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利用含δ介子的相对论平均场理论研究中子星潮汐形变性质

刁彬 许妍 黄修林 王夷博

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利用含δ介子的相对论平均场理论研究中子星潮汐形变性质

刁彬, 许妍, 黄修林, 王夷博

Study of tidal deformabilities of neutron stars using relativistic mean field theory containing δ mesons

Diao Bin, Xu Yan, Huang Xiu-Lin, Wang Yi-Bo
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  • 开展中子星宏观性质的研究, 对于揭示中子星内部组成和结构具有重要意义. 本文基于相对论平均场理论模型, 研究了 δ 介子对传统中子星和超子星物态方程、最大质量、勒夫数和潮汐形变能力的影响. 结果表明, 对于中小质量传统中子星(或超子星), δ介子使其潮汐形变能力变强; 随着传统中子星(或超子星)质量的增加, δ介子对其潮汐形变能力影响逐渐减弱; 尤其对于大质量超子星, 含有δ介子的超子星潮汐形变能力相比不含δ介子的超子星变弱. 此外, 在相同质量下超子的存在会降低星体的潮汐形变能力, 在本文所选的参数下, 含有δ介子的星体中, 仅同时含Λ, Σ和Ξ超子的超子星潮汐形变能力能同时满足GW170817和GW190814天文观测约束. 随着与中子星相关的引力波数据逐渐增加, 将为人们判断超子星内超子种类提供一个可能的途径.
    The research on the macroscopic properties of neutron stars is of great significance in revealing the internal composition and structure of neutron star. In this work, We analyze the influence of δ mesons on the equation of states, the maximum mass, the tidal Love numbers and the tidal deformabilities for the conventional neutron stars and the hyperon stars within the relativistic mean field theory. It is found that the presence of δ mesons can strengthen the tidal deformabilities of the low and medium-mass conventional neutron stars (or hyperon stars). However, the strengthening trends of the tidal deformabilities with δ mesons gradually weaken with the increase of the mass of the conventional neutron stars (or hyperon stars). Especially for massive hyperon stars, the tidal deformabilities of the superstars with δ mesons is weaker than the corresponding values without δ mesons. Moreover, the presence of hyperons can reduce the tidal deformabilities of stars with the same mass. For the stars containing δ mesons, only the tidal deformabilities in the hyperon stars with Λ, Σ and Ξ hyperons can satisfy the constraints of GW170817 and GW190814 events under the parameters selected in the paper. As the data about gravitational waves associated with the neutron stars gradually increase, there will be a possible way of judging the hyperon species in the hyperon stars.
      通信作者: 许妍, xuy@cho.ac.cn ; 黄修林, huangxl@cho.ac.cn ; 王夷博, wangyb@cho.ac.cn
      Corresponding author: Xu Yan, xuy@cho.ac.cn ; Huang Xiu-Lin, huangxl@cho.ac.cn ; Wang Yi-Bo, wangyb@cho.ac.cn
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  • 图 1  6种情况下, 星体物态方程

    Fig. 1.  Equation of states for neutron star matter in the six cases.

    图 2  6种情况下, 星体质量-半径关系. 不同颜色条纹区域分别表示PSRs J1903+0327和J0453+1559的质量测量值 $ {1.666}_{-0.01}^{+0.01}{\rm{M}}_{\odot } $$ {1.559}_{-0.004}^{+0.004}{\rm{M}}_{\odot } $[50,51], 橙色误差棒表示PSR J0030+0415的质量和半径测量值范围, 其质量测量值为$ {1.34}_{-0.16}^{+0.15}{\rm{M}}_{\odot } $$ {1.44}_{-0.14}^{+0.15}{\rm{M}}_{\odot } $, 相应半径值为 ${12.71}_{-1.19}^{+1.14}\;\rm{k}\rm{m}$${13.02}_{-1.06}^{+1.24}\;\rm{k}\rm{m}$[52]

    Fig. 2.  Mass - radius carves for the six equation of states. The striped areas of different colors stand for the constraints inferred from PSRs J1903+0327 and J0453+1559, and their mass measurement values are $ {1.666}_{-0.01}^{+0.01}{\rm{M}}_{\odot } $ and $ {1.559}_{-0.004}^{+0.004}{\rm{M}}_{\odot } $[50,51], respectively. The orange error bars express the constraints on the mass-radius limits of PSR J0030+0451, and its mass measurement values are $ {1.34}_{-0.16}^{+0.15}{\rm{M}}_{\odot } $ and $ {1.44}_{-0.14}^{+0.15}{\rm{M}}_{\odot } $, the corresponding radius values are ${12.71}_{-1.19}^{+1.14}\;\rm{k}\rm{m}$ and ${13.02}_{-1.06}^{+1.24}\;\rm{k}\rm{m}$, respectively [52]

    图 3  6种情况下, 星体勒夫数-质量关系. 其中不同颜色条纹区域分别表示PSRs J1903+0327和J0435+1559的勒夫数理论值范围, 黑色虚线表示星体质量取 $ 1.4{\rm{M}}_{\odot } $时勒夫数理论值

    Fig. 3.  Tidal Love numbers as a function of the masses for the six equation of states. The striped areas of different colors stand for the theoretical values ranges of the tidal Love numbers for PSRs J1903+0327 and J0435+1559, respectively. The vertical dashed line indicates as $M=1.4~{\rm{M}}_{\odot }$.

    图 4  6种情况下, 星体潮汐形变因子-质量关系. 不同颜色条纹区域分别表示PSRs J1903+0327和J0453+1559脉冲星的潮汐形变因子理论值范围, 彩色误差棒分别表示GW170817和GW190814对于星体潮汐形变的约束

    Fig. 4.  Tidal deformabilities as a function of the masses for the six equation of states. The different colors striped areas stand for the theoretical values of the tidal deformabilities for PSRs J1903+0327 and J0751+1087, respectively. The color error bar expresses the constraints from GW170817 and GW190814 events for the tidal deformabilities.

    表 1  各参数的取值. 其中, ${f}_{i}={\left( {{g}_{i}}/{{m}_{i}}\right)}^{2}\left({\rm{f}\rm{m}}^{2}\right)$, $ i=\sigma , \omega , \rho \rm{和}\delta $. 介子质量取值如下: ${m}_{\sigma }=550\;\rm{M}\rm{e}\rm{V}$, ${m}_{\omega }=783\;\rm{M}\rm{e}\rm{V}$, ${m}_{\rho }=763\;\rm{M}\rm{e}\rm{V}$${m}_{\delta }=983\;\rm{M}\rm{e}\rm{V}$. 超子耦合常数表示为与核子耦合常数的比值, 即 ${x}_{i}= {{g}_{iH}}/{{g}_{i}}$, $ i=\sigma , \omega , \rho \rm{和}\delta $, 具体取值为 $ {x}_{\omega B}=0.783 $, $ {x}_{\sigma B}={x}_{\delta B}={x}_{\rho B}=0.7 $[49]

    Table 1.  Parameter sets. ${f}_{i}={\left( {{g}_{i}}/{{m}_{i}}\right)}^{2}\left({\rm{f}\rm{m}}^{2}\right)$, $i=\sigma , \omega , \rho \;\rm{a}\rm{n}\rm{d}\;\delta$, we take ${m}_{\sigma }=550\;\rm{M}\rm{e}\rm{V}$, ${m}_{\omega }=783\;\rm{M}\rm{e}\rm{V}$, ${m}_{\rho }=763\;\rm{M}\rm{e}\rm{V}$ and ${m}_{\delta }=983\;\rm{M}\rm{e}\rm{V}$. The ratios of coupling constants between hyperons and nucleons can be expressed ${x}_{i}= {{g}_{iH}}/{{g}_{i}}$, $i=\sigma , \omega , \rho \;\rm{a}\rm{n}\rm{d}\;\delta$. Their values $ {x}_{\omega B} $ and $ {x}_{\sigma B} $, $ {x}_{\delta B} $, $ {x}_{\rho B} $ are 0.783 and 0.7, respectively [49].

    参数$ {f}_{\sigma } $$ {f}_{\omega } $$ {f}_{\rho } $$ {f}_{\delta } $$ {g}_{2}/{\rm{f}\rm{m}}^{-1} $$ {g}_{3} $
    不包含$ \rm{\delta } $介子10.335.420.950.00$ 0.033{g}_{\sigma }^{3} $$ -0.0048{g}_{\sigma }^{4} $
    包含$ \rm{\delta } $介子10.335.423.152.50$ 0.033{g}_{\sigma }^{3} $$ -0.0048{g}_{\sigma }^{4} $
    下载: 导出CSV

    表 2  饱和核物质性质, 饱和密度值以及在饱和密度处对称能、对称斜率和不可压缩系数值[49]

    Table 2.  Properties of nuclear saturation density, namely, the values of the nuclear saturation density $ {\rho }_{0} $, the symmetry energy $ {E}_{\rm{s}\rm{y}\rm{m}} $, the symmetry energy slope L and the incompressibility $ {K}_{\rm{v}} $[49].

    参数$ {\rho }_{0}/{\rm{f}\rm{m}}^{-3} $$ {E}_{\rm{s}\rm{y}\rm{m}}/\rm{M}\rm{e}\rm{V} $$ L/\rm{M}\rm{e}\rm{V} $$ {K}_{\rm{v}}/\rm{M}\rm{e}\rm{V} $
    不包含$ \rm{\delta } $介子0.1631.384240
    包含$ \rm{\delta } $介子0.1631.3103240
    下载: 导出CSV

    表 3  6情况下, 星体最大质量及其对应的半径、勒夫数和潮汐形变因子; 星体最大半径及其对应的质量、勒夫数和潮汐形变因子

    Table 3.  Values of the maximum masses M and the corresponding radii R, the tidal Love numbers $ {k}_{2} $and the tidal deformabilities Λtidal. Values of the maximum radii R and the corresponding masses M, the tidal Love numbers $ {k}_{2} $and the tidal deformabilities Λtidal with the six cases.

    中子星最大质量处中子星最大半径处
    $ M/{\rm{M}}_{\odot } $$ R/\rm{k}\rm{m} $$ {k}_{2} $Λtidal$ M/{\rm{M}}_{\odot } $$ R/\rm{k}\rm{m} $$ {k}_{2} $Λtidal
    1)2.08810.890.02180.99512.9730.1244405
    2)2.11911.310.01981.13813.5700.1052417
    3)1.77610.890.032280.99512.9730.1244405
    4)1.76311.400.031361.13813.5700.1052417
    5)1.70910.710.033310.99512.9370.1244405
    6)1.69110.910.028311.10913.5660.1072791
    下载: 导出CSV

    表 4  6种情况下, $1.4~{\rm{M}}_{\odot }$中子星、PSRs J1903+0327和PSR J0453+1559半径、勒夫数和潮汐形变因子的理论值

    Table 4.  Theoretical values for the radii, the tidal Love numbers and the tidal deformabilities for the $1.4~{\rm{M}}_{\odot }$ neutron star, PSRs J1903+0327 and J0751+1087, respectively.

    R/km$ {K}_{2} $$\varLambda$

    ($ 1.4{\rm{M}}_{\odot } $中子星)
    1)12.800.090545
    2)13.510.085682
    3)12.810.090548
    4)13.510.085682
    5)12.580.084468
    6)13.250.079568
    PSR J1903+0327
    ($ {1.666}_{-0.01}^{+0.01}{\rm{M}}_{\odot } $)
    1)[12.53, 12.56][0.066, 0.067][146, 162]
    2)[13.26, 13.29][0.061, 0.064][180, 205]
    3)[12.28, 12.37][0.060, 0.063][120, 140]
    4)[13.04, 13.13][0.058, 0.061][158, 184]
    5)[11.29, 11.48][0.042, 0.046][055, 070]
    6)[11.49, 11.80][0.034, 0.039][050, 070]
    PSR J0453+1559
    ($ {1.559}_{-0.004}^{+0.004}{\rm{M}}_{\odot } $)
    1)[12.67, 12.68][0.076, 0.077][255, 265]
    2)[13.39, 13.40][0.072, 0.073][313, 329]
    3)[12.63, 12.64][0.075, 0.075][251, 256]
    4)[13.37, 12.38][0.071, 0.073][309, 328]
    5)[12.04, 12.08][0.061, 0.062][159, 169]
    6)[12.61, 12.65][0.055, 0.057][179, 194]
    下载: 导出CSV
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    赵诗艺, 刘承志, 黄修林, 王夷博, 许妍 2021 物理学报 70 222601Google Scholar

    Zhao S Y, Liu C Z, Huang X L, Wang Y B, Xu Y 2021 Acta Phys. Sin. 70 222601Google Scholar

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    詹琼, 宋汉峰, 邰丽婷, 王江涛 2015 物理学报 64 089701Google Scholar

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    李昂, 胡金牛, 鲍世绍, 申虹, 徐仁新 2019 原子核物理评论 36 1Google Scholar

    Li A, Hu J N, Bao S S, Shen H, Xu R X 2019 Nucl. Phys. Rev. 36 1Google Scholar

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    来小禹, 徐仁新 2019 物理 48 554Google Scholar

    Lai X Y, Xun R X 2019 Phys. 48 554Google Scholar

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    龚武坤, 郭文军 2020 物理学报 69 242101Google Scholar

    Gong W K, Guo W J 2020 Acta Phys. Sin. 69 242101Google Scholar

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    包特木巴根, 杨兴强, 喻孜 2013 物理学报 62 012101Google Scholar

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    [9]

    Pattersons M L, Sulaksono A 2021 Eur. Phys. J. C 81 698Google Scholar

    [10]

    Zhao X F 2015 Phys. Rev. C 92 055802Google Scholar

    [11]

    Rather I A, Usmani, Patra S K 2021 Nucl. Phys. A 1010 122189Google Scholar

    [12]

    Sun B Y, Liu Z W, Xing R Y 2019 AIP. Conf. Proc. 2127 020020Google Scholar

    [13]

    Abbott B P, LIGO Scientific, Virgo Collaboration 2017 Phys. Rev. Lett. 119 161101Google Scholar

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    Abbott B P, LIGO Scientific, Virgo Collaboration 2018 Phys. Rev. Lett. 121 161101Google Scholar

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    Tang S P, Jiang J L, Gao W H, Wei D M 2021 Phys. Rev. D 103 063026Google Scholar

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    Lim Y, Holt J W 2018 Phys. Rev. Lett. 121 062701Google Scholar

    [20]

    Chatziioannou K, Haster C J Zimmerman A 2018 Phys. Rev. D 97 104036Google Scholar

    [21]

    Han S, Steiner A W 2019 Phys. Rev. D 99 083014Google Scholar

    [22]

    Jin H M, Xia C J, Sun T T, Peng G X 2022 Phys. Lett. B 829 137121Google Scholar

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    Zhu Z Y, Zhou E P, Li A 2018 Astrophys. J. 862 98Google Scholar

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    Biswas B, Nandi R Char P, Bose S 2019 Phys. Rev. D 100 044056Google Scholar

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    Essick R, Landry P, Holz D E 2020 Phys. Rev. D 101 063007Google Scholar

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    Miao Z Q, Li A, Dai Z G 2022 Mon. Not. R. Astron. Soc. 515 5071Google Scholar

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    Huang K X, Hu J N, Zhang Y, Shen H 2022 arXiv: 2203. 12357 v1 [nucl-th]

    [28]

    Kubis S, Kutschera M 1997 Phys. Lett. B 399 191Google Scholar

    [29]

    Yu Z, Liu G Z, Zhu M F, Xu Y, Zhao E G 2009 Chin. Phys. Lett. 26 022601Google Scholar

    [30]

    Shao G Y, Liu Y X 2010 Phys. Rev. C 82 055801Google Scholar

    [31]

    Qian Z, Xin R Y, Sun B Y 2018 Sci. Chin. Phys. Mech. Astron. 61 082011Google Scholar

    [32]

    Roca-Maza X, Viñas X, Centelles M, Ring P, Schuck P 2016 Phys. Rev. C 93 069905Google Scholar

    [33]

    Kumar B, Singh S K, Agrawal B K, Patra S K 2017 Nucl. Phys. A 996 197Google Scholar

    [34]

    Bunta J K, Gmuca Š 2003 Phys. Rev. C 68 054318Google Scholar

    [35]

    Xu Y, Liu G Z, Wu Y R, Zhu M F, Wang H Y, Zhao E G 2012 Plasma Sci. Technol. 14 375Google Scholar

    [36]

    Xu Y, Liu G Z, Fan C B, Han X W, Zhu M F Wang H Y, Zhang X J 2013 Chin. Phys. Lett. 20 062101Google Scholar

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    Liu B, Greco V, Baran V, Colonna M, Di Toro M 2002 Phys. Rev. C 65 045201Google Scholar

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    Santos A M S, Menezes D P 2004 Phys. Rev. C 69 045803Google Scholar

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    Avancini S S, Brito L, Menezes D P, Providência C 2004 Phys. Rev. C 70 015203Google Scholar

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    Menezes D P, Providência C 2003 Phys. Rev. C 68 035804Google Scholar

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    Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 55 378Google Scholar

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    Tolman R C 1939 Phys. Rev. 55 364Google Scholar

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    Thome K S 1998 Phys. Rev. D 58 124031Google Scholar

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    Hinderer T 2008 Astrophys. J. 677 1216Google Scholar

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    Damour T, Nagar A 2009 Phys. Rev. D 80 084035Google Scholar

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    Hinderer T, Lackey B D, Lang R N, Read J S 2010 Phys. Rev. D 81 123016Google Scholar

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    Liu B, Guo H, Di Toro M, et al. 2005 Eur. Phys. J. A 25 293Google Scholar

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    Riley T E, Watts A L, Bogdanov S, et al. 2019 Astrophys. J. Lett. 887 L21Google Scholar

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出版历程
  • 收稿日期:  2022-08-08
  • 修回日期:  2022-09-09
  • 上网日期:  2022-11-03
  • 刊出日期:  2023-01-20

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