Torque lags from magnetic unlocking in neutron stars and gravitational-wave smearing

In canonical twisted-torus models of hydromagnetic equilibrium in neutron stars, the toroidal field is confined to regions where the poloidal field lines are closed. As spindown torques applied at the stellar surface need not be communicated efficiently to such magnetically unlocked regions, toroidal zones or magnetic voids can rotate faster than the electromagnetically braked part of the star. Continuous gravitational radiation from the associated non-corotating quadrupole can therefore be emitted at higher frequencies than poloidal ones to a degree that depends on the diffusive microphysics controlling angular momentum transport. Dissipative processes can suppress long-lived lags, and we estimate the relevant timescales and their sensitivity to microphysics. Nevertheless, we show that a quadrupole component whose pattern speed differs from the observed spin is shifted, or smeared, over a finite frequency band. Single-template or narrowband upper limits therefore constrain only the quadrupole contribution lying inside the searched frequency window, not necessarily the full frequency-integrated quadrupole. Using simple models, we quantify this spectral redistribution over finite observation windows and discuss its implications for continuous-wave searches.