标题： 多晶中子星地壳剪切模量的约束：Hashin-Shtrikman变分方法 显示英文标题

标题： Constraining shear modulus of polycrystalline neutron star crust: Hashin-Shtrikman variational approach

摘要： 中子星外壳的弹性性质被认为在中子星的各种现象（如突然跃变、振荡、引力波辐射）中起着关键作用，应该进行定量描述以模拟这些现象。 这种描述的基本问题是与外壳的多晶体性质有关：类似于地球上的材料，严格来说，弹性模量取决于晶体颗粒的形状和取向，但对于外壳，这些值是未知的。 因此，通常需要一些假设来预测弹性性质或限制其可能的范围。 在本文中，我们遵循普遍接受的假设，即外壳是（局部）各向同性的，这使我们能够通过两个（有效）参数——体积模量和剪切模量来描述弹性性质。 体积模量由 Voigt-Reuss 界确定，我们通过应用变分 Hashin-Shtrikman 方法来限制剪切模量，这是在致密星体天体物理中首次应用该方法，基于额外的假设，即晶体颗粒的取向之间没有相关性。 我们分析了考虑电子屏蔽和核运动的一组分外壳的 Hashin-Shtrikman 界，以及两组分静态晶体的情况。 特别是，我们证明在所应用的假设下，有效剪切模量应低于通常在天体物理文献中应用的 Voigt 估计值。 显示英文摘要

摘要： The elastic properties of the neutron star crust are thought to play a crucial role in various phenomena of neutron stars (glitches, oscillations, gravitational wave emission) and should be described quantitatively to model these phenomena. The fundamental problem of this description is associated with the polycrystalline nature of the crust: similar to terrestrial materials, the elastic moduli, strictly speaking, depend on the shape and orientation of crystallites, but for the crust, they are unknown. As a result, some assumptions are generally required to predict the elastic properties or constrain their possible range. In this paper, we follow the commonly believed assumption that the crust is (locally) isotropic, which allows us to describe elastic properties by two (effective) parameters: bulk and shear moduli. The bulk modulus is well determined by the Voigt-Reuss bounds, and we constrain the shear modulus by applying, for the first time in astrophysics of compact stars, the variational Hashin-Shtrikman approach, based on the additional assumption that there are no correlations in the orientation of crystallites. We analyse the Hashin-Shtrikman bounds for the one-component crust taking into account the electron screening and the motion of the nuclei, and for two-component static crystals. In particular, we demonstrate that within applied assumptions the effective shear modulus should be lower than the Voigt estimate, typically applied in the astrophysical literature.