磁化中子星中地壳破裂的弹性应变积累
Accumulation of elastic strain toward crustal fracture in magnetized neutron stars
摘要：
本研究探讨磁化中子星地壳中霍尔漂移驱动的弹性形变。虽然最初的动态平衡没有弹性位移，磁场的演变改变了长期的时间尺度上的洛伦兹力，这不可避免地导致弹性形变，以解决在一个新的力的平衡。因此，弹性能量积累，地壳最终破裂超过特定的阈值。我们假设磁场是轴对称的，我们明确地计算破裂时间，最大弹性能量存储在地壳中，和空间剪应力分布。对于正压平衡的极向偶极场驱逐出内部核心没有一个环向场，分裂时间对应于几年的磁星与磁场强度为$\sim 10^{15}$ G;然而，它超过1百万年的正常无线电磁星。破裂前储存在地壳中的弹性能量的范围从$10^{41}$到$10^{45}$ erg，取决于能量的空间分布。一般来说，大量的能量沉积在地壳深处。当弹性位移重排仅发生在脆弱的浅壳中时，破裂释放的能量通常为$\sim 10^{41}$ erg。能量的数量与磁星上的爆发能量相当。
英文摘要：
This study investigates elastic deformation driven by the Hall drift in a magnetized neutron-star crust. Although the dynamic equilibrium initially holds without elastic displacement, the magnetic-field evolution changes the Lorentz force over a secular timescale, which inevitably causes the elastic deformation to settle in a new force balance. Accordingly, elastic energy is accumulated, and the crust is eventually fractured beyond a particular threshold. We assume that the magnetic field is axially symmetric, and we explicitly calculate the breakup time, maximum elastic energy stored in the crust, and spatial shear-stress distribution. For the barotropic equilibrium of a poloidal dipole field expelled from the interior core without a toroidal field, the breakup time corresponds to a few years for the magnetars with a magnetic field strength of $\sim 10^{15}$G; however, it exceeds 1 Myr for normal radio pulsars. The elastic energy stored in the crust before the fracture ranges from $10^{41}$ to $10^{45}$ erg, depending on the spatial-energy distribution. Generally, a large amount of energy is deposited in a deep crust. The energy released at fracture is typically $\sim 10^{41}$ erg when the rearrangement of elastic displacements occurs only in the fragile shallow crust. The amount of energy is comparable to the outburst energy on the magnetars.
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