Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars

TL;DR

This paper investigates how radiative back-reaction affects the motion of charged particles in a neutron star's dipole magnetosphere, revealing effects like orbit widening and particle infall depending on the Lorentz force's nature.

Contribution

It provides a detailed analysis of conservative circular orbits and incorporates the Landau-Lifshitz equation to examine radiative back-reaction effects on particle dynamics in curved spacetime.

Findings

Back-reaction causes particles to fall onto the neutron star surface under attractive Lorentz force.

For repulsive Lorentz force, stable orbit regions widen and shift toward the equatorial plane.

Critical latitude determines whether orbits widen or lead to surface infall.

Abstract

The motion of charged particles under the Lorentz force in the magnetosphere of neutron stars, represented by a dipole field in the Schwarzschild spacetime, can be determined by an effective potential, whose local extrema govern circular orbits both in and off the equatorial plane, which coincides with the symmetry plane of the dipole field. In this work, we provide a detailed description of the properties of these "conservative" circular orbits and, using the approximation represented by the Landau-Lifshitz equation, examine the role of the radiative back-reaction force that influences the motion of charged particles following both the in and off equatorial circular orbits, as well as the chaotic orbits confined to belts centered around the circular orbits. To provide clear insight into these dynamics, we compare particle motion with and without the back-reaction force. We demonstrate that, in the case of an attractive Lorentz force, the back-reaction leads to the charged particles falling onto the neutron star's surface in all scenarios considered. For the repulsive Lorentz force, in combination with the back-reaction force, we observe a widening of stable equatorial circular orbits; the off-equatorial orbits shift toward the equatorial plane and subsequently widen if they are sufficiently close to the plane. Otherwise, the off-equatorial orbits evolve toward the neutron star surface. The critical latitude, which separates orbital widening from falling onto the surface, is determined numerically as a function of the electromagnetic interaction's intensity.