Quadrupole Moment of a Magnetically Confined Mountain on an Accreting Neutron Star in General Relativity

Abstract

General relativistic corrections are calculated for the quadrupole moment of a magnetically confined mountain on an accreting neutron star. The hydromagnetic structure of the mountain satisfies the general relativistic Grad-Shafranov equation supplemented by the flux-freezing condition of ideal magnetohydrodynamics, as in previous calculations of the magnetic dipole moment. It is found that the ellipticity and hence the gravitational wave strain are up to $12\%$ greater than in the analogous Newtonian system. The direct contribution of the magnetic field to the nonaxisymmetric component of the stress-energy tensor is shown to be negligible in accreting systems such as low-mass X-ray binaries.