Magnetic field distribution in magnetars

Abstract

Using an axisymmetric numerical code, we perform an extensive study of the magnetic field configurations in non-rotating neutron stars, varying the mass, magnetic field strength and the equation of state. We find that the monopolar (spherically symmetric) part of the norm of the magnetic field can be described by a single profile, that we fit by a simple eighth-order polynomial, as a function of the star's radius. This new generic profile applies remarkably well to all magnetized neutron star configurations built on hadronic equations of state. We then apply this profile to build magnetized neutron stars in spherical symmetry, using a modified Tolman-Oppenheimer-Volkov (TOV) system of equations. This new formalism produces slightly better results in terms of massradius diagrams than previous attempts to add magnetic terms to these equations. However, we show that such approaches are less accurate than usual, non-magnetized TOV models, and that consistent models must depart from spherical symmetry. Thus, our "universal" magnetic field profile is intended to serve as a tool for nuclear physicists to obtain estimates of magnetic field inside neutron stars, as a function of radial depth, in order to deduce its influence on composition and related properties. It possesses the advantage of being based on magnetic field distributions from realistic self-consistent computations, which are solutions of Maxwell's equations.

Gravitational wave signatures of highly magnetized neutron stars

“…We comment next on our results and the validity of the chaotic magnetic field approximation in the light of a study published in Ref. [58] concerning the magnetic field distribution in magnetar interiors. Using a full relativistic numerical calculation, it was found that the magnetic field can be expressed as a multipolar expansion that accounts for the monopole contribution, the dipole term, the quadrupole and so on.…”

“…As pointed out in Ref. [58] in most cases, T θθ = T rr . However, exactly due to the monopole nature of the chaotic magnetic field, we always obtain T θθ = T rr , which guarantees that the TOV approximation can be used in this case.…”

“…3 of Ref. [58], the monopole term is dominant throughout almost the entire star. Moreover, the monopole term is specially dominant in the neutron star core, when the magnetic field is stronger.…”

Magnetic fields in compact stars and related phenomena

“…In these approaches, the magnetic field intensity might be either constant or depend on the star inner radius or its baryon density (see e.g. [74,78,79]). In most cases, this dependency is completely ad-hoc, only based on some physical constraints such as the intensity has to decrease from the center to the surface of the star, and reproduce some reasonable magnetic field values at these points [78].…”

“…The relevance of the anisotropic character of the energymomentum tensor has been questioned by some authors [94]. The main reason being the emergence, during the resolution of the coupled Einstein-Maxwell equations for the specific case of rotating stars, of a term related to Lorentz force that cancels with the magnetic pressure −M B in the magnetostatic equilibrium condition [79]. In this respect, we would like to remark that the presence of the term −M B in the transversal pressure is a microscopic result, independent from any macroscopic analysis.…”