# Limiting magnetic field for minimal deformation of a magnetised neutron star

## TL;DR

This paper investigates the maximum magnetic field strength neutron stars can sustain without significant deformation, considering various compositions and equations of state, and discusses implications for their internal structure and observable phenomena.

## Contribution

It determines the limiting magnetic field for neutron stars with different compositions using relativistic models, highlighting the impact on star deformation and internal composition.

## Key findings

- Maximum magnetic field of ~10^{16} G at surface and ~10^{17} G at core.
- Deformation becomes significant above a magnetic moment of 2×10^{31} Am^2.
- Strong magnetic fields disfavor the presence of exotic matter like hyperons or quark cores.

## Abstract

In this work we study the structure of neutron stars under the effect of a poloidal magnetic field and determine the limiting highest magnetic field intensity which still allows a satisfactory description of magnetic neutron stars in the spherical symmetry regime. We describe different compositions of stars (nucleonic, hyperonic, and hybrid), using three state-of-the-art relativistic mean field models for the microscopic description of matter, which are in agreement with experimental and observational data. The structure of stars is described by the general relativistic solution of both Einstein's field equations assuming a spherical symmetry, and Einstein-Maxwell's field equations assuming an axi-symmetric deformation. We find a limiting magnetic moment of the order of $2\times 10^{31}$Am$^2$, which corresponds to magnetic fields of the order of 10$^{16}$ G at the surface, and $ \sim 10^{17}$ G at the centre of the star, above which the deformation due to the magnetic field is not negligible. We show that the intensity of the magnetic field developed in the star depends on the EoS, and, for a given baryonic mass and fixed magnetic moment, larger fields are attained with softer EoS. We also show that the appearance of exotic degrees of freedom, such as hyperons or a quark core, is disfavored in the presence of a very strong magnetic field. As a consequence, a highly magnetized nucleonic star may suffer an internal conversion due to the decay of the magnetic field, which could be accompanied by a sudden cooling of the star or a gamma ray burst.