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Strang Quark Matter (SQM) is considered to be the true ground state of the strong interactions, but recent studies have shown that ordinary quark matter (u-d Quark Matter, u-d QM) may also be the ground state of the strong interactions.By inserting an attenuation factor of Woods-Saxon type in the quark mass scaling, the resulting calculations of equation of state of u-d QM based on equiv-particle model show that the stability window of model parameters for stable u-d QM can be significantly enlarged with proper model parameters, which can be seen in the following figure. In this figure, the red solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when the minimum value of the average energy per baryon is set to 930 MeV; the blue solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when $ m_\mathrm{u}=0 $. Thereby, the red and blue shaded areas are the absolute stable regions for u-d QM without and with attenuation factor in mass scaling. It is obvious that with the inclusion of attenuation factor and proper model parameters the absolute stable region (blue shaded area) for u-d QM can be much larger than that without the attenuation factor (red shaded area).The introduction of the attenuation factor makes it possible that the maximum mass of ordinary quark star (u-d quark star, u-d QS) can be larger than 2 times the solar mass, and meanwhile the tidal deformability satisfies $ \Lambda_{1.4} \in [70,580] $, which are both consistent with the current astronomical observations. Therefore, the pulsars may be essentially the u-d QSs. This result offers a possibility for understanding the nature of pulsars, and it also further deepens the understanding of the strong interactions.
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Keywords:
- quark matter /
- quark star /
- equation of state /
- tidal deformability
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图 1 u-d QM的稳定窗口, 红色区域表示在没有考虑衰减因子时的u-d QM的稳定区域, 而蓝色区域表示衰减因子引入后u-d QM的稳定区域. 在以上三个分图中, 红色实线与红色虚线分别表示包含衰减因子与不包含衰减因子且当平均重子能量最小值等于930 MeV时$ \sqrt{D} $随C的变化曲线; 蓝色实线与蓝色虚线分别表示包含衰减因子与不包含衰减因子且当$ m_\mathrm{u}=0 $时$ \sqrt{D} $随C的变化曲线. 三个分图中的$ (w/\mathrm{fm}^{-3} $, $ n_a/\mathrm{fm}^{-3}) $参数取值从上往下分别为(4.0, 0.6), (1.0, 0.6) 和(1.0, 2.0)
Figure 1. Stability window for u-d QM, the red and blue areas are the absolute stable regions for u-d QM without and with attenuation factor in mass scaling. In the three sub-figures above, the red solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when the minimum value of the average energy per baryon is 930 MeV. The blue solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when $ m_\mathrm{u}=0 $. The values of parameters $ (w/\mathrm{fm}^{-3}, n_a/\mathrm{fm}^{-3}) $ in the three sub-figures are (4.0, 0.6), (1.0, 0.6), and (1.0, 2.0) from top to bottom.
图 2 衰减因子随密度的变化曲线
Figure 2. Curves of the attenuasion factor as function of baryon number density.
图 3 平均重子能量与压强随密度的变化曲线
Figure 3. Curves of Energy per baryon and pressure as functions of baryon number density.
图 4 潮汐形变Λ和QS质量M随QS中心密度$ n_0 $的变化曲线. 其中, 各分图中的蓝色实线为Λ随$ n_0 $的变化曲线, 其值对应于左纵轴; 红色实线为M随$ n_0 $的变化曲线, 其值对应于右纵轴. 从上往下三个分图中的参数值与图 1中从上往下三个分图中的参数值相同
Figure 4. Curves of tidal deformability Λ and QS mass M as functions of central density $ n_0 $ of quark star. In the three sub-figures, the blue solid curves corresponding to the left axis represent Λ versus $ n_0 $; the red solid curves corresponding to right axis represent M versus $ n_0 $. The parameters for the three sub-figures are the same with that in Fig. 1 from top to bottom.
表 1 在图 4中的三组参数下u-d QS的最大质量, 最大质量u-d QS的半径, 以及与潮汐形变范围$ \Lambda_{1.4} \in $$ [70, 580] $相对应的u-d QS中心密度范围和质量范围
Table 1. The maximum masses and corresponding radii of u-d QSs under three parameter sets in FIG. 4, as well as the central density range and mass range of u-d quark stars for the tidal deformability range $ \Lambda_{1.4} \in [70, 580] $.
Parameter sets $ M_\mathrm{max}/\mathrm{M}_\odot $ R/km $ n_0/\mathrm{fm}^{-3} $ $ M/\mathrm{M}_\odot $ (a) 2.136 11.681 [0.369, 0.560] [1.449, 1.990] (b) 2.150 10.927 [0.421, 0.562] [1.302, 1.869] (c) 2.090 11.021 [0.410, 0.582] [1.343, 1.887] 
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