Rotational asymmetry of pulsar profiles

Abstract

We analyse the influence of rotation on shapes of pulse profiles of fast-rotating (millisecond) pulsars. Corotation has two opposing effects: 1) the caustic enhancement of the trailing side (TS) by aberration and retardation (AR), which squeezes the emission into a narrower phase interval; 2) the weakening of the TS caused by the asymmetry of curvature radiation about the dipole axis. Analysis of the radii of curvature of electron trajectories in the inertial observer's frame (IOF) enables these two effects to be considered together. We demonstrate that for dipolar magnetic field lines on the TS there exists a `caustic phase' beyond which no emission can be observed. This phase corresponds to the zero (or minimum) curvature of the IOF trajectories and maximum bunching of the emission. The maximum gradient of polarisation angle (PA) in the S-shaped PA curve is also associated with the curvature minimum and occurs at exactly the same phase. The asymmetry of trajectory curvature with respect to the dipole axis affects the curvature emissivity and the efficiency of pair production, suggesting a minimum at the caustic phase. Emission over a fixed range of altitudes, as expected in millisecond pulsars, leads to broad leading profiles and sharp peaks with a cutoff phase on the TS. We apply our results to the main pulse of the 5 ms pulsar J1012+5307.