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

Abstract

Neutron stars are known to host extremely powerful magnetic fields. Among other 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. Such relations are quasi-universal, meaning that they are mostly independent on the equation of state of the neutron star and only slightly dependent on the magnetic field configuration. Being formulated 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 considering also the scalar charge. We show that even in this case general relations hold that account for deviations from general relativity, that could potentially be used to set constraints on the gravitational theory.

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

“…We found that c B , c H and c s are similar for all standard EoS (i.e. all EoS except SQM1, SQM2 and POL2) as functions of the Komar mass 57 . For this reason, we chose to consider the dependence also on another potentially observable quantity, namely the circumferential radius Rc , to understand whether the spread among the various EoS could be further reduced.…”

“…We focus only on the range of masses corresponding to stable configurations. All the results shown are computed using the XNS code 19,[55][56][57]66,80,82 , which solves the coupled equations for the metric, scalar field, and MHD structure of a NS under the assumptions of stationarity and axisymmetry, adopting conformal flatness and maximal slicing.…”

“…4 are found using a simple polytropic law which, while allowing us to compare our results to previous studies 16,19 , is not allowed by observations. For this reason, we further computed the distortion coefficients for a selection of EoS allowed by observational and nuclear physics constraints 57 . In particular, we selected 13 different EoS that span a diverse range of calculation methods and particle contents.…”

“…NSs), while it remains unconstrained in the weak-field limit. The presence of a scalar field leads to an enrichment of the physics of NSs, for example by causing the emission of additional modes of GWs 49,50 or by modifing the mass-radius relation of NSs, the binary NS merger dynamics 51 , the frequency of NS normal modes 52 , their tidal and rotational deformation 53,54 , their magnetic deformation [55][56][57] and the light propagation properties in their vicinity 58 . While massless STTs have been mostly ruled out by observations [59][60][61] , STTs with a massive scalar field are still viable [62][63][64] .…”

A precessing magnetar model for GLEAM-X J162759.5-523504.3

“…Given the presence of magnetars with low dipole magnetic fields (Rea et al 2010), it is possibly this strong toroidal field that makes a magnetar different from a rotationally powered pulsar. Magnetic stresses deform such a neutron star into a prolate spheroid (Ioka 2001;Cutler 2002;Ioka & Sasaki 2004;Haskell et al 2008;Mastrano et al 2011Mastrano et al , 2013Mastrano et al , 2015Frieben & Rezzolla 2012;Frederick et al 2021;Zamani & Bigdeli 2021;Soldateschi et al 2021) with asphericity…”