Universality of gravitational radiation from magnetar magnetospheres

The intense magnetic fields inferred from magnetars suggest they may be strong gravitational-wave emitters. Although emissions due to hydromagnetic deformations are more promising from a detection standpoint, exterior fields also contribute a strain. However, numerical evidence suggests that the free energy of stable magnetospheric solutions cannot exceed a few tens of percent relative to the potential state, implying that the magnetospheric contribution to the gravitational-wave luminosity cannot differ significantly between models. This prompts ``universality,'' in the sense that the strain provides a direct probe of the near-surface field without being muddied by magnetospheric currents. Using a suite of three-dimensional, force-free, general-relativistic solutions for dipole and dipole-plus-quadrupole fields, we find that space-based interferometers may enable marginal detections out to $\ensuremath{\lesssim}\mathrm{kpc}$ distances for slowly rotating magnetars with fields of $\ensuremath{\gtrsim}{10}^{15}\text{ }\text{ }\mathrm{G}$ independently of internal deformations.