Synchrotron X-ray emission from old pulsars

TL;DR

This paper investigates the origin of non-thermal X-ray emission in old pulsars through synchrotron radiation, analyzing particle acceleration mechanisms and pair production processes in their magnetospheres.

Contribution

It provides an analytical model linking pulsar spin-down luminosity to the location of particle acceleration and X-ray emission, considering magnetic and photon-photon pair production mechanisms.

Findings

For pulsars with L_sd ≲ 10^33 erg/s, acceleration occurs within 10^7 cm of the neutron star.

Synchrotron radiation explains non-thermal X-ray components in pulsars with higher luminosities.

For very low luminosity pulsars like J0108-1431, synchrotron emission struggles to account for observed X-ray features.

Abstract

We study the synchrotron radiation as the observed non-thermal X-ray emission from old pulsars ($\gtrsim1-10$Myr) to investigate the particle acceleration in their magnetospheres. We assume that the power-law component of the observed X-ray spectra is caused by the synchrotron radiation from electrons and positrons in the magnetosphere. We consider two pair production mechanisms of X-ray emitting particles, the magnetic and the photon-photon pair productions. High-energy photons, which ignite the pair production, are emitted via the curvature radiation of the accelerated particles. We use the analytical description for the radiative transfer and estimate the luminosity of the synchrotron radiation. We find that for pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{33}$ erg s$^{-1}$, the locations of the particle acceleration and the non-thermal X-ray emission are within $\lesssim10^7$cm from the centre of the neutron star, where the magnetic pair production occurs. For pulsars with the spin-down luminosity $L_{\rm sd}\lesssim10^{31}$ erg s$^{-1}$ such as J0108-1431, the synchrotron radiation is difficult to explain the observed non-thermal component even if we consider the existence of the strong and small-scale surface magnetic field structures.