With a selected sample of neutron star (NS) equations of state (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass M_g and baryonic mass M_b, and the relations between the maximum NS mass supported through uniform rotation (M_max) and that of nonrotating NSs (M_TOV). We find that for an EOS-independent quadratic, universal transformation formula \(({M_b} = {M_g}\; + A\; \times \;M_g^2)\), the best-fit A value is 0.080 for non-rotating NSs, 0.064 for maximally rotating NSs, and 0.073 when NSs with arbitrary rotation are considered. The residual error of the transformation is ∼ 0.1M_⊙ for non-spin or maximum-spin, but is as large as ∼ 0.2M_⊙ for all spins. For different EOSs, we find that the parameter A for non-rotating NSs is proportional to \(R_{1.4}^{- 1}\) (where R_1.4 is NS radius for 1.4M_⊙ in units of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01M_⊙ for the quadratic form and less than 0.01M_⊙ for the cubic form (\(({M_b} = {M_g}\; + \,{A_1}\; \times \;M_g^2\; + \,{A_2}\; \times \;M_g^3)\)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (M_max − M_TOV)/M_TOV and the spin period normalized to the Keplerian period \(\mathcal{P}\), i.e., \({\log _{10}}{\rm{\Delta}}m = (- 2.74 \pm 0.05){\log _{10}}{\mathcal P} + {\log _{10}}(0.20 \pm 0.01)\), which is independent of EOS models. These empirical relations are helpful to study NS-NS mergers with a long-lived NS merger product using multi-messenger data. The application of our results to GW170817 is discussed.

中文翻译：

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非旋转和快速旋转的中子星的重力质量与重子质量之间的关系

通过选择与当前观测值一致且具有最大质量范围的中子星（NS）状态方程（EOS）样本，我们研究了NS重力质量M _g和重子质量M _b之间的关系，以及这些关系均匀旋转所支撑的最大NS质量（M _max）和非旋转NSs所承受的最大质量（M _TOV）之间。我们发现，对于独立于EOS的二次通用变换公式\（（{M_b} = {M_g} \; + A \; \ times ;; M_g ^ 2）\），最佳拟合A对于不旋转的NS，该值为0.080；对于最大旋转的NS，该值为0.064；当考虑任意旋转的NS时，该值为0.073。变换的残差〜0.1中号_⊙用于非自旋或最大-自旋，但大到〜0.2中号_⊙对所有自旋。对于不同的EOSS，我们发现参数甲对于非旋转NSS是正比于\（R_ {1.4} ^ { - 1} \）（其中，[R _1.4为1.4 NS半径中号_⊙单位为公里）。对于特定的EOS，如果一个采用不同的自旋周期的最佳拟合参数，变换的残余误差较小，这是0.01的量级中号_⊙为二次形式和小于0.01中号_⊙为立方形式（\（（{M_B} = {M_g} \; + \ {A_1} \; \倍\; M_g ^ 2 \ + \ {A_2} \; \ times \; M_g ^ 3）\））。我们也找到了归一化的质量增益之间的非常紧密的和一般相关性由于自旋Δ米=（中号_最大值-中号_TOV）/中号_TOV和归一化到开普勒周期的旋转周期\（\ mathcal {P} \） ，即，\（{\ log _ {10}} {\ rm {\ Delta}} m =（-2.74 \ pm 0.05）{\ log _ {10}} {\ mathcal P} + {\ log _ {10}} （0.20 \ pm 0.01）\），它独立于EOS模型。这些经验关系有助于使用多信使数据研究具有长期使用寿命的NS合并产品的NS-NS合并。讨论了我们的结果在GW170817中的应用。