Three aspects of the radius-to-frequency mapping in fast radio bursts

Abstract: We further explored the radius-to-frequency mapping in cases of FRBs. An analytical treatment of Lyutikov (2020) is presented. The frequency dependence of the drifting rate and the drifting timescale are obtained. The aberration effect and the twist of the magnetic field lines may result in drifting in both directions. For one FRB, the burst width is larger at lower frequency according to the radius-to-frequency mapping. For the FRB population, the magnetic fields of the repeaters may be larger than that of the non-repeaters. Then, according to the radius-to-frequency mapping, the burst widths of the repeaters will be wider than that of the apparent non-repeaters. If similar window function (or emission cones) like that of pulsars and magnetars is also at work in the case of FRBs, then the window function may explain the single or multiple components of FRB profiles. The radius-to-frequency mapping modeling is to some degree independent of the underlying radio emission mechanism.