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

We study the rotational distortions of the vacuum dipole magnetic field in the context of geometric 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/R-1c, r is the radial distance, and R-1c is the light cylinder radius. To the lowest (i.e., second) order in r(n), this distortion is symmetric with respect to the plane containing the dipole axis and the rotation axis [(Omega, mu) plane]. The lowest order distortion that is asymmetric with respect to the (Omega, mu) plane is third-order in r(n). These results confirm the common assumption that the rotational sweepback has negligible effect on the position angle ( P. A.) curve. 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 backward with respect to the rotation direction by an angle delta(ov) similar to 0.2 sin alphar(n)(1/2), where alpha is the dipole inclination with respect to the rotation axis. The associated phase shift of the pulse profile Deltaphi(ov) similar to 0.2r(n)(1/2) can easily exceed the shift caused by combined effects of aberration and propagation time delays (approximate to2r(n)). This strongly affects the misalignment of the center of the P. A. 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) less than or similar to3 x 10(-3) the shift becomes negative; i.e., the center of the P. A. 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).