Neutron star crust in Voigt approximation: general symmetry of the stress–strain tensor and an universal estimate for the effective shear modulus
Neutron star crust in Voigt approximation: general symmetry of the stress–strain tensor and an universal estimate for the effective shear modulus
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Voigt 近似中的中子星地壳：应力应变张量的一般对称性和有效剪切模量的通用估计
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发表时间：
2020
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通讯作者：
A. Chugunov
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作者：
A. Chugunov
在静态库仑实体模型的框架下讨论了当原子核被视为非振动点电荷时中子星地壳的弹性特性；电子筛选被忽视。结果也适用于凝固的白矮星核心和其他材料，可以将其建模为库仑固体（尘埃等离子体、捕获离子等）。我证明应力应变张量的库仑部分具有额外的对称性：收缩 Bijil = 0。它不依赖于结构（结晶或非晶）和成分。我表明，由于这种对称性，多晶或无定形物质的有效（沃伊特平均）剪切模量等于未变形状态下库仑（马德隆）能量密度的-2/15。该结果在所应用的模型内是普遍且精确的。由于使用了线性混合规则和离子球模型，我可以建议对有效剪切模量进行简单的通用估计：$sum _Z 0.12, n_Z Z^{5/3}e^2 /a_mathrm{e}$。这里对离子种类进行求和，nZ 是带电荷 Ze 的离子的数密度。最后，ae = (4πne/3)−1/3 是电子球半径。假设准中性条件 ne = ΣZZnZ。
I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modelled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress–strain tensor has additional symmetry: contraction Bijil = 0. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to −2/15 of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $sum _Z 0.12, n_Z Z^{5/3}e^2 /a_mathrm{e}$. Here summation is taken over ion species, nZ is number density of ions with charge Ze. Finally, ae = (4πne/3)−1/3 is electron sphere radius. Quasi-neutrality condition ne = ∑ZZnZ is assumed.