In this study, we develop an analytic treatment, which would allow us to model magnetic deformation of neutron stars in the quasi-Newtonian framework. We assume non-magnetic, spherical relativistic stars as backgrounds and regard the magnetic fields as the perturbation. We analyze the problem by taking density profiles from various analytic approaches. The first density profile is the n = 1 solution of the Lane-Emden equation, the second one is a parabolic ansatz for density and the last density distribution is a fourth-order polynomial with a free parameter fit to a relativistic solution obtained from a microphysical equation of state (EoS). In this article, the EoS of neutron matter is obtained from the lowest order constraint variational (LOCV) method. Furthermore, both purely poloidal and purely toroidal magnetic field configurations are obtained by solving the Euler's magnetohydrodynamic equations. We almost incorporate all the magnetic field configurations assessed from different density profiles. In order to study the structure of the neutron stars, the magnetic pressure, and density should be treated as perturbations of non-magnetized stars. We find out that the stellar shape is prolate for positive distortion (purely toroidal magnetic field) and oblate for negative distortion (purely poloidal magnetic field). The magnetic effect on the gravitational mass is also explained.

中文翻译：

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磁变形中子星的解析处理

在这项研究中，我们开发了一种解析处理，这将使我们能够模拟准牛顿框架中中子星的磁变形。我们假设非磁性的球形相对论恒星作为背景，并将磁场视为扰动。我们通过从各种分析方法中获取密度分布来分析问题。第一个密度分布是 Lane-Emden 方程的 n = 1 解，第二个是密度的抛物线 ansatz，最后一个密度分布是四阶多项式，其自由参数拟合从微物理中获得的相对论解状态方程 (EoS)。在本文中，中子物质的 EoS 是通过最低阶约束变分 (LOCV) 方法获得的。此外，纯极向和纯环向磁场配置都是通过求解欧拉磁流体动力学方程获得的。我们几乎结合了从不同密度分布评估的所有磁场配置。为了研究中子星的结构，磁压和密度应该被视为非磁化星的扰动。我们发现恒星的形状对于正畸变（纯环向磁场）是扁长的，对于负畸变（纯极向磁场）是扁圆的。还解释了对引力质量的磁效应。磁压和密度应被视为非磁化恒星的扰动。我们发现恒星的形状对于正畸变（纯环向磁场）是扁长的，对于负畸变（纯极向磁场）是扁圆的。还解释了对引力质量的磁效应。磁压和密度应被视为非磁化恒星的扰动。我们发现恒星的形状对于正畸变（纯环向磁场）是扁长的，对于负畸变（纯极向磁场）是扁圆的。还解释了对引力质量的磁效应。