We describe two fitting schemes that aim to represent the high-density part of realistic equations of state for numerical simulations such as neutron star oscillations. The low-density part of the equation of state is represented by an arbitrary polytropic crust, and we propose a generic procedure to stitch any desired crust to the high-density fit, which is performed to ensure continuity of the internal energy, pressure, and sound speed for barotropic equations of state that describe cold neutron stars in $\beta$ equilibrium. An extension of the fitting schemes to equations of state with an additional compositional argument is proposed. In particular we develop a formalism that ensures the existence of a $\beta$ equilibrium at low densities. An additional feature of this low-density model is that it can be, in principle, applied to any parametrization. The performance of the fits is checked on mass, radius and tidal deformability as well as on the dynamical radial oscillation frequencies. To that end, we use a pseudospectral single neutron star evolution code based on a nonconservative form of the hydrodynamical equations. A comparison to existing parametrizations is proposed, as far as possible, and to published radial frequency values in the literature. The static and dynamic quantities are well reproduced by the fitting schemes. Our results suggest that, even though the radius is very sensitive to the choice of the crust, this choice has little influence on the oscillation frequencies of a neutron star.

中文翻译：

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用于中子星模拟的具有连续声速的一参数和二参数状态参数化方程

我们描述了两种拟合方案，旨在表示中子星振荡等数值模拟的现实状态方程的高密度部分。状态方程的低密度部分由任意多变地壳表示，我们提出了一种通用程序，将任何所需的地壳缝合到高密度拟合中，执行该程序是为了确保内能、压力和热能的连续性。描述冷中子星的正压状态方程的声速$\beta$平衡。提出了将拟合方案扩展到带有附加成分参数的状态方程。特别是，我们开发了一种形式主义，以确保$\beta$低密度下的平衡。这种低密度模型的另一个特点是原则上它可以应用于任何参数化。根据质量、半径和潮汐变形以及动态径向振荡频率检查拟合性能。为此，我们使用基于非保守形式的流体动力学方程的伪谱单中子星演化代码。建议尽可能与现有参数化以及文献中公布的径向频率值进行比较。拟合方案很好地再现了静态和动态量。我们的结果表明，尽管半径对地壳的选择非常敏感，但这种选择对中子星的振荡频率影响很小。