Modelling magnetohydrodynamic equilibrium in magnetars with applications to continuous gravitational wave production

Possessing the strongest magnetic fields in our Universe, magnetars mark an extremum of physical phenomena. The strength of their magnetic fields is sufficient to deform the shape of the stellar body, and when the rotational and magnetic axes are not aligned, these deformations lead to the production of gravitational waves (GWs) via a time-varying quadrupole moment. Such gravitational radiation differs from signals presently detectable by the Laser Interferometer Gravitational-Wave Observatory. These signals are continuous rather than the momentary 'chirp' waveforms produced by binary systems during the phases of inspiral, merger, and ringdown. Here, we construct a computational model for magnetar stellar structure with strong internal magnetic fields. We implement an n = 1 polytropic equation of state (EOS) and adopt a mixed poloidal and toroidal magnetic field model constrained by the choice of EOS. We utilize fiducial values for magnetar magnetic field strength and various stellar physical attributes. Via computational simulation, we measure the deformation of magnetar stellar structure to determine upper bounds on the strength of continuous GWs formed as a result of these deformations inducing non-axisymmetric rotation. We compute predictions of upper limit GW strain values for sources in the McGill Magnetar Catalog, an index of all detected magnetars.