arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2201.05209gr-qc
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新的中子星内部模型

New interior model of neutron stars

Camilo Posada, Jan Hladík, Zdeněk Stuchlík

摘要:

托尔曼VII解被认为是爱因斯坦方程的少数解析解之一,它近似地描述了中子星(NS)的内部。该解的特征在于质量$M$、半径$R$和随径向坐标$r$二次变化的能量密度。最近,Jiang和Yagi提出了一个修改的解决方案,所谓的修改托尔曼七(MTVII)解决方案,通过引入一个额外的四次项的能量密度径向分布。MTVII解是爱因斯坦方程的近似解,其包括新的参数$α$,该参数允许解与现实NS的能量密度分布具有更好的一致性。在这里,我们认为MTVII解决方案,表明对于某些值的参数$α$和紧凑性$\mathcal{C}$,该解决方案体现了一个区域的负压附近的表面,导致负值的潮汐勒夫数。为了减轻这些缺点,我们引入了一个精确的版本的MTVII解决方案,通过数值求解爱因斯坦方程的MTVII能量密度配置文件。作为我们的新的精确MTVII(EMTVII)解决方案的应用程序,我们计算的潮汐勒夫数和潮汐变形,作为$\mathcal{C}$的函数,对于不同的参数$α$值。我们发现,EMTVII解决方案预测一个积极的潮汐勒夫数的参数$(\mathcal{C},α)$的允许值的整个范围内,与以前的结果为现实的NS。

英文摘要:

The Tolman VII solution is considered by some as one of the few analytical solutions to Einstein's equations, which describes approximately well the interior of neutron stars (NSs). This solution is characterized by the mass $M$, radius $R$, and an energy density that varies quadratically with the radial coordinate $r$. Recently, Jiang and Yagi proposed a modification of this solution, the so-called modified Tolman VII (MTVII) solution, by introducing an additional quartic term to the energy density radial profile. The MTVII solution is an approximate solution to Einstein's equation, which includes a new parameter $α$ that allows the solution to have a better agreement with the energy density profiles for realistic NSs. Here we consider the MTVII solution, showing that for certain values of the parameter $α$ and compactness $\mathcal{C}$ this solution manifests a region of negative pressure near the surface which leads to negative values of the tidal Love number. To alleviate these drawbacks, we introduce an exact version of the MTVII solution obtained by solving numerically Einstein's equations for the MTVII energy density profile. As an application of our new exact MTVII (EMTVII) solution, we calculate the tidal Love number and tidal deformability, as a function of $\mathcal{C}$, for different values of the parameter $α$. We find that the EMTVII solution predicts a positive tidal Love number for the whole range of allowed values of parameters $(\mathcal{C},α)$, in agreement with previous results for realistic NSs.

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