Fast Radio Bursts with Narrow Beaming Angles Can Escape from Magnetar Magnetospheres

Fast radio bursts (FRBs) are millisecond duration transients observed in the radio band, with their origin and radiation mechanism remaining unclear to date. Growing evidence indicates that at least some FRBs originate from magnetars and are likely generated within the magnetospheres of these highly magnetized neutron stars. However, a recent study suggested that FRBs originating from magnetar magnetospheres would be scattered by magnetospheric electron--positron pair plasma, making it impossible for them to escape successfully. In this paper, we first demonstrate that the scattering effect can be greatly attenuated if the angle between the FRB propagation direction and the background magnetic field is $\sim10^{-2} \text{ rad}$ or smaller. When the angle is around $10^{-1} \text{ rad}$, the beaming effect of FRBs becomes significant in reducing scattering. Such FRBs have small transverse spatial sizes, which can help them instantly push the front plasma laterally out of the radiation region. This significantly mitigates the FRB-induced two-photon annihilation reaction, $\gamma+\gamma\to e^{-}+e^{+}$, which was previously regarded as a key factor hindering the propagation of FRBs. A critical radiation cone half-opening angle between $10^{-3}-10^{-2}\text{ rad}$ is found for an FRB with isotropic luminosity $L_{\text{iso}}\sim 10^{42}\text{ erg s}^{-1}$ and emitted at a radius $r_{\text{em}}\lesssim 10^9\text{ cm}$ in the magnetosphere of a magnetar. Smaller beaming angles and larger emission radii can be more advantageous for the propagation of FRBs in magnetospheres. Our result supports the scenario that FRBs could originate from magnetar magnetospheres.