Stably stratified magnetized stars in general relativity

Abstract

We construct magnetized stars composed of a fluid stably stratified by entropy gradients in the framework of general relativity, assuming ideal magnetohydrodynamics and employing a barotropic equation of state. We first revisit basic equations for describing stably-stratified stationary axisymmetric stars containing both poloidal and toroidal magnetic fields. As sample models, the magnetized stars considered by Ioka and Sasaki [23], inside which the magnetic fields are confined, are modified to the ones stably stratified. The magnetized stars newly constructed in this study are believed to be more stable than the existing relativistic models because they have both poloidal and toroidal magnetic fields with comparable strength, and magnetic buoyancy instabilities near the surface of the star, which can be stabilized by the stratification, are suppressed.

Equilibrium solutions of relativistic rotating stars with mixed poloidal and toroidal magnetic fields

“…1 In this paper, we present a formulation and numerical solutions for rapidly rotating relativistic stars with strong mixed poloidal and toroidal magnetic fields. Our solutions extend the above works [11][12][13][14] to highly deformed configurations as a result of rapid rotation and stronger magnetic fields, which can not be calculated from perturbative methods. We assume stationarity and axisymmetry of the gravitational, electromagnetic and matter fields, but we do not assume the spacetime to be circular, or spatially conformally flat.…”

“…Under the assumptions of stationarity and axisymmetry, however, one can find a set of integrability conditions and algebraic relations that the fluid variables must satisfy. Such a formulation for the system of relativistic ideal MHD equations is found in [10,11,13], and a fully covariant geometric formulation is derived in our previous work [15]. We rewrite the formulation in [10,11,13] as suited to our numerical method.…”

“…Such a formulation for the system of relativistic ideal MHD equations is found in [10,11,13], and a fully covariant geometric formulation is derived in our previous work [15]. We rewrite the formulation in [10,11,13] as suited to our numerical method. We introduce the basis, {t α , φ α , e α A }, associated with the coordinates t, φ and two other spatial coordinates x A , where t and φ are chosen along the symmetry vectors t α and φ α and normalized as t…”

“…Such noncircular spacetimes have been calculated in the slow rotation and weak magnetic field limit as in [11][12][13], and in the fully nonlinear regime for non-magnetized compact star with large meridional flow in [24]. A proposed formulation for computing non-circular spacetimes invokes a 2+1+1 spacetime decomposition [24,25].…”

“…In these computations, the spacetime is assumed to be orthogonally transitive (circular -invariant under a simultaneous inversion of t → −t, and φ → −φ), because the configuration of magnetic fields is restricted to either purely poloidal or toroidal fields and the velocity field is to circular [6][7][8][9] A relativistic formulation for more general magnetized relativistic stars with mixed poloidal and toroidal fields has been derived by Bekenstein and Oron [10]. The formulation has been used to obtain slowly rotating and weakly magnetized solutions [11,12], and has been improved for obtaining more stable solutions [13]. More recently, numerical solutions for mixed poloidal and toroidal fields have been obtained under a simplified relativistic gravity [14].…”