Spectral properties of the nonspherically decaying radiation generated by a rotating superluminal source

TL;DR

This paper analyzes the spectral properties of nonspherically decaying radiation from a superluminally rotating source, revealing its decay behavior and potential relevance to pulsar giant pulses.

Contribution

It introduces an alternative asymptotic expansion to accurately describe the radiation field near the rotation axis, improving upon previous approximations.

Findings

The equatorial radiation field decays as the inverse square root of distance.

The decay rate with frequency is slower by a factor of mu^(2/3).

The spectral flux density follows a power-law with specific indices.

Abstract

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu^(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: it, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: the focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density proportional to mu^alpha) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.