Rotational Sweepback of Magnetic Field Lines in Geometric Models of Pulsar Radio Emission

Abstract

We study the rotational distortions of the vacuum dipole magneticfield in the context of geometric models of the radio emission frompulsars. We find that at low altitudes the rotation deflects the localdirection of the magnetic field by at most an angle of the order ofr2n, where rn=r/Rlc, r is the radialdistance, and Rlc is the light cylinder radius. To thelowest (i.e., second) order in rn, this distortion issymmetric with respect to the plane containing the dipole axis and therotation axis [(Omega,mu) plane]. The lowest order distortion that isasymmetric with respect to the (Omega,mu) plane is third-order inrn. These results confirm the common assumption that the rotationalsweepback has negligible effect on the position angle (P.A.) curve.We show, however, that the influence of the sweepback on the outerboundary of the open field line region (open volume) is a much largereffect, of the order of r1/2n. The open volume isshifted backward with respect to the rotation direction by an angledeltaov~0.2sinalphar1/2n, where alpha is the dipole inclination with respect tothe rotation axis. The associated phase shift of the pulse profileDeltaphiov~0.2r1/2n can easily exceed theshift caused by combined effects of aberration and propagation timedelays (~2rn). This strongly affects the misalignment ofthe center of the P.A. curve and the center of the pulse profile,thereby modifying the delay-radius relation. Contrary to intuition, theeffect of sweepback dominates over other effects when emission occursat low altitudes. For rn-3 the shiftbecomes negative; i.e., the center of the P.A. curve precedes theprofile center. With the sweepback effect included, the modifieddelay-radius relation predicts larger emission radii and is in much betteragreement with the other methods of determining rn.