Quasi-universality of the magnetic deformation for neutron stars in general relativity and beyond

TL;DR

This study reveals quasi-universal relations linking magnetic deformation, mass, and radius of neutron stars across different equations of state and gravitational theories, aiding in understanding their internal magnetic properties and gravitational wave detectability.

Contribution

It introduces simple, nearly equation-of-state-independent relations for magnetic deformation in neutron stars within general relativity and scalar-tensor theories, including strange quark stars.

Findings

Relations are mostly independent of the equation of state.

Relations depend on scalar charge in scalar-tensor theories.

Potential to constrain gravity theories via neutron star observations.

Abstract

Neutron stars harbour extremely powerful magnetic fields, leading to their shape being deformed. Their magnetic deformation depends both on the geometry - and strength - of their internal magnetic field and on their composition, encoded by the equation of state. However, both the details of the internal magnetic structure and the equation of state of the innermost part of neutron stars are mostly unkown. We performed a study of numerical models of magnetised, static, axisymmetric neutron stars in general relativity and in one of its most promising extensions, scalar-tensor theories. We did so by using several realistic equations of state currently allowed by observational and nuclear physics constraints, considering also those for strange quark stars. We show that it is possible to find simple relations among the magnetic deformation of a neutron star, its Komar mass, and its circumferential radius in the case of purely poloidal and purely toroidal magnetic configurations satisfying the equilibrium criterion in the Bernoulli formalism. These relations are quasi-universal, in the sense that they mostly do not depend on the equation of state. Our results, being formulated in terms of potentially observable quantities, could help to understand the magnetic properties of neutron stars interiors and the detectability of continuous gravitational waves by isolated neutron stars, independently of their equation of state. In the case of scalar-tensor theories, these relations depend also on the scalar charge of the neutron stars, thus potentially providing a new way to set constraints on the theory of gravitation.