Proto-magnetars within quasiparticle model

Wang Yi-Nong; Chu Peng-Cheng; Jiang Yao-Yao; Pang Xiao-Di; Wang Sheng-Bo; Li Pei-Xin

doi:10.7498/aps.71.20220795

Abstract

We investigate the thermodynamical properties of strange quark matter (SQM) at zero/finite temperature and under constant magnetic field within quasiparticle model. The quark matter symmetry energy, energy per baryon, free energy per baryon, anisotropic pressures are also studied and the result indicates that both the effects of temperature and magnetic field can significantly influence the thermodynamical properties of quark matter and proto-quark stars (PQSs). Our result also indicates that the maximum mass and the core temperature of PQSs not only depends on the heating process at the isentropic stages, but also but also the magnetic field strength and orientation distribution inside the magnetar within quasiparticle model.

Keywords:

Authors and contacts

School of Science, Qingdao University of Technology, Qingdao 266033, China

Corresponding author: Chu Peng-Cheng, kyois@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132, 12205158, 11505100) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2022JQ04, ZR2021QA037, ZR2019YQ01)

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References

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[2]	Weber F 1999 Pulsars as Astrophyical Laboratories for Nuclear and Particle Physics (London: IOP Publishing Ltd)
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[9]	Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379 Google Scholar
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[11]	Weber F 2005 Prog. Part. Nucl. Phys. 54 193 Google Scholar
[12]	Bombaci I, Parenti I, Vidana I 2004 Astrophy. J. 614 314 Google Scholar
[13]	Staff J, Ouyed R, Bagchi M 2007 Astrophy. J. 667 340 Google Scholar
[14]	Herzog T M, Röpke F K 2011 Phys. Rev. D 84 083002 Google Scholar
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[60]	Alford M, Braby M, Paris M, Reddy S 2005 Astrophys. J. 629 969 Google Scholar
[61]	Rehberg P, Klevansky S P, Hüfner J 1996 Phys. Rev. C 53 410
[62]	Hanauske M, Satarov L M, Mishustin I N, Stocker H, Greiner W 2001 Phys. Rev. D 64 043005 Google Scholar
[63]	Rüster S B, Rischke D H 2004 Phys. Rev. D 69 045011 Google Scholar
[64]	Menezes D P, Providencia C, Melrose D B 2006 J. Phys. G 32 1081 Google Scholar
[65]	Chao J Y, Chu P C, Huang M 2013 Phys. Rev. D 88 054009 Google Scholar
[66]	Chu P C, Wang X, Chen L W, Huang M 2015 Phys. Rev. D 91 023003 Google Scholar
[67]	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
[68]	Chu P C, Chen L W 2017 Phys. Rev. D 96 083019 Google Scholar
[69]	Roberts C D, Williams A G 1994 Prog. Part. Nucl. Phys. 33 477 Google Scholar
[70]	Zong H S, Chang L, Hou F Y, Sun W M, Liu Y X 2005 Phys. Rev. C 71 015205 Google Scholar
[71]	Peng G X, Chiang H C, Yang J J, Li L, Liu B 1999 Phys. Rev. C 61 015201 Google Scholar
[72]	Peng G X, Chiang H C, Zou B S, Ning P Z, Luo S J 2000 Phys. Rev. C 62 025801
[73]	Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807 Google Scholar
[74]	Li A, Peng G X, Lu J F 2011 Res. Astron. Astrophys. 11 482 Google Scholar
[75]	Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659
[76]	Schertler K, Greiner C, Sahu P K, Thoma M H 1998 Nucl. Phys. A 637 451
[77]	Chu P C, Chen L W 2014 Astrophys. J. 780 135 Google Scholar
[78]	Chu P C 2018 Phys. Lett. B 778 447 Google Scholar
[79]	Chu P C, Chen L W 2017 Phys. Rev. D 96 103001 Google Scholar
[80]	Schertler K, Greiner C, Thoma M H, Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659 Google Scholar
[81]	Pisarski R D 1989 Nucl. Phys. A 498 423
[82]	Wen X J 2009 J. Phys. G: Nucl. Part. Phys. 36 025011 Google Scholar
[83]	Zhang Z, Chu P C, Li X H, Liu H, Zhang X M 2021 Phys. Rev. D 103 103021 Google Scholar
[84]	Chu P C, Jiang Y Y, Liu H, Zhang Z, Zhang X M, Li X H 2021 Eur. Phys. J. C 81 569 Google Scholar
[85]	Chu P C, Li X H, Liu H, Zhang J W 2021 Phys. Rev. C 104 045805 Google Scholar
[86]	Chu P C, Zhou Y, Jiang Y Y, Ma H Y, Liu H, Zhang X M 2021 Eur. Phys. J. C 81 93 Google Scholar
[87]	Steiner A W, Prakash M, Lattimer J M 2001 Phys. Lett. B 509 10 Google Scholar
[88]	Reddy S, Praskash M, Lattimer J M 1998 Phys. Rev. D 58 013009 Google Scholar
[89]	Steiner A W, Prakash M, Lattimer J M 2000 Phys. Lett. B 486 239 Google Scholar
[90]	Menezes D P, Deppman A, Megias E, Castro L B 2015 Eur. Phys. J. A 51 155
[91]	Shao G Y 2011 Phys. Lett. B 704 343 Google Scholar
[92]	Chu P C, Chen L W, Wang X 2014 Phys. Rev. D 90 063013 Google Scholar
[93]	Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett. A 28 1350138

Cited By

图 1 基于不同参数的夸克物质对称能

Figure 1. Quark matter symmetry energy with different parameter sets

DownLoad: Full-Size Img PowerPoint

图 2 零温、有限温度、强磁场下奇异夸克物质的每核子自由能/能量、压强随重子数密度的变化

Figure 2. The energy per baryon, free energy per baryon, and the corresponding pressure as functions of baryon density with g-2 in zero temperature, finite temperature, and strong magnetic field cases

DownLoad: Full-Size Img PowerPoint

图 3 零温、有限温度、强磁场下奇异夸克物质的组分随重子数密度和磁场的变化

Figure 3. The fractions of SQM as functions of baryon density and magnetic fields with g-2 in zero temperature, finite temperature, and strong magnetic field cases

DownLoad: Full-Size Img PowerPoint

图 4 不同温度下奇异夸克物质的声速随重子数密度的变化

Figure 4. The sound velocity of SQM as functions of baryon density with g-2 at different temperatures

DownLoad: Full-Size Img PowerPoint

图 5 零温磁星中心压强以及磁星最大质量与对应半径按径向分布与横向分布随$ B_0 $的变化

Figure 5. Pressure for the central density, the maximum mass of magnetar, and the radius of longitudinal orientation case and transverse orientation case as functions of $ B_0 $

DownLoad: Full-Size Img PowerPoint

图 6 原生星演化中不同阶段的原生磁星质量半径关系

Figure 6. Mass-radius relations of the stages along the star evolution line of PQS with g-2 under the density-dependent magnetic field

DownLoad: Full-Size Img PowerPoint

图 7 磁场与零磁场下原生星核心温度随中心密度的变化关系

Figure 7. The core temperature for the star matter as a function of the central baryon density under zero magnetic field and $ B_0=4\times 10^{18} $ G

DownLoad: Full-Size Img PowerPoint

图 8 纵向、横向磁场情况都考虑时, 在g-2参数、$B_0=4\times $$ 10^{18}$G 情况下基于不同$ \theta $角所计算的零温磁星质量半径关系

Figure 8. Mass-radius relation for magnetars at zero temperature with g-2 and $ B_0=4\times 10^{18} $G at different $ \theta $.

DownLoad: Full-Size Img PowerPoint

[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]	Ivanenko D, Kurdgelaidze D F 1969 Lett. Nuovo Cimento 2 13 Google Scholar
[6]	Itoh N 1970 Prog. Theor. Phys. 44 291 Google Scholar
[7]	Bodmer A R 1971 Phys. Rev. D 4 1601 Google Scholar
[8]	Witten E 1984 Phys. Rev. D 30 272 Google Scholar
[9]	Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379 Google Scholar
[10]	Alcock C, Farh E, Olinto A 1986 Astrophy. J. 310 261 Google Scholar
[11]	Weber F 2005 Prog. Part. Nucl. Phys. 54 193 Google Scholar
[12]	Bombaci I, Parenti I, Vidana I 2004 Astrophy. J. 614 314 Google Scholar
[13]	Staff J, Ouyed R, Bagchi M 2007 Astrophy. J. 667 340 Google Scholar
[14]	Herzog T M, Röpke F K 2011 Phys. Rev. D 84 083002 Google Scholar
[15]	Stephanov M A, Rajagopal K, Shuryak E V 1998 Phys. Rev. Lett. 81 4816 Google Scholar
[16]	Terazawa H 1979 INS-Report (Tokyo: Univ. of Tokyo) p336
[17]	Alford M, Reddy S 2003 Phys. Rev. D 67 074024 Google Scholar
[18]	Alford M, Jotwani P, Kouvaris C, Kundu J, Rajagopal K 2005 Phys. Rev. D 71 114011 Google Scholar
[19]	Baldo M 2003 Phys. Lett. B 562 153 Google Scholar
[20]	Ippolito N D, Ruggieri M, Rischke D H, Sedrakian A, Weber F 2008 Phys. Rev. D 77 023004 Google Scholar
[21]	Lai X Y, Xu R X 2011 Res. Astron. Astrophys. 11 687 Google Scholar
[22]	Avellar M G B de, Horvath J E, Paulucci L 2011 Phys. Rev. D 84 043004 Google Scholar
[23]	Bonanno L, Sedrakian A 2012 A&A 539 A16
[24]	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
[25]	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
[26]	Chu P C, Zhou Y, Chen C, Li X H, Ma H Y 2020 J. Phys. G: Nucl. Part. Phys. 47 085201 Google Scholar
[27]	Antoniadis J 2013 Science 340 6131
[28]	Shahbaz T, Casares J 2018 Astrophys. J. 859 54 Google Scholar
[29]	Cromartie H T, Fonseca E, Ransom S M, et al. 2020 Nat. Astron. 4 72 Google Scholar
[30]	Abbott R 2020 Astrophys. J. Lett. 896 L44 Google Scholar
[31]	Deng Z L 2020 Astrophys. J. 892 4 Google Scholar
[32]	Deng Z L 2021 Astrophys. J. 909 174 Google Scholar
[33]	Prakash M, Bombaci I, Prakash M, Ellis P J, Lattimer J M, Knorren R 1997 Phys. Rept. 280 1 Google Scholar
[34]	Gupta V K, Gupta Asha, Singh S, Anand J D 2003 Int. J. Mod. Phys. D 12 583 Google Scholar
[35]	Shen J, Zhang Y, Wang B, Su R K 2005 Int. J. Mod. Phys. A 20 7547 Google Scholar
[36]	Dexheimer V, Torres J R, Menezes D P 2013 Eur. Phys. J. C 73 2569 Google Scholar
[37]	Dexheimer V, Menezes D P, Strickland M 2014 J. Phys. G: Nucl. Part. Phys. 41 015203 Google Scholar
[38]	Drago A, Lavagno A, Pagliara G 2014 Phys. Rev. D 89 043014 Google Scholar
[39]	Drago A, Pagliara G 2016 Eur. Phys. J. A 52 41 Google Scholar
[40]	Bauswein A, Stergioulas N, Janka H 2016 Eur. Phys. J. A 52 56 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
[46]	Isayev A A, Yang J 2011 Phys. Rev. C 84 065802
[47]	Isayev A A, Yang J 2012 Phys. Lett. B 707 163 Google Scholar
[48]	Isayev A A, Yang J 2013 J. Phys. G: Nucl. Part. Phys. 40 035105 Google Scholar
[49]	Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys Rev. Lett. 79 2176 Google Scholar
[50]	Bandyopadhyay D, Pal S, Chakrabarty S 1998 J. Phys. G: Nucl. Part. Phys. 24 1647 Google Scholar
[51]	Menezes D P, Benghi Pinto M, Avancini S S, et al. 2009 Phys. Rev. C 79 035807 Google Scholar
[52]	Menezes D P, Benghi Pinto M, Avancini S S, et al. 2009 Phys. Rev. C 80 065805 Google Scholar
[53]	Ryu C Y, Kim K S, Cheoun Myung-Ki 2010 Phys. Rev. C 82 025804 Google Scholar
[54]	Ryu C Y, Cheoun Myung-Ki, Kajino T, Maruyama T, Mathews Grant J 2012 Astropart. Phys. 38 25 Google Scholar
[55]	Zhong S Q, Dai Z G 2020 Astrophys. J. 893 9 Google Scholar
[56]	Gao Z F, Li X D, Wang N, Yuan J P, Peng Q H, Du Y J 2016 MNRAS 456 55 Google Scholar
[57]	Gao Z F 2021 Astron. Nachr. 342 369 Google Scholar
[58]	Zhu C 2016 Mod. Phys. Lett. A 31 1650070
[59]	Chodos A, Jaffe R L, Ohnson K, Thorn C B, Weisskopf V F 1974 Phys. Rev. D 9 3471 Google Scholar
[60]	Alford M, Braby M, Paris M, Reddy S 2005 Astrophys. J. 629 969 Google Scholar
[61]	Rehberg P, Klevansky S P, Hüfner J 1996 Phys. Rev. C 53 410
[62]	Hanauske M, Satarov L M, Mishustin I N, Stocker H, Greiner W 2001 Phys. Rev. D 64 043005 Google Scholar
[63]	Rüster S B, Rischke D H 2004 Phys. Rev. D 69 045011 Google Scholar
[64]	Menezes D P, Providencia C, Melrose D B 2006 J. Phys. G 32 1081 Google Scholar
[65]	Chao J Y, Chu P C, Huang M 2013 Phys. Rev. D 88 054009 Google Scholar
[66]	Chu P C, Wang X, Chen L W, Huang M 2015 Phys. Rev. D 91 023003 Google Scholar
[67]	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
[68]	Chu P C, Chen L W 2017 Phys. Rev. D 96 083019 Google Scholar
[69]	Roberts C D, Williams A G 1994 Prog. Part. Nucl. Phys. 33 477 Google Scholar
[70]	Zong H S, Chang L, Hou F Y, Sun W M, Liu Y X 2005 Phys. Rev. C 71 015205 Google Scholar
[71]	Peng G X, Chiang H C, Yang J J, Li L, Liu B 1999 Phys. Rev. C 61 015201 Google Scholar
[72]	Peng G X, Chiang H C, Zou B S, Ning P Z, Luo S J 2000 Phys. Rev. C 62 025801
[73]	Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807 Google Scholar
[74]	Li A, Peng G X, Lu J F 2011 Res. Astron. Astrophys. 11 482 Google Scholar
[75]	Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659
[76]	Schertler K, Greiner C, Sahu P K, Thoma M H 1998 Nucl. Phys. A 637 451
[77]	Chu P C, Chen L W 2014 Astrophys. J. 780 135 Google Scholar
[78]	Chu P C 2018 Phys. Lett. B 778 447 Google Scholar
[79]	Chu P C, Chen L W 2017 Phys. Rev. D 96 103001 Google Scholar
[80]	Schertler K, Greiner C, Thoma M H, Schertler K, Greiner C, Thoma M H 1997 Nucl. Phys. A 616 659 Google Scholar
[81]	Pisarski R D 1989 Nucl. Phys. A 498 423
[82]	Wen X J 2009 J. Phys. G: Nucl. Part. Phys. 36 025011 Google Scholar
[83]	Zhang Z, Chu P C, Li X H, Liu H, Zhang X M 2021 Phys. Rev. D 103 103021 Google Scholar
[84]	Chu P C, Jiang Y Y, Liu H, Zhang Z, Zhang X M, Li X H 2021 Eur. Phys. J. C 81 569 Google Scholar
[85]	Chu P C, Li X H, Liu H, Zhang J W 2021 Phys. Rev. C 104 045805 Google Scholar
[86]	Chu P C, Zhou Y, Jiang Y Y, Ma H Y, Liu H, Zhang X M 2021 Eur. Phys. J. C 81 93 Google Scholar
[87]	Steiner A W, Prakash M, Lattimer J M 2001 Phys. Lett. B 509 10 Google Scholar
[88]	Reddy S, Praskash M, Lattimer J M 1998 Phys. Rev. D 58 013009 Google Scholar
[89]	Steiner A W, Prakash M, Lattimer J M 2000 Phys. Lett. B 486 239 Google Scholar
[90]	Menezes D P, Deppman A, Megias E, Castro L B 2015 Eur. Phys. J. A 51 155
[91]	Shao G Y 2011 Phys. Lett. B 704 343 Google Scholar
[92]	Chu P C, Chen L W, Wang X 2014 Phys. Rev. D 90 063013 Google Scholar
[93]	Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett. A 28 1350138

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