Magnetic Field and Neutron stars: A comprehensive study

Abstract

The extremely dense matter and frequently strong magnetic fields of neutron stars (NS’s) affect profoundly their observable manifestations, including thermal and magnetic evolution, rotation dynamics, and seismology. The ultra-strong magnetic fields present in some anomalous X-ray pulsars (AXP) and soft-gamma repeaters (SGR) (usually reffered to as magnetars) can be as high as 10 14 − 10 15 G on the surface. Simple estimates from the Virial theorem show that the mag- netic field at the core of a NS can be of few times 10 18 G. Such strong magnetic fields can play an effective role in determining the structure and the observable signatures of NS’s. Numerical calculations of such axisymmetric deformation of NS’s with poloidal and toroidal magnetic fields found deformations of the order of few ten of percent. On the other extreme, there are calcu- lations discussing the effect of the magnetic field on the equation of state (EoS) of the neutron stars. In most of these calculations, a density-dependent magnetic field profile with large central field strengths is assumed. In this work, a general 2D technique is employed, where the Einstein equations are solved by epanding the magnetic field and the perturbed metric in terms of spher- ical harmonics. The maximum deformation is seen to be of few percent which is in agreement with numerical calculations. When the rotation and magnetic axes are not aligned, higher or- der perturbation terms may contribute significantly, paving the way for strong gravitational wave (GW) signals. The possibility of vector rho-meson condensation in dense matter subject to strong magnetic fields is also briefly discussed in this manuscript.