Mechanism of generation of the emission bands in the dynamic spectrum of the Crab pulsar

TL;DR

This paper explains the emission bands in the Crab pulsar's spectrum as resulting from oscillations of a Bessel function linked to a superluminal polarization current, matching observed spectral features and broad spectrum data.

Contribution

It introduces a model based on superluminal polarization currents to quantitatively explain the emission bands and broadband spectrum of the Crab pulsar, connecting spectral features to oscillations of a Bessel function.

Findings

Emission bands fit Bessel function oscillations with superluminal current model

Parameter ratio $\,rac{ ext{oscillation frequency}}{ ext{rotation frequency}}$ matches observed spectral peaks

Broadband spectrum over 16 orders of magnitude is consistent with superluminal current emission

Abstract

We show that the proportionately spaced emission bands in the dynamic spectrum of the Crab pulsar (Hankins T. H. & Eilek J. A., 2007, ApJ, 670, 693) fit the oscillations of the square of a Bessel function whose argument exceeds its order. This function has already been encountered in the analysis of the emission from a polarization current with a superluminal distribution pattern: a current whose distribution pattern rotates (with an angular frequency $\omega$) and oscillates (with a frequency $\Omega>\omega$ differing from an integral multiple of $\omega$) at the same time (Ardavan H., Ardavan A. & Singleton J., 2003, J Opt Soc Am A, 20, 2137). Using the results of our earlier analysis, we find that the dependence on frequency of the spacing and width of the observed emission bands can be quantitatively accounted for by an appropriate choice of the value of the single free parameter $\Omega/\omega$. In addition, the value of this parameter, thus implied by Hankins & Eilek's data, places the last peak in the amplitude of the oscillating Bessel function in question at a frequency ($\sim\Omega^3/\omega^2$) that agrees with the position of the observed ultraviolet peak in the spectrum of the Crab pulsar. We also show how the suppression of the emission bands by the interference of the contributions from differring polarizations can account for the differences in the time and frequency signatures of the interpulse and the main pulse in the Crab pulsar. Finally, we put the emission bands in the context of the observed continuum spectrum of the Crab pulsar by fitting this broadband spectrum (over 16 orders of magnitude of frequency) with that generated by an electric current with a superluminally rotating distribution pattern.