Title: Shear oscillations in neutron stars and the nuclear symmetry energy Show Chinese title

Title: 中子星中的剪切振荡与核对称能

Abstract: The shear and interface modes excited inside the neutron star due to the presence of elasticity depend on the properties of both the crust and core region. To examine how such eigenfrequencies depend on the neutron star properties, we solve the eigenvalue problem by adopting the relativistic Cowling approximation. Then, we confirm that the number of the interface modes excited in the star is generally equivalent to the number of the interface where the shear modulus discontinuously becomes zero, but we also find that the number of interface modes becomes smaller than that of the interface for the stellar model with lower or higher value of the slope parameter $L$. Furthermore, we derive the empirical relations for expressing the shear modes and one of the interface modes ($i_1$-mode in the text), which is the mode whose amplitude becomes dominant at the interface between the crust and envelopes and at the interface between the phases of slablike and cylindrical nuclei. At the end, we also show the possibility of identifying the higher QPO frequencies observed in GRB 200415A with the shear oscillations, as an alternative possibility instead of the torsional oscillations. Show Chinese abstract

Abstract: 由于存在弹性，中子星内部激发的剪切模态和界面模态取决于外壳和核心区域的性质。 为了研究这些本征频率如何依赖于中子星的性质，我们采用相对论性的Cowling近似来求解本征值问题。 然后，我们确认在恒星中激发的界面模态的数量通常与剪切模量不连续变为零的界面数量相当，但我们还发现，对于斜率参数 $L$ 值较低或较高的恒星模型，界面模态的数量小于界面的数量。 此外，我们推导了表达剪切模态和其中一个界面模态（文本中的 $i_1$-模态）的经验关系，该模态的振幅在壳层和包层之间的界面以及板状和柱状核相之间的界面处占主导地位。 最后，我们还展示了通过剪切振动识别GRB 200415A中观测到的较高QPO频率的可能性，作为扭转振动的替代可能性。