Pulsar radio emission height as a function of phase

TL;DR

This paper provides an analytical model for pulsar radio emission height as a quadratic function of phase and impact angle, linking geometry with emission mechanisms and observational data.

Contribution

It introduces a simplified analytical framework connecting pulsar emission height with phase and impact angle under dipole magnetic field assumptions.

Findings

Emission height varies quadratically with phase and impact angle.

Higher emission heights occur at the edges of the pulse profile.

The model allows estimation of particle Lorentz factors as a function of phase.

Abstract

We present an analytical treatment of the pulsar radio emission height as a function of phase based on a set of simplifying assumptions. Assuming a dipole field geometry, the emission height can be expressed as a function of phase and the impact angle. We found that: (1) The emission height is a quadratic function of the phase, given the magnetospheric geometry. The emission height is higher at the edge of the pulse profile than at the center. (2) The emission height is also a quadratic function of the impact angle. This point can be compared directly with the observations of the geodetic precessing pulsar PSR J1906+0746. (3) Larger inclination angle may imply a higher emission height, when other parameters are similar. (4) By assuming curvature radiation, or inverse Compton scattering, the Lorentz factor of the radio emitting particles can be obtained as a function of phase.