# Efficiency of Synchrotron Radiation from Rotation-Powered Pulsars

## TL;DR

This paper models synchrotron radiation in pulsar magnetospheres to estimate energy conversion efficiency and explains observed non-thermal emissions, highlighting the importance of magnetic field components and multiple accelerators.

## Contribution

It provides an analytical model linking synchrotron luminosity to energy conversion efficiency and compares it with observations to constrain pulsar emission mechanisms.

## Key findings

- Energy conversion efficiency is near unity in the magnetosphere.
- Non-dipole magnetic fields are needed for low luminosity pulsars.
- Multiple accelerators may coexist in the magnetosphere.

## Abstract

Synchrotron radiation is widely considered as the origin of the pulsed non-thermal emissions from rotation-powered pulsars in optical and X-ray bands. In this paper, we study the synchrotron radiation emitted by the created electron and positron pairs in the pulsar magnetosphere to constrain on the energy conversion efficiency from the Poynting flux to the particle energy flux. We model two pair creation processes, two-photon collision which efficiently works in young $\gamma$-ray pulsars ($\lesssim10^6$ yr), and magnetic pair creation which is the dominant process to supply pairs in old pulsars ($\gtrsim10^6$ yr). Using the analytical model, we derive the maximum synchrotron luminosity as a function of the energy conversion efficiency. From the comparison with observations, we find that the energy conversion efficiency to the accelerated particles should be an order of unity in the magnetosphere, even though we make a number of the optimistic assumptions to enlarge the synchrotron luminosity. In order to explain the luminosity of the non-thermal X-ray/optical emission from pulsars with low spin-down luminosity $L_{\rm sd}\lesssim10^{34}$ erg s$^{-1}$, non-dipole magnetic field components should be dominant at the emission region. For the $\gamma$-ray pulsars with $L_{\rm sd}\lesssim10^{35}$ erg s$^{-1}$, observed $\gamma$-ray to X-ray and optical flux ratios are much higher than the flux ratio between curvature and the synchrotron radiations. We discuss some possibilities such as the coexistence of multiple accelerators in the magnetosphere as suggested from the recent numerical simulation results. The obtained maximum luminosity would be useful to select observational targets in X-ray and optical bands.