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

Neutron stars are known to host extremely powerful magnetic fields. Among its effects, one of the consequences of harbouring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves. On the one hand, the details of their internal magnetic fields are mostly unknown. Likewise, their internal structure, encoded by the equation of state, is highly uncertain. Here, we present a study of axisymmetric models of isolated magnetised neutron stars for various realistic equations of state considered viable by observations and nuclear physics constraints. We show that it is possible to find simple relations between 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 that satisfy the criterion for equilibrium in the Bernoulli formalism. Such relations are quasi-universal, meaning that they are mostly independent from the equation of state of the neutron star. Thanks to their formulation in terms of potentially observable quantities, as we discuss, our results could help to constrain the magnetic properties of the neutron star interior and to better assess the detectability of continuous gravitational waves by isolated neutron stars, without knowing their equation of state. Our results are derived both in general relativity and in scalar-tensor theories (one of the most promising extensions of general relativity), in this case by also considering the scalar charge. We show that even in this case, general relations that account for deviations from general relativity still hold, which could potentially be used to set constraints on the gravitational theory.