On the very high energy spectrum of the Crab pulsar

TL;DR

This paper develops a self-consistent theoretical model explaining the simultaneous generation of radio and very high energy gamma-ray emissions from the Crab pulsar's magnetosphere, aligning well with observational data.

Contribution

It introduces a novel application of quasi-linear diffusion via cyclotron instability to explain VHE emission in pulsars, providing specific spectral predictions.

Findings

Spectral index of VHE emission is 2.

Exponential cutoff energy is 23 GeV.

Model matches MAGIC telescope observations.

Abstract

In the present paper we construct a self-consistent theory, interpreting the observations of the MAGIC Cherenkov Telescope of the very high energy (VHE) pulsed emission from the Crab pulsar. In particular, on the basis of the Vlasov's kinetic equation we study the process of the quasi-linear diffusion(QLD) developed by means of the cyclotron instability. This mechanism provides simultaneous generation of low (radio) and VHE (0.01-25GeV) emission on the light cylinder scales, in one location of the pulsar magnetosphere. A different approach of the synchrotron theory is considered, giving the spectral index of VHE emission ($\beta=2$) and the exponential cutoff energy (23 GeV) in a good agreement with the observational data.