Rotating Vector Model and Radius-to-frequency Mapping in the Presence of a Multipole Magnetic Field

Abstract The rotating vector model and radius-to-frequency mapping in the presence of a multipole magnetic field in pulsars and magnetars are considered. An axisymmetric potential field is assumed, and the following is found: (1) The radiation beam in the case of a multipole field is wider than the dipole case. This may account for the increasing pulse width at the higher frequency of pulsars (anti-radius-to-frequency mapping); (2) The expression for the polarization position angle is unchanged. Only the inclination angle α and phase constant ϕ 0 will change. The angle between the rotational axis and line of sight and the position angle constant ψ 0 will not change. When fitting the varying position angle of magnetars, these constraints should be considered. The appearance and disappearance of a multipole field may account for the changing slope of the position angle in the radio-emitting magnetar Swift J1818.0–1607. A similar but more active process in magnetar magnetospheres may account for the diverse position angle in fast radio bursts.