Beyond the Rotational Deathline: Radio Emission from Ultra-long Period Magnetars

Abstract: Motivated by the recent detection of ultra-long period radio transients, we investigate new models of coherent radio emission via low-altitude electron-positron pair production in neutron stars beyond rotationally-powered curvature radiation deathlines. We find that plastic motion (akin to 'continental drift') and qualitatively similar thermoelectric action by temperature gradients in the crusts of slowly rotating, highly magnetized neutron stars could impart mild local magnetospheric twists. Regardless of which mechanism drives twists, we find that particle acceleration initiates pair cascades across charge-starved gaps above a mild critical twist. Cascades are initiated via resonant inverse-Compton scattered photons or curvature radiation, and may produce broadband coherent radio emission. We compute the pair luminosity (maximum allowed radio luminosity) for these two channels, and derive deathlines and 'active zones' in $P-\dot{P}$ space from a variety of considerations. We find these twist-initiated pair cascades only occur for magnetar-like field strengths $B \gtrsim 10^{14}$ G and long periods: $P_{\rm RICS} \gtrsim 120 \; (T/10^{6.5} {\rm K})^{-5} \, {\rm sec}$ and $P_{\rm curv} \gtrsim 150 \; ({\rm v_{\rm pl}}/10^{3} {\, \rm cm \, yr^{-1}})^{-7/6} \, {\rm sec}$. Using a simplified geometric model, we find that plastic motion or thermoelectrically driven twists might naturally reproduce the observed luminosities, timescales, and timing signatures. We further derive 'active zones' in which rotationally-powered pair creation occurs via resonantly scattered photons, beyond standard curvature deathlines for pulsars. All cascades are generically accompanied by simultaneous (non-)thermal X-ray/UV counterparts which might be detectable with current instrumentation.