Hadron-quark deconfinement phase transition in hybrid stars

Gong Wu-Kun; Guo Wen-Jun

doi:10.7498/aps.69.20200925

Abstract

Astronomical statistics shows that the mass of neutron star is of the order of the solar mass, but the radius is only about ten kilometers. Therefore, the neutron star is highly condensed and there may be a variety of competing material phases inside the compact star. Hadron-quark deconfinement phase transition that is poorly understood at high density can be studied by the matter properties of hybrid star. The hybrid star contains many kinds of material phases, which cannot be described uniformly by one theory. So, different material phases are described by different theories. The hadronic phase is described by the relativistic mean-field theory with parameter set FSUGold including ω²ρ² interaction term, and the quark phase is described by an effective mass bag model in which the quark mass is density-dependent. The hadron-quark mixed phase is constructed by the Gibbs phase transition, and the properties of hybrid star in β equilibrium is studied in this model. It is found that the bag constant B has a great influence on the starting point and ending point of the hadron-quark deconfinement phase transition and the particle composition in the hybrid star. Comparing with the starting point of phase transition, the influence of B on the ending point of phase transition is very obvious. For the hybrid star, the equation of state of matter becomes stiffer at low density and softer at high density as B increases. The overall effect is that the slope of the mass-radius curve increases with B increasing. The calculated results show that the maximum mass of hybrid star is between 1.3 solar mass and 1.4 solar mass (M_☉), and the radius is between 9 km and 12 km. In addition, the influence of attractive and repulsive Σ potential on the properties of hybrid stars are studied. The results show that the Σ potential has a great influence on the particle composition in the hybrid star. We also find that the repulsive Σ potential makes the hybrid star have a greater maximum mass then an attractive Σ potential. For the attractive Σ potential, the maximum mass of hybrid star is 1.38M_☉, while for the repulsive Σ potential, the maximum mass of hybrid stars is 1.41M_☉.

Keywords:

Authors and contacts

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Corresponding author: Guo Wen-Jun, impgwj@126.com

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References

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[52]	Bao T, Liu G Z, Zhao E G, Zhu M F 2008 Eur. Phys. J. A 38 287 Google Scholar

Cited By

图 1 强子相(划线)、混合相(实线)、夸克相(点线)中, 每核子能量与物质密度的关系(a)以及压强与物质密度的关系(b), 取$ {{B}}^{{1/4}} $ = 195 MeV, $U_\varSigma^{(N)} $ = –30 MeV

Figure 1. Relationships of each nucleon (a) and pressure (b) with matter density in hadron phase (dashed line), mixed phase (solid line) and quark phase (dotted line), respectively, with $ {{B}}^{{1/4}} $ = 195 MeV, $U_\varSigma^{(N)} $ = –30 MeV.

DownLoad: Full-Size Img PowerPoint

图 2 $U_\varSigma^{(N)} $ = –30 MeV下$ {{B}}^{{1/4}} $ = 185 MeV (实线)、190 MeV (划线)、195 MeV (点线)时夸克相在混合星内的占比χ

Figure 2. Proportion of quark phase χ in hybrid stars when $ {{B}}^{{1/4}} $ taking 185 MeV (solid line), 190 MeV (dashed line) and 195 MeV (dotted line), respectively, with $U_\varSigma^{(N)} $ = –30 MeV.

DownLoad: Full-Size Img PowerPoint

图 3 混合星粒子分布图($ {{B}}^{{1/4}} $分别取185, 190, 195 MeV)　(a), (b), (c) $U_\varSigma^{(N)} $ = 30 MeV; (d), (e), (f) $U_\varSigma^{(N)} $ = –30 MeV

Figure 3. Particle composition in the hybrid star: (a), (b), (c) $U_\varSigma^{(N)} $ = 30 MeV; (d), (e), (f) $U_\varSigma^{(N)} $ = –30 MeV. $ {{B}}^{{1/4}} $ taking 185, 190, and 195 MeV.

DownLoad: Full-Size Img PowerPoint

图 4 $U_\varSigma^{(N)} $ = –30 MeV下$ {{B}}^{{1/4}} $ = 185 MeV (实线)、190 MeV (划线)、195 MeV (点线)时的EOS曲线

Figure 4. EOS when $ {{B}}^{{1/4}} $ taking 185 MeV (solid line), 190 MeV (dashed line) and 195 MeV (dotted line), respectively, with $U_\varSigma^{(N)} $ = –30 MeV.

DownLoad: Full-Size Img PowerPoint

图 5 不同口袋常数下, 混合星质量-半径关系　(a)和质量-能量密度关系(b)

Figure 5. Mass-radius (a) and mass-energy density (b) curves of hybrid stars, respectively, with different bag constant.

DownLoad: Full-Size Img PowerPoint

图 6 $ {{B}}^{{1/4}} $ = 195 MeV下混合星内夸克相比份χ分布, 其中实线表示$U_\varSigma^{(N)} $ = –30 MeV的情况; 虚线表示$U_\varSigma^{(N)} $ = 30 MeV的情况

Figure 6. Proportion of quark phase χ in hybrid stars when $U_\varSigma^{(N)} $ taking –30 MeV (solid line) and 30 MeV (dashed line) at $ {{B}}^{{1/4}} $ = 195 MeV, respectively.

DownLoad: Full-Size Img PowerPoint

图 7 $ {{B}}^{{1/4}} $ = 195 MeV下混合星的质量-半径关系(a)和质量-能量密度关系(b), 其中实线表示$U_\varSigma^{(N)} $ = –30 MeV, 虚线表示$U_\varSigma^{(N)} $ = 30 MeV

Figure 7. Mass-radius (a) and mass-energy density (b) curves of hybrid stars, respectively, with $U_\varSigma^{(N)} $ taking –30 MeV (solid line) and 30 MeV (dashed line) at $ {{B}}^{{1/4}} $ = 195 MeV.

DownLoad: Full-Size Img PowerPoint

[1]	Norsen T 2002 Phys. Rev. C 65 045805 Google Scholar
[2]	Mintz B W, Fraga E S, Pagliara G, Schaffner-Bielich J 2010 Phys. Rev. D 81 123012 Google Scholar
[3]	Mintz B W, Fraga E S, Schaffner-Bielich J, Pagliara G 2010 J. Phys. G Nucl. Part. Phys. 37 094066 Google Scholar
[4]	Weissenborn S, Sagert I, Pagliara G, Hempel M, Schaffner-Bielich J 2011 Astrophys. J. 740 L14 Google Scholar
[5]	Orsaria M, Rodrigues H, Weber F, Contrera G A 2013 Phys. Rev. D 87 023001 Google Scholar
[6]	Schaffner-Bielich J, Dover C B, Gal A, Greiner C, Stöcker H 1993 Phys. Rev. Lett. 71 1328 Google Scholar
[7]	Drago A, Pagliara G 2016 Eur. Phys. J. A 52 1 Google Scholar
[8]	Torres J R, Gulminelli F, Menezes D P 2017 Phys. Rev. C 95 025201 Google Scholar
[9]	Sedrakian A 2019 Phys. Rev. D 99 043011 Google Scholar
[10]	Wu C, Qian W L, Ma Y G, Yang J F 2013 Int. J. Mod. Phys. E 22 1350026 Google Scholar
[11]	Lim Y, Kwak K, Hyun C H, Lee C H 2014 Phys. Rev. C 89 055804 Google Scholar
[12]	Mallick R, Schramm S, Dexheimer V, Bhattacharyya A 2015 Mon. Not. R. Astron. Soc. 449 1347 Google Scholar
[13]	Kolomeitsev E E, Maslov K A, Voskresensky D N 2018 Nucl. Phys. A 970 291 Google Scholar
[14]	Kiziltan B, Kottas A, De Yoreo M, Thorsett S E 2013 Astrophys. J. 778 66 Google Scholar
[15]	Glendenning N K 2000 Phys. Rev. Lett. 85 1150 Google Scholar
[16]	Harko T, Cheng K S, Tang P S 2004 Astrophys. J. 608 945 Google Scholar
[17]	Li A, Peng G X, Lombardo U 2009 Chin. Phys. C 33 61 Google Scholar
[18]	Alaverdyan A G, Alaverdyan G B, Chiladze A O 2010 Int. J. Mod. Phys. D 19 1557 Google Scholar
[19]	Bhattacharyya A, Mishustin I N, Greiner W 2010 J. Phys. G Nucl. Part. Phys. 37 025201 Google Scholar
[20]	Chen S W, Gao L, Peng G X 2012 Chin. Phys. C 36 947 Google Scholar
[21]	Orsaria M, Rodrigues H, Weber F, Contrera G A 2014 Phys. Rev. C 89 015806 Google Scholar
[22]	陈建玲, 王辉, 贾焕玉, 马紫微, 李永宏, 谭俊 2019 物理学报 68 180401 Google Scholar Cheng J L, Wang H, Jia H Y, Ma Z W, Li Y H, Tan J 2019 Acta Phys. Sin. 68 180401 Google Scholar
[23]	Wu F, Wu C 2020 Eur. Phys. J. A 56 20 Google Scholar
[24]	Duez M D, Liu Y T, Shapiro S L, Stephens B C 2004 Phys. Rev. D 69 104030 Google Scholar
[25]	Roark J, Dexheimer V 2018 Phys. Rev. C 98 055805 Google Scholar
[26]	Zdunik J L 2002 Astron. Astrophys. 394 641 Google Scholar
[27]	Vartanyan Y L, Grigoryan A K, Sargsyan T R 2004 Astrophysics 47 189 Google Scholar
[28]	Wu C, Su R K 2009 J. Phys. G Nucl. Part. Phys. 36 095101 Google Scholar
[29]	Liu Y X, Gao D F, Guo H 2001 Nucl. Phys. A 695 353 Google Scholar
[30]	Zhou E P, Zhou X, Li A 2018 Phys. Rev. D 97 083015 Google Scholar
[31]	Li Z H, Schulze H J 2012 Phys. Rev. C 85 064002 Google Scholar
[32]	Kohno M 2013 Phys. Rev. C 88 064005 Google Scholar
[33]	Fukukawa K, Baldo M, Burgio G F, Lo Monaco L, Schulze H J 2015 Phys. Rev. C 92 065802 Google Scholar
[34]	Hebeler K, Bogner S K, Furnstahl R J, Nogga A, Schwenk A 2011 Phys. Rev. C 83 031301 Google Scholar
[35]	Coraggio L, Holt J W, Itaco N, Machleidt R, Marcucci L E, Sammarruca F 2014 Phys. Rev. C 89 044321 Google Scholar
[36]	Drischler C, Hebeler K, Schwenk A 2016 Phys. Rev. C 93 054314 Google Scholar
[37]	Xu R L, Wu C, Ren Z Z 2012 J. Phys. G Nucl. Part. Phys. 39 085107 Google Scholar
[38]	高朋林, 郑皓, 孙光爱 2019 物理学报 68 181102 Google Scholar Gao P L, Zheng H, Sun G A 2019 Acta Phys. Sin. 68 181102 Google Scholar
[39]	Menezes D P, Providência C 2003 Phys. Rev. C 68 035804 Google Scholar
[40]	Bao T, Liu G Z, Zhu M F 2009 Chin. Phys. C 33 340 Google Scholar
[41]	Bao T, Li G Q, Wang Z C, Yang X Q, Liu G Z 2011 Chin. Phys. C 35 539 Google Scholar
[42]	Baldo M, Burgio G F, Castorina P, Plumari S, Zappalà D 2007 Phys. Rev. C 75 035804 Google Scholar
[43]	Peng G X, Li A, Lombardo U 2008 Phys. Rev. C 77 065807 Google Scholar
[44]	Wu C, Ren Z Z 2011 Phys. Rev. C 83 025805 Google Scholar
[45]	Glendenning N K 1982 Phys. Lett. B 114 392 Google Scholar
[46]	Todd-Rutel B G, Piekarewicz J 2005 Phys. Rev. Lett. 95 122501 Google Scholar
[47]	Millener D J, Dover C B, Gal A 1988 Phys. Rev. C 38 2700 Google Scholar
[48]	Schaffner-Bielich J, Gal A 2000 Phys. Rev. C 62 034311 Google Scholar
[49]	Schaffner-Bielich J, Dover C B, Gal A, Greiner C, Millener D J, Stöcker H 1994 Ann. Phys. (N.Y). 235 35 Google Scholar
[50]	Schertler K, Greiner C, Thoma M H 1997 J. Phys. G Nucl. Part. Phys. 23 2051 Google Scholar
[51]	Schertler K, Greiner C, Schaffner-Bielich J, Thoma M H 2000 Nucl. Phys. A 677 463 Google Scholar
[52]	Bao T, Liu G Z, Zhao E G, Zhu M F 2008 Eur. Phys. J. A 38 287 Google Scholar

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