Compact formulae, dynamics and radiation of charged particles under synchro-curvature losses

TL;DR

This paper revises and simplifies the formulas for synchro-curvature radiation, analyzes particle dynamics under these conditions, and explores how different parameters influence the emitted spectrum in astrophysical contexts.

Contribution

It introduces more compact expressions for synchro-curvature radiation and provides a self-consistent numerical solution for particle motion and spectrum in pulsar magnetospheres.

Findings

The key parameter controlling the transition between curvature and synchrotron regimes.

Spectrum slope depends on emission region location and size.

Pure synchrotron or curvature losses are often insufficient to describe radiation.

Abstract

We consider the fundamental problem of charged particles moving along and around a curved magnetic field line, revising the synchro-curvature radiation formulae introduced by Cheng and Zhang (1996). We provide more compact expressions to evaluate the spectrum emitted by a single particle, identifying the key parameter that controls the transition between the curvature-dominated and the synchrotron-dominated regime. This parameter depends on the local radius of curvature of the magnetic field line, the gyration radius, and the pitch angle. We numerically solve the equations of motion for the emitting particle by considering self-consistently the radiative losses, and provide the radiated spectrum produced by a particle when an electric acceleration is balanced by its radiative losses, as it is assumed to happen in the outer gaps of pulsar's magnetospheres. We compute the average spectrum radiated throughout the particle trajectory finding that the slope of the spectrum before the peak depends on the location and size of the emission region. We show how this effect could then lead to a variety of synchro-curvature spectra. Our results reinforce the idea that the purely synchrotron or curvature losses are, in general, inadequate to describe the radiative reaction on the particle motion, and the spectrum of emitted photons. Finally, we discuss the applicability of these calculations to different astrophysical scenarios.