-
In this work, we investigate the thermodynamical properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter under strong magnetic fields by using a quasiparticle model. We calculate the energy density and the corresponding anisotropic pressure of both SQM and CFL quark matter. Our results indicate that CFL quark matter exhibits greater stability than the SQM, and the pressure of CFL quark matter increases with the energy gap constant
$\varDelta $ increasing. We also observe that the oscillation effects coming from the lowest Landau level can be reduced by increasing the energy gap constant$ \varDelta $ , which cannot be observed in SQM under a similar strong magnetic field. The equivalent quark mass for u, d, and s quark and the chemical potential for each flavor of quarks decrease with the energy gap constant$ \varDelta $ increasing, which matches the conclusion that CFL quark matter is more stable than SQM. From the calculations of the magnetars with SQM and CFL quark matter, we find that the maximum mass of magnetars increases with the energy gap constant$\varDelta $ increasing for both the longitudinal and the transverse orientation distribution of magnetic field. Additionally, the tidal deformability of the magnetars increases with the$\varDelta $ increasing. On the other hand, the central baryon density of the maximum mass of the magnetars decreases with the$\varDelta $ increasing. The results also indicate that the mass-radius lines of the CFL quark star can also satisfy the new estimates of the mass-radius region from PSR J0740 + 6620, PSR J0030 + 0451, and HESS J1731-347.-
Keywords:
- quark matter /
- quark star /
- magnetar
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-
表 1 不同磁场方向分布情况下($ B_0 = 4\times \text{10}^{18} $G)磁星最大质量中心密度、1.4倍太阳质量潮汐形变率随Δ的变化
Table 1. The central density and tidal deformability of the magnetars considering “radial orientation” and “transverse orientation” at $ B_0 = 4\times \text{10}^{18} $G with g-2 within quasiparticle model with different Δ.
$ B_{{/ /}} $ $ B_{{/ /}} $ $ B_{\perp} $ $ B_{\perp} $ Δ/MeV 50 100 50 100 $ n_{\mathrm{c}} $/$ \text{fm}^{-3} $ 0.95 0.82 0.91 0.8 $ \varLambda_{1.4} $/MeV 741 1256 805 1351 -
[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
Google Scholar
[5] Demorest P 2010 Nature 467 1081
Google Scholar
[6] Antoniadis J 2013 Science 340 6131
Google Scholar
[7] Shahbaz T, Casares J 2018 Astrophys. J. 859 54
Google Scholar
[8] Cromartie H T, Fonseca E, Ransom S M et al. 2020 Nat. 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
Google Scholar
[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
[33] Chu P C, Zhou Y, Chen C, Li X H, Ma H Y 2020 J. Phys. G: Nucl. Part. Phys. 47 085201
Google Scholar
[34] Bailin D and 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] Woltjer L 1964 Astrophys. J. 140 1309
Google Scholar
[42] Mihara T A 1990 Nature 346 250
Google Scholar
[43] Chanmugam G 1992 Annu. Rev. Astron. Astrophys. 30 143
Google Scholar
[44] Lai D, Shapiro S L 1991 Astrophys. J. 383 745
Google Scholar
[45] Ferrer E J, Incera V, Keith J P, Portillo I, Springsteen P L 2010 Phys. Rev. C 82 065802
Google Scholar
[46] Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys Rev. Lett. 79 2176
Google Scholar
[47] Bandyopadhyay D, Pal S, Chakrabarty S 1998 J. Phys. G: Nucl. Part. Phys. 24 1647
Google Scholar
[48] Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 79 035807
Google Scholar
[49] Menezes D P, Pinto M, Benghi, Avancini S, Providência C 2009 Phys. Rev. C 80 065805
Google Scholar
[50] Ryu C Y, Kim K S, Cheoun Myung-Ki 2010 Phys. Rev. C 82 025804
Google Scholar
[51] Ryu C Y, Cheoun Myung-Ki, Kajino T, Maruyama T, Mathews Grant J 2012 Astropart. Phys. 38 25
Google Scholar
[52] Li X H, Gao Z F, Li X D, Xu Y, Wang P, WangN, Peng Q H 2016 Int. J. Mod. Phys. D 25(1) 1650002
Google Scholar
[53] Gao Z F, Wang N, Shan H, L i, X D, Wang W 2017 Astrophys. J. 849 19
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[58] Deng Z L, Li X D, Gao Z F, Shao Y 2021 Astrophys. J. 909 174
Google Scholar
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Google Scholar
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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] Schertler K, Greiner C, Thoma M H, Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659
Google Scholar
[64] Pisarski R D 1989 Nucl. Phys. A 498 423
[65] Wen X J 2009 J. Phys. G: Nucl. Part. Phys. 36 025011
Google Scholar
[66] Zhang Z, Chu P C, Li X H, Liu H, Zhang X M 2021 Phys. Rev. D 103 103021
Google Scholar
[67] Chu P C, Chen L W 2014 Astrophys. J. 780 135
Google Scholar
[68] Chu P C 2018 Phys. Lett. B 778 447
Google Scholar
[69] Chu P C, Chen L W 2017 Phys. Rev. D 96 103001
Google Scholar
[70] Chodos A, Jaffe R L, Ohnson K, Thorn C B, Weisskopf V F 1974 Phys. Rev. D 9 3471
Google Scholar
[71] Alford M, Braby M, Paris M, Reddy S 2005 Astrophys. J. 629 969
Google Scholar
[72] Rehberg P, Klevansky S P, Hüfner J 1996 Phys. Rev. C 53 410
Google Scholar
[73] Hanauske M, Satarov L M, Mishustin I N, Stocker H, Greiner W 2001 Phys. Rev. D 64 043005
Google Scholar
[74] Rüster S B, Rischke D H 2004 Phys. Rev. D 69 045011
Google Scholar
[75] Menezes D P, Providencia C, Melrose D B 2006 J. Phys. G 32 1081
Google Scholar
[76] Chao J Y, Chu P C, Huang M 2013 Phys. Rev. D 88 054009
Google Scholar
[77] Chu P C, Wang X, Chen L W, Huang M 2015 Phys. Rev. D 91 023003
Google Scholar
[78] 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
[79] Chu P C, Chen L W 2017 Phys. Rev. D 96 083019
Google Scholar
[80] Roberts C D, Williams A G 1994 Prog. Part. Nucl. Phys. 33 477
Google Scholar
[81] Zong H S, Chang L, Hou F Y, Sun W M, Liu Y X 2005 Phys. Rev. C 71 015205
Google Scholar
[82] Peng G X, Chiang H C, Yang J J, Li L, Liu B 1999 Phys. Rev. C 61 015201
Google Scholar
[83] Peng G X, Chiang H C, Zou B S, Ning P Z, Luo S J 2000 Phys. Rev. C 62 025801
Google Scholar
[84] Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807
Google Scholar
[85] Li A, Peng G X, Lu J F 2011 Res. Astron. Astrophys. 11 482
Google Scholar
[86] Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659
[87] Schertler K, Greiner C, Sahu P K, Thoma M H 1998 Nucl. Phys. A 637 451
[88] Alford M, Kouvaris C, Rajagopal K 2005 Phys. Rev. D 71 054009
Google Scholar
[89] Giannakis I, Hou D, Ren H C, et al. 2004 Phys. Rev. Lett. 93 232301
Google Scholar
[90] 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
[91] Ferrer E J, Vivian de la Incera 2005 Phys. Rev. Lett. 95 152002
Google Scholar
[92] Ferrer E J, Vivian de la Incera, Cristina Manuel 2006 Nucl. Phys. B 747 88
Google Scholar
[93] Feng B, Ferrer E J, Vivian de la Incera 2011 Nucl. Phys. B 853 213
Google Scholar
[94] Paulucci L, Ferrer E J, Vivian de la Incera, Horvath J E 2011 Phys. Rev. D 83 043009
Google Scholar
[95] Isayev A A, Yang J 2011 Phys. Rev. C 84 065802
Google Scholar
[96] Isayev A A, Yang J 2012 Phys. Lett. B 707 163
Google Scholar
[97] Isayev A A, Yang J 2013 J. Phys. G: Nucl. Part. Phys. 40 035105
Google Scholar
[98] Feng B, Hou D F, Ren H C, Wu P P 2010 Phys. Rev. Lett. 105 042001
Google Scholar
[99] Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 33 374
[100] 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
[101] Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett. A 28 1350138
Google Scholar
[102] Chu P C, Chen L W, Wang X 2014 Phys. Rev. D 90 063013
Google Scholar
[103] Miller M C, Lamb F K, Dittmannet A J, et al. 2019 Astrophys. J. Lett. 887 L24
Google Scholar
[104] Doroshenko V, Suleimanov V, Pühlhofer G, Santangelo A 2022 Nat. Astron. 6 1444
Google Scholar
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