Suppression of Magnetar Quadrupolar Deformation and Continuous‐Gravitational‐Wave Amplitude by Nonuniform Toroidal‐Field Topology

Magnetic stresses can deform magnetars and generate continuous gravitational waves when the deformation and rotation axes are misaligned. Predictions based solely on field strength may overestimate the signal because the quadrupolar response also depends on the internal field distribution. We use the published general‐relativistic, purely toroidal equilibrium sequence to examine the effect of the toroidal magnetization index . Increasing shifts the magnetic field toward the outer stellar layers. For the benchmark sequence with , the mean deformation magnitude decreases from at to at , giving a ratio of approximately . Under an explicit deformation‐to‐radiative‐ellipticity mapping, this ratio also applies to the continuous‐wave amplitude and idealized detection reach. Absolute amplitudes are treated as fiducial upper‐envelope estimates, while the deformation ratio comes directly from the equilibrium sequence. Purely toroidal configurations are likely unstable, and mixed poloidal–toroidal fields may produce smaller quadrupoles. Internal magnetic topology therefore introduces substantial uncertainty into continuous‐wave predictions.