Transparency of Fast Radio Burst Waves in Magnetar Magnetospheres

At least some fast radio bursts (FRBs) are produced by magnetars. Even though mounting observational evidence points towards a magnetospheric origin of FRB emission, the question of the location for FRB generation continues to be debated. One argument suggested against the magnetospheric origin of bright FRBs is that the radio waves associated with an FRB may lose most of their energy before escaping the magnetosphere because the cross-section for $e^\pm$ to scatter large-amplitude EM waves in the presence of a strong magnetic field is much larger than the Thompson cross-section. We have investigated this suggestion and find that FRB radiation traveling through the open field line region of a magnetar's magnetosphere does not suffer much loss due to two previously ignored factors. First, the plasma in the outer magnetosphere ($r \gta 10^9 \ $cm), where the losses are potentially most severe, is likely to be flowing outward at a high Lorentz factor $\gamma_p \geq 10^3$. Second, the angle between the wave vector and the magnetic field vector, $\theta_B$, in the outer magnetosphere is likely of the order of 0.1 radian or smaller due in part to the intense FRB pulse that tilts open magnetic field lines so that they get aligned with the pulse propagation direction. Both these effects reduce the interaction between the FRB pulse and the plasma substantially. We find that a bright FRB with an isotropic luminosity $L_{\rm frb} \gta 10^{42} \ {\rm erg \ s^{-1}}$ can escape the magnetosphere unscathed for a large section of the $\gamma_p-\theta_B$ parameter space, and therefore conclude that the generation of FRBs in magnetar magnetosphere passes this test.