Rotational sweepback of magnetic field lines in geometrical models of pulsar radio emission

TL;DR

This paper investigates how rotational distortions of the magnetic field in pulsars affect radio emission models, revealing that sweepback significantly influences pulse profiles and the delay-radius relation, especially at low emission altitudes.

Contribution

It provides a detailed analysis of the rotational sweepback effect on magnetic field lines and its impact on pulsar radio emission geometry, improving the understanding of pulse profile shifts.

Findings

Sweepback causes a backward shift of the open field line region.

Phase shift due to sweepback can exceed aberration and delay effects.

Including sweepback leads to larger estimated emission radii.

Abstract

We study the rotational distortions of the vacuum dipole magnetic field in the context of geometrical models of the radio emission from pulsars. We find that at low altitudes the rotation deflects the local direction of the magnetic field by at most an angle of the order of r_n^2, where r_n = r/Rlc, r is the radial distance of the radio emission and Rlc is the light cylinder radius. To the second order in r_n, this distortion is symmetrical with respect to the plane containing the dipole axis and the rotation axis (Omega-mu plane). The lowest order distortion which is asymmetrical with respect to the Omega-mu plane is third order in r_n. We show, however, that the influence of the sweepback on the outer boundary of the open field line region (open volume) is a much larger effect, of the order of r_n^1/2. The open volume is shifted backwards with respect to the rotation direction by an angle delta_ov ~ 0.2 sin(alpha) r_n^1/2 where alpha is the dipole inclination with respect to the rotation axis. The associated phase shift of the pulse profile Delta_phi_ov ~ 0.2 r_n^1/2 can easily exceed the shift due to combined effects of aberration and propagation time delays (=~ 2r_n). This strongly affects the misalignment of the center of the PA curve and the center of the pulse profile, thereby modifying the delay-radius relation. Contrary to intuition, the effect of sweepback dominates over other effects when emission occurs at low altitudes. For r_n <~ 0.003 the shift becomes negative, ie. the center of the position angle curve precedes the profile center. With the sweepback effect included, the modified delay-radius relation predicts larger emission radii and is in much better agreement with the other methods of determining r_n.