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

Authors: R. O. Gomes; H. Pais; V. Dexheimer; C. Providência; S. Schramm

Ref.: Astronomy & Astrophysics Journal 627, A61 (2019)

Abstract: Aims. In this work, we study the structure of neutron stars under the effect of a poloidal magnetic field and determine the limiting largest magnetic field strength that induces a deformation such that the ratio between the polar and equatorial radii does not exceed 2%. We consider that, under these conditions, the description of magnetic neutron stars in the spherical symmetry regime is still satisfactory. Methods. We describe different compositions of stars (nucleonic, hyperonic, and hybrid), using three state-of-the-art relativistic mean field models (NL3ωρ, MBF, and CMF, respectively) for the microscopic description of matter, all in agreement with standard experimental and observational data. The structure of stars is described by the general relativistic solution of both Einstein’s field equations assuming spherical symmetry and Einstein-Maxwell’s field equations assuming an axi-symmetric deformation. Results. 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 $10^{17}$ G at the centre of the star, above which the deformation due to the magnetic field is above 2%, therefore, 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.