J. 629 969 Google Scholar
[85]	Rehberg P, Klevansky S P, Hüfner J 1996 Phys. Rev. C 53 410
[86]	Hanauske M, Satarov L M, Mishustin I N, Stocker H, Greiner W 2001 Phys. Rev. D 64 043005 Google Scholar
[87]	Rüster S B, Rischke D H 2004 Phys. Rev. D 69 045011 Google Scholar
[88]	Menezes D P, Providencia C, Melrose D B 2006 J. Phys. G 32 1081 Google Scholar
[89]	Chao J Y, Chu P C, Huang M 2013 Phys. Rev. D 88 054009 Google Scholar
[90]	Chu P C, Wang X, Chen L W, Huang M 2015 Phys. Rev. D 91 023003 Google Scholar
[91]	Chu P C, Liu H, Du X B 2024 Acta Phys. Sin. 73 052101 Google Scholar
[92]	Chu P C, Wang B, Ma H Y, Dong Y M, Chang S L, Zheng C H, Liu J T, Zhang X M 2016 Phys. Rev. D 93 094032 Google Scholar
[93]	Chu P C, Chen L W, Wang X 2014 Phys. Rev. D 90 063013 Google Scholar
[94]	Chu P C, Chen L W 2017 Phys. Rev. D 96 083019 Google Scholar
[95]	Roberts C D, Williams A G 1994 Prog. Part. Nucl. Phys. 33 477 Google Scholar
[96]	Zong H S, Chang L, Hou F Y, Sun W M, Liu Y X 2005 Phys. Rev. C 71 015205 Google Scholar
[97]	Peng G X, Chiang H C, Yang J J, Li L, Liu B 1999 Phys. Rev. C 61 015201 Google Scholar
[98]	Peng G X, Chiang H C, Zou B S, Ning P Z, Luo S J 2000 Phys. Rev. C 62 025801
[99]	Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807 Google Scholar
[100]	Li A, Peng G X, Lu J F 2011 Research Astron. Astrophys. 11 482 Google Scholar
[101]	Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659 Google Scholar
[102]	Schertler K, Greiner C, Sahu P K, Thoma M H 1998 Nucl. Phys. A 637 451 Google Scholar
[103]	Alford M, Rajagopal K, and Wilczek F 2023 Eur. Phys. J. C 83 858 Google Scholar
[104]	Shovkovy I A and Wijewardhana L C 1999 Phys. Lett. B 470 189 Google Scholar
[105]	Rajagopal K and Wilczek F 2001 Phys. Rev. L 86 3492 Google Scholar
[106]	Chu P C et al 2023 Eur. Phys. J. C 83 858 Google Scholar
[107]	Chu P C, Liu H, Liu H M, Li X H, Ju M, Wu X H, and Zhou Y 2024 Phys. Rev. D 110 123031 Google Scholar
[108]	Chu P C, Liu H, Ju M, Wu X H, Liu H M, Zhou Y, Liu H, Lu S Y, and Li X H 2024 Phys. Rev. D 110 043032 Google Scholar
[109]	Chu P C, Liu H, Li X H, Ju M, Wu X H, and Zhang X M 2024 J. Phys. G: Nucl. Part. Phys. 51 065202 Google Scholar
[110]	Ferrer E J and Vivian de la Incera 2005 Phys. Rev. Lett. 95 152002 Google Scholar
[111]	Ferrer E J, Vivian de la Incera, Cristina Manuel 2006 Nucl.Phys. B 747 88 Google Scholar
[112]	Sun G W, He D L, Ma W L, Zhu D J 2025 Astron.Nachr. doi. 10.1002/asna.70030.
[113]	Wang Z, Wen Z G, Yuan J P et al 2024 Astrophys. J. 968 169
[114]	Isayev A A, Yang J 2011 Phys. Rev. C 84 065802
[115]	Isayev A A, Yang J 2012 Phys. lett. B 707 163 Google Scholar
[116]	Isayev A A, Yang J 2013 J. Phys. G: Nucl. Part. Phys. 40 035105 Google Scholar
[117]	Dong A J 2023 Acta Phys. Sin. 72 030502 Google Scholar
[118]	Oppenheimer J R, and Volkoff G M 1939 Phys. Rev. 33 374
[119]	B. P. Abbott 2017 Phys. Rev. Lett. 119 161101 Google Scholar
[120]	Gao Z F, Li X D, Wang N, Yuan J P, Wang P, Peng Q H, Du Y J 2016 Mon. Not. R. Astron. Soc. 456 55 Google Scholar
[121]	Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett A 28 1350138
[122]	Chu P C, Liu H, Liu H M et al. 2025 Phys. Rev. D 111, 12, 123045
[123]	Chu P C, Liu H, Liu H M, Ju M, Wu X H, Zhou Y, and Li X H 2025 Eur. Phys. J. C 85 466 Google Scholar
[124]	Chu P C, Jiang Y Y, Liu H et al. 2021 Eur. Phys. J. C 81, 7, 569;
[125]	Chu P C, Zhou Y, Jiang Y Y et al. 2021 Eur. Phys. J. C 81, 1, 93.
[126]	Wu X H, Chu P C, Ju M, Liu H et al 2025 Eur. Phys. J. C 85 362 Google Scholar

[1]	兰恒, 李嘉栋, 曹宇豪, 沈军峰, 李嘉诚, 许宇鸿, 孙腾飞, 何梦圆, 冯宇轩, 吴丹妮, 程钧, 刘海峰, SHIMIZUAkihiro, 王先驱, 宣伟民, 张美勇, 邹千, 罗珺, 杨权, 张欣, 刘海, 黄捷, 胡军, 邵俊仁, 李伟, 栗钰彩, 周红, 王捷, 苏祥, 唐昌建. CFQS-T准环对称仿星器高频磁探针阵列诊断的研制及初步应用. , doi: 10.7498/aps.74.20250957
[2]	李丹, 刘海峰. 中国首台准环对称仿星器中线圈形变对磁拓扑结构的影响. , doi: 10.7498/aps.74.20241606
[3]	徐建峰, 王靖涛, 夏铖君. 新质量标度下u-d夸克星及其潮汐形变. , doi: 10.7498/aps.74.20250535
[4]	初鹏程, 刘玉珩, 刘鹤, 刘宏铭, 杨永杭. 强磁场与有限温度下色味锁夸克星的唯象模型. , doi: 10.7498/aps.74.20250451
[5]	邢晔, 李娜, 杨翎彬, 胡晓会. 基于分子态构型研究单粲味五夸克态的产生. , doi: 10.7498/aps.73.20240447
[6]	初鹏程, 刘鹤, 杜先斌. 色味锁夸克物质与夸克星. , doi: 10.7498/aps.73.20231649
[7]	苏祥, 王先驱, 符添, 许宇鸿. CFQS准环对称仿星器低$\boldsymbol \beta$等离子体中三维磁岛的抑制机制. , doi: 10.7498/aps.72.20230546
[8]	董爱军, 高志福, 杨晓峰, 王娜, 刘畅, 彭秋和. 在超强磁场中修正的相对论电子压强. , doi: 10.7498/aps.72.20220092
[9]	王谊农, 初鹏程, 姜瑶瑶, 庞晓迪, 王圣博, 李培新. 基于准粒子模型的原生磁星研究. , doi: 10.7498/aps.71.20220795
[10]	龚武坤, 郭文军. 混合中子星内强子-夸克退禁闭相变. , doi: 10.7498/aps.69.20200925
[11]	陈建玲, 王辉, 贾焕玉, 马紫微, 李永宏, 谭俊. 超强磁场下中子星壳层的电导率和磁星环向磁场欧姆衰变. , doi: 10.7498/aps.68.20190760
[12]	吉日木图, 敖登, 薛康. 坐标空间中构造的Breit夸克势与介子和夸克偶素的质量劈裂. , doi: 10.7498/aps.67.20172155
[13]	刘向远, 钱仙妹, 朱文越, 刘丹丹, 范传宇, 周军, 杨欢. 基于波长330 nm激光激发多色激光导星回波光子数的数值计算与探讨. , doi: 10.7498/aps.67.20171025
[14]	黄金书, 罗鹏晖, 鲁公儒. 关于光子对撞机上底夸克对产生的研究. , doi: 10.7498/aps.58.8166
[15]	赖祥军, 罗志全, 刘晶晶, 刘宏林. 超新星核中的夸克相变及夸克质量效应. , doi: 10.7498/aps.57.1535
[16]	陈　洪, 梅　花, 沈彭年, 姜焕清. 重夸克偶素质量谱的相对论夸克模型研究（已撤稿）. , doi: 10.7498/aps.54.1136
[17]	戴子高, 陆埮. 奇异星的冷却. , doi: 10.7498/aps.43.198
[18]	戴子高, 陆埮, 彭秋和. 中子星内部非奇异-奇异夸克物质的相变. , doi: 10.7498/aps.42.1210
[19]	谢凤仙. t夸克偶素能谱的计算. , doi: 10.7498/aps.36.778
[20]	王青德, 陆埮. π凝聚态中的弱过程对中子星振动的阻尼效应. , doi: 10.7498/aps.34.892

计量

文章访问数: 510
PDF下载量: 8
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

基于MIT袋模型的零温与强磁场下夸克物质与磁星的性质研究

Properties of quark matter and quark stars at zero temperature or under strong magnetic fields within MIT bag model

摘要

Abstract

文章全文

施引文献

计量

作者中心

审稿中心

关于期刊

关于我们

搜索

留言板

基于MIT袋模型的零温与强磁场下夸克物质与磁星的性质研究

Properties of quark matter and quark stars at zero temperature or under strong magnetic fields within MIT bag model

摘要

Abstract

文章全文

施引文献

计量

出版历程

作者中心

审稿中心

关于期刊

关于我们