Radius-to-frequency Mapping and FRB Frequency Drifts

Abstract

We build a model of radius-to-frequency mapping in magnetospheres of neutron stars and apply it to frequency drifts observed in Fast Radio Bursts. We assume that an emission patch propagates along the dipolar magnetic field lines producing coherent emission with frequency, direction and polarization defined by the local magnetic field. The observed temporal evolution of the frequency depends on relativistic effects of time contraction and the curvature of the magnetic field lines. The model generically produces linear scaling of the drift rate, $\dot{\omega} \propto - \omega$, matching both numerically and parametrically the rates observed in FBRs; a more complicated behavior of $\dot{\omega} $ is also possible. Fast rotating magnetospheres produce higher drifts rates for similar viewing parameters than the slowly rotating ones. In the case of repeaters same source may show variable drift pattens depending on the observing phase. We expect rotational of polarization position angle through a burst, though by smaller amount than in radio pulsars. All these findings compare favorably with properties of FBRs, strengthening their possible loci in the magnetospheres of neutron stars.