-
The properties of the color-flavor-locked (CFL) quark matter under strong magnetic fields at finite temperatures within a quasiparticle model are investigated in this work. Our results indicate that CFL quark matter pressure becomes anisotropic under strong magnetic fields, while its equation of state (EOS) and equivalent quark mass are both strongly affected by temperature, energy gap constant Δ, and strong magnetic field inside the CFL quark matter. The equivalent quark mass of CFL quark matter decreases with temperature and magnetic field strength increasing, which implies an inverse magnetic catalysis phenomenon. The results also indicate that the entropy per baryon of the CFL quark matter increases with temperature rising and decreases with Δ increasing. Furthermore, the properties of CFL magnetars in different isentropic stages are studied. The star mass and radius depend primarily on the strength and orientation of magnetic fieldinside the CFL magnestars. The maximum star mass increases with entropy per baryon increasing, while the star matter temperature rises at high isentropic stage. Moreover, the polytropic index of the CFL quark matter decreases with star mass increasing.
-
Keywords:
- color-flavor-locked phase /
- quark star /
- magnetar
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图 1 不同温度与能隙常数下色味锁态物质的每核子自由能与横纵向压强随着$ n_{\mathrm{B}} $的变化关系
Figure 1. The free energy per baryon and pressures of CFL quark matter with $ n_{\mathrm{B}} $ at finite temperature and with different $ \varDelta $.
图 2 不同温度与能隙常数下u夸克的有效质量随磁感应强度的变化
Figure 2. The equivalent mass of u quarks as a function of the magnetic field with different temperature and $ \varDelta $.
图 3 色味锁态下夸克星物质的每核子熵随着不同温度、磁场、能隙常数的变化
Figure 3. The entropy per baryon of the quark star matter in MCFL state with various temperature, magnetic field and $ \varDelta $
图 4 MCFL下夸克物质的多方指数随磁场、温度、能隙常数的变化规律
Figure 4. The polytropic index of the MCFL quark star matter as a function of the magnetic field strength, temperature, and $ \varDelta $.
图 5 不同等熵阶段中的色味锁磁星的质量-半径情况
Figure 5. The star mass as functions of the radius of the MCFL quark stars along different isentropic stages.
图 6 不同等熵阶段下色味锁夸克星内部温度随$ n_{\mathrm{B}} $与磁场的变化
Figure 6. The temperature of the MCFL quark star matter as functions of $ n_{\mathrm{B }}$ and magnetic field along different isentropic stages.
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[1] Glendenning N K 2000 Compact Stars (2nd Ed.) (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, 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 467 1081
Google Scholar
[6] Antoniadis J 2013 Science 340 6131
[7] Shahbaz T, Casares J 2018 Astrophys. J. 859 54
Google Scholar
[8] Thankful H, Cromartie 2020 Nature Astron. Lett. 4 72
[9] Fonseca E, Cromartie H T, Pennucci T T, et al. 2021 Astrophys. J. Lett. 915 L12
Google Scholar
[10] Miller M C, Lamb F K, Dittmann A J, et al. 2021 Astrophys. J. Lett. 918 L28
Google Scholar
[11] Abbott R 2020 Astrophys. J. Lett. 896 L44
Google Scholar
[12] Ivanenko D, Kurdgelaidze D F 1969 Lett. Nuovo Cimento 2 13
Google Scholar
[13] Itoh N 1970 Prog. Theor. Phys. 44 291
Google Scholar
[14] Bodmer A R 1971 Phys. Rev. D 4 1601
Google Scholar
[15] Witten E 1984 Phys. Rev. D 30 272
Google Scholar
[16] Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379
Google Scholar
[17] Alcock C, Farh E, Olinto A 1986 Astrophys. J. 310 261
Google Scholar
[18] Weber F 2005 Prog. Part. Nucl. Phys. 54 193
Google Scholar
[19] Bombaci I, Parenti I, Vidana I 2004 Astrophys. J. 614 314
Google Scholar
[20] Staff J, Ouyed R, Bagchi M 2007 Astrophys. J. 667 340
Google Scholar
[21] Herzog T M, Röpke F K 2011 Phys. Rev. D 84 083002
Google Scholar
[22] Stephanov M A, Rajagopal K, Shuryak E V 1998 Phys. Rev. Lett. 81 4816
Google Scholar
[23] Terazawa H 1979 INS-Report (Tokyo: Univ. of Tokyo) p336
[24] Alford M, Reddy S 2003 Phys. Rev. D 67 074024
Google Scholar
[25] Alford M, Jotwani P, Kouvaris C, Kundu J, Rajagopal K 2005 Phys. Rev. D 71 114011
Google Scholar
[26] Baldo M 2003 Phys. Lett. B 562 153
Google Scholar
[27] Ippolito N D, Ruggieri M, Rischke D H, Sedrakian A, Weber F 2008 Phys. Rev. D 77 023004
Google Scholar
[28] Lai X Y, Xu R X 2011 Res. Astron. Astrophys. 11 687
Google Scholar
[29] Avellar M G B de, Horvath J E, Paulucci L 2011 Phys. Rev. D 84 043004
Google Scholar
[30] Bonanno L, Sedrakian A 2012 A&A 539 A16
[31] 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
[32] 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
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Google Scholar
[34] Bailin D, Love A 1984 Phys. Rep. 107 325
Google Scholar
[35] Alford M G, Rajagopal K, Reddy S, Wilczek F 2001 Phys. Rev. D 64 074017
Google Scholar
[36] Shovkovy I A 2005 Found. Phys. 35 1309
Google Scholar
[37] Rajagopal K, Wilczek F 2001 Phys. Rev. L 86 3492
Google Scholar
[38] Alford M G, Rajagopal K, Schaefer T, Schmitt A 2008 Rev. Mod. Phys. 80 1455
Google Scholar
[39] Lugones G, Horvath J E 2003 Astron. Astrophys. 403 173
Google Scholar
[40] Horvath J E, Lugones G 2004 Astron. Astrophys. 422 L1
Google Scholar
[41] Li X H, Gao Z F, Li X D, Xu Y, Wang P, WangN, Peng Q H 2016 Int. J. Mod. Phys. D 25 165000
[42] Gao Z F, Wang N, Shan H, L i, X D, Wang W 2017 Astrophys. J. 849 19
Google Scholar
[43] Deng Z L, Gao Z F, Li X D, Shao Y 2020 Astrophys. J. 892 4
Google Scholar
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Google Scholar
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Google Scholar
[46] Li B P, Gao Z F 2023 Astron. Nachr. 344 e20220111
[47] Deng Z L, Li X D, Gao Z F, Shao Y 2021 Astrophys. J. 909 174
Google Scholar
[48] G ao, Z F, Omar N, Shi X C, Wang N 2019 Astron. Nachr. 340 1030
Google Scholar
[49] Lander S K 2023 Astrophys.J. 947 L16
Google Scholar
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Google Scholar
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Google Scholar
[52] Chanmugam G 1992 Annu. Rev. Astron. Astrophys. 30 143
Google Scholar
[53] Lai D, Shapiro S L 1991 Astrophys. J. 383 745
Google Scholar
[54] Ferrer E J, Incera V, Keith J P, Portillo I, Springsteen P L 2010 Phys. Rev. C 82 065802
[55] Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys Rev. Lett. 79 2176
Google Scholar
[56] Bandyopadhyay D, Pal S, Chakrabarty S 1998 J. Phys. G: Nucl. Part. Phys. 24 1647
Google Scholar
[57] Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 79 035807
Google Scholar
[58] Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 80 065805
Google Scholar
[59] Ryu C Y, Kim K S, Cheoun Myung-Ki 2010 Phys. Rev. C 82 025804
Google Scholar
[60] Ryu C Y, Cheoun Myung-Ki, Kajino T, Maruyama T, Mathews Grant J 2012 Astropart. Phys. 38 25
Google Scholar
[61] Dong J M 2021 Mon. Not. R. Astron. Soc. 500 1505
[62] Fu G Z, Xing C C, Wang N 2020 Eur. Phys. J. C 80 582
Google Scholar
[63] Aidala C, Akiba Y, Alfred M, et al. 2018 Phys. Rev. L 120 022001
Google Scholar
[64] Zhang C, Mann R B 2021 Phys. Rev. D 103 063018
Google Scholar
[65] Yuan L W, Li A, Miao Z Q, Zuo B J, Bai Z 1984 Phys. Rev. D 105 123004
[66] Schertler K, Greiner C, Thoma M H, Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659
Google Scholar
[67] Pisarski R D 1989 Nucl. Phys. A498 423
[68] Wen X J 2009 J. Phys. G: Nucl. Part. Phys. 36 025011
Google Scholar
[69] Zhang Z, Chu P C, Li X H, Liu H, Zhang X M 2021 Phys. Rev. D 103 103021
Google Scholar
[70] Chu P C, Chen L W 2014 Astrophys. J. 780 135
[71] Chu P C 2018 Phys. Lett. B 778 447
Google Scholar
[72] Chu P C, Chen L W 2017 Phys. Rev. D 96 103001
Google Scholar
[73] Chodos A, Jaffe R L, Ohnson K, Thorn C B, Weisskopf V F 1974 Phys. Rev. D 9 3471
Google Scholar
[74] Alford M, Braby M, Paris M, Reddy S 2005 Astrophys. J. 629 969
Google Scholar
[75] Rehberg P, Klevansky S P, Hüfner J 1996 Phys. Rev. C 53 410
[76] Hanauske M, Satarov L M, Mishustin I N, Stocker H, Greiner W 2001 Phys. Rev. D 64 043005
Google Scholar
[77] Rüster S B, Rischke D H 2004 Phys. Rev. D 69 045011
Google Scholar
[78] Menezes D P, Providencia C, Melrose D B 2006 J. Phys. G 32 1081
Google Scholar
[79] Chao J Y, Chu P C, Huang M 2013 Phys. Rev. D 88 054009
Google Scholar
[80] Chu P C, Wang X, Chen L W, Huang M 2015 Phys. Rev. D 91 023003
Google Scholar
[81] 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
[82] Chu P C, Chen L W 2017 Phys. Rev. D 96 083019
Google Scholar
[83] Roberts C D, Williams A G 1994 Prog. Part. Nucl. Phys. 33 477
Google Scholar
[84] Zong H S, Chang L, Hou F Y, Sun W M, Liu Y X 2005 Phys. Rev. C 71 015205
Google Scholar
[85] Peng G X, Chiang H C, Yang J J, Li L, Liu B 1999 Phys. Rev. C 61 015201
Google Scholar
[86] Peng G X, Chiang H C, Zou B S, Ning P Z, Luo S J 2000 Phys. Rev. C 62 025801
[87] Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807
Google Scholar
[88] Li A, Peng G X, Lu J F 2011 Res. Astron. Astrophys. 11 482
Google Scholar
[89] Schertler K, Greiner C, Sahu P K, Thoma M H 1998 Nucl. Phys. A 637 451
Google Scholar
[90] Alford M, Kouvaris C, Rajagopal K 2005 Phys. Rev. D 71 054009
Google Scholar
[91] Giannakis I, Hou D F, Ren H C, Rischke D H 2004 Phys. Rev. L 93 232301
Google Scholar
[92] 董爱军, 高志福, 杨晓峰等 2023 物理学报 72 030502
Google Scholar
Dong A J, Gao Z F, Yang X F, et al. 2023 Acta Phys. Sin. 72 030502
Google Scholar
[93] Ferrer E J, Vivian de la Incera 2005 Phys. Rev. Lett. 95 152002
Google Scholar
[94] Ferrer E J, Vivian de la Incera, Cristina M 2006 Nucl.Phys. B 747 88
Google Scholar
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Google Scholar
[96] Paulucci L, Ferrer E J, Vivian de la Incera, Horvath J E 2011 Phys. Rev. D 83 043009
Google Scholar
[97] Isayev A A, Yang J 2011 Phys. Rev. C 84 065802
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Google Scholar
[99] Isayev A A, Yang J 2013 J. Phys. G: Nucl. Part. Phys. 40 035105
Google Scholar
[100] Feng B, Hou D F, Ren H C, Wu P P 2010 Phys. Rev. L 105 042001
Google Scholar
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Google Scholar
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[103] Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 33 374
[104] Chu P C, Chen L W, Wang X 2014 Phys. Rev. D 90 063013
Google Scholar
[105] Chu P C, Liu H, Liu H M, Ju M, Wu X H, Zhou Y, Li X H 2025 Eur. Phys. J. C 85 466
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Google Scholar
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