A Maximum-Likelihood Analysis of Observational Data on Fluxes and Distances of Radio Pulsars: Evidence for Violation of the Inverse-Square Law

Abstract

We analyze pulsar fluxes at 1400 MHz ($S_{1400}$) and distances ($d$) extracted from the Parkes Multibeam Survey. Under the assumption that distribution of pulsar luminosities is distance-independent, we find that either (a) pulsar fluxes diminish with distance according to a non-standard power law, due, we suggest, to the presence of a component with $S_{1400} \propto 1/d$, or (b) that there are very significant (i.e. order of magnitude) errors in the dispersion-measure method for estimating pulsar distances. The former conclusion (a) supports a model for pulsar emission that has also successfully explained the frequency spectrum of the Crab and 8 other pulsars over 16 orders of magnitude of frequency, whilst alternative (b) would necessitate a radical re-evaluation of both the dispersion-measure method and current ideas about the distribution of free electrons within our Galaxy.