Non-thermal emissions from outer magnetospheric accelerators of middle-aged pulsars

TL;DR

This study models gamma-ray emissions from the outer magnetospheric gaps of middle-aged pulsars, using electrodynamic and geometrical approaches to match observed spectra and pulse profiles, especially for the Geminga pulsar.

Contribution

It introduces a comprehensive two- and three-dimensional modeling framework for gamma-ray emissions from middle-aged pulsars' outer gaps, clarifying emission regions and pulse morphology.

Findings

Outer gap extends between last-open and critical magnetic field lines.

Spectrum above 10 MeV dominated by outward curvature radiation.

Model matches observed X-ray to gamma-ray spectra and suggests specific inclination and viewing angles.

Abstract

We discuss $\gamma$-ray emissions from the outer gap accelerators of middle-aged pulsars for part of the series of our studies. A two-dimensional electrodynamic model is used to solve the distribution of accelerating electric fields with electron and positron pair creation and radiation processes in the magnetic meridional plane. We compute the curvature radiation and the synchrotron radiation by solving the evolution of the Lorentz factor and the pitch angle. The calculated spectra are compared with observed phase-averaged spectra. We also use a three-dimensional geometrical model to discuss the pulse profiles. We argue that the outer gap of middle-aged pulsars occupies the whole region between the last-open field lines and the critical magnetic field lines, which are perpendicular to the rotational axis at the light cylinder. We assume that there is no outer gap accelerator inside the light cylinder between the rotational axis and the critical magnetic field lines. For the Geminga pulsar, we demonstrate that the outward curvature radiation dominates in the spectrum above 10 MeV, while the inward synchrotron radiation dominates below 10 MeV. We find that the computed spectrum is consistent with the observations in X-ray through $\gamma$-ray bands. With the pulse morphology of the $\gamma$-ray emissions, we argue that the inclination angle and the viewing angle for the Geminga pulsar are $\alpha\sim 50^{\circ}$ and $\xi\sim 90^{\circ}$, respectively.