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

Abstract

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 2 n , where r n ¼ r=R lc , r is the radial distance, and R lc 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 [ 6; m ð Þplane]. The lowest order distortion that is asymmetric with respect to the (6; m) 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 1=2n . The open volume is shifted backward with respect to the rotation direction by an angle ov $ 0:2 sin r 1=2 n , where is the dipole inclination with respect to the rotation axis. The associated phase shift of the pulse profile Á ov $ 0:2r 1=2 n can easily exceed the shift caused by combined effects of aberration and propagation time delays (%2r 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 P 3 ; 10 À3 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 .

Pair Cascades and Deathlines in Magnetic Fields with Offset Polar Caps

“…Distortions of the dipole field could be intrinsic to the NS through asymmetries in the interior currents, present either from birth or as a result of spin-up or spin-down evolution. Distortion of the niagnetic field by rotation or magnetospheric currents also produce offsets of the PC [8] by as much as 20-30% of the PC radius and this should be taken into account in PC acceleration and pair cascades.…”

Accelerating High-Energy Pulsar Radiation Codes

“…There are at least two ways to decrease t A , and therefore maximize the impact of the proposed spectral approximation technique. In the case of very complicated magnetospheric structure, where the B-field and/or E-field have to be calculated numerically (and where the light cylinder and polar cap have to be found numerically; see, e.g., Dyks & Harding 2004), it may be wise to pre-calculate these fields for a range of (P ,Ṗ , χ), where P andṖ are the pulsar period and its time derivative, and save these results. Any recalculation of these fields are then unnecessary when performing a population study, as they may simply be read in from memory as required.…”

Magnetic Pair Creation Transparency in Gamma-Ray Pulsars

“…The computation here for the optical depth is first derived for the most general case of arbitrary emission colatitudes and altitudes in an oblique rotating neutron star, and then restricted to special cases where one can derive incisive analytic approximations. In these calculations, we consider only a rotating rigid dipole field and neglect effects near the pole caused by sweepback of field lines near the light cylinder (e.g., Dyks & Harding 2004). We will also neglect general relativity effects, which have already been explored extensively.…”