Trajectories and Radiation of Charged Particles in the Pulsar Magnetosphere

TL;DR

This paper models the trajectories and radiation of electrons in pulsar magnetospheres using Deutsch's solutions, revealing how pitch angles and spectral energy distributions depend on position and parameters, with implications for X-ray and gamma-ray emissions.

Contribution

It introduces a detailed model of electron trajectories considering radiation reaction forces and calculates synchro-curvature radiation spectra in pulsar magnetospheres.

Findings

Pitch angle varies with position and inclination angle.

Radius of curvature increases along particle trajectories.

Spectral energy distribution shows double peaks in X-ray and GeV bands.

Abstract

Trajectories and radiation of the accelerating electrons are studied in the pulsar magnetosphere approximated as the electromagnetic field of the Deutsch's solutions. Because the electrons are accelerated rapidly to ultra-relativistic velocity near the neutron star surface, the electron velocity vector (and then its trajectory) is derived from the balance between Lorentz force and radiation reaction force, which makes the pitch angle between electron trajectories and magnetic field lines nonzero in most part of the magnetosphere. In such a case, the spectral energy distributions (SEDs) of synchro-curvature radiation for the accelerating electrons with a mono-energetic form are calculated. Our results indicate that: (i) the pitch angle is the function of electron position ($r, \theta, \phi$) in the open field line regions, and increases with increasing $r$ and $\theta$ as well as increasing the inclination angle; (ii) the radius of curvature becomes large along the particle trajectory, and (iii) the SED appears a double peak structure depending on the emission position, where the synchrotron radiation plays an important role in X-ray band and curvature radiation mainly works in GeV band, which is only determined by parameters $\alpha$ and $\zeta$