Axisymmetric equilibrium models for magnetised neutron stars in scalar-tensor theories

Abstract

Among the possible extensions of general relativity that have been put forward to address some long-standing issues in our understanding of the Universe, scalar-tensor theories have received a lot of attention for their simplicity. Interestingly, some of these predict a potentially observable non-linear phenomenon, known as spontaneous scalarisation, in the presence of highly compact matter distributions, as in the case of neutron stars. Neutron stars are ideal laboratories for investigating the properties of matter under extreme conditions and, in particular, they are known to harbour the strongest magnetic fields in the Universe. Here, for the first time, we present a detailed study of magnetised neutron stars in scalar-tensor theories. First, we showed that the formalism developed for the study of magnetised neutron stars in general relativity, based on the “extended conformally flat condition”, can easily be extended in the presence of a non-minimally coupled scalar field, retaining many of its numerical advantages. We then carried out a study of the parameter space considering the two extreme geometries of purely toroidal and purely poloidal magnetic fields, varying both the strength of the magnetic field and the intensity of scalarisation. We compared our results with magnetised general-relativistic solutions and un-magnetised scalarised solutions, showing how the mutual interplay between magnetic and scalar fields affect the magnetic and the scalarisation properties of neutron stars. In particular, we focus our discussion on magnetic deformability, maximum mass, and range of scalarisation.

Detectability of Continuous Gravitational Waves from Magnetically Deformed Neutron Stars

“…where I xx , I zz are the moments of inertia of the NS computed with the Newtonian formula (see Appendix C of [64]), and the z axis is the symmetry axis of the system. It was shown that the Newtonian value of e is a good approximation for the correct GR one [67].…”

“…where B s is the surface magnetic field at the pole, in units of 10 18 G, and c s is called the 'distortion coefficient'. By computing ∼ 65,000 full GR, multi-dimensional axisymmetric magnetized equilibrium models of NSs with the XNS 1 code [31,64,68], adopting a variety of different EoS, we found that c s can be approximated with great accuracy by the following quasi-universal relation: c s = 2.97R 4.61 10 M −2.80…”

“…In this work, we apply our recent results [63][64][65] regarding a quasi-universal relation linking the NS mass, radius, magnetic deformation and surface magnetic field both to the case of the observed pulsar population as contained in the ATNF catalogue [66] and to a generic galactic sample simulated through a population synthesis approach. In particular, we assess the detectability of CGWs through the use of present and future GW detectors, showing that a significant fraction of the MSP population in the galaxy may be observable even with existing detectors when they reach their design sensitivity, while canonical pulsars seem to be beyond the reach of even third generation ones.…”

Magnetic deformation of neutron stars in scalar-tensor theories

“…We adopted a polytropic equation of state (EoS) p = K a ργ a , where p and ρ are the pressure and rest mass density of the fluid, respectively, with γ a = 2 and K a = 110 in dimensionless units. This has already been used by several authors (Bocquet et al 1995;Kiuchi & Yoshida 2008;Frieben & Rezzolla 2012;Pili et al 2014;Soldateschi et al 2020) as an approximation of more complex and physically motivated EoSs (Lattimer & Prakash 2007;Baym et al 2018), above nuclear densities. We chose to solve the metric and scalar field equations in the E-frame and the MHD equations in the J-frame, converting quantities from one frame to the other when needed.…”

“…Moreover, this is relevant to the study of how the presence of an additional channel for the emission of quadrupolar waves -that of "scalar waves" -affects the overall emission of quadrupolar GWs, establishing the extent to which the emission of scalar waves competes with the tensor one. In this paper, we build upon (Soldateschi et al 2020;hereafter SBD20), where we studied the general problem of axisymmetric models of NSs in STTs in the presence of spontaneous scalarisation to investigate the magnetic deformation of NSs in a class of STTs containing spontaneous scalarisation in light of GW emissions. In SBD20, we showed that the scalar field is expected to modify the magnetic deformation of NSs, but we investigated just a few select configurations for a single STT.…”