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 (S1400) 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 S1400 ∝ 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 dispersionmeasure method and current ideas about the distribution of free electrons within our Galaxy.

Radio pulsar populations

“…Note that in the absence of prior knowledge about beaming, geometrical factors are usually ignored and the resulting 'pseudoluminosity' is quoted at some standard observing frequency; e.g., at 1400 MHz, L 1400 ≡ S 1400 d 2 . Recently, the validity of the inverse square law has been called into question by Singleton et al [1], and that perhaps the flux scales as 1/d instead. It is important to fully investigate this claim.…”

“…Because of the strong connection between distance and luminosity, any uncertainty in the pulsar distance scale propagates through to an uncertainty in the luminosity function [32]. Two critical questions concerning pulsar luminosities we wish to an-swer are: (1) what, if any, evolution in luminosity is there with pulsar age? ( 2) what is the shape of the luminosity function?…”

Do pulsar radio fluxes violate the inverse-square law?

“…2 Comparison of the convergence error ( ) as a funcof the distance exponent (n) normalized to its value at n = 2 using our application of the SWML algorithm with two different guesses for the initial luminosity function (Method 1 and 2) vs the same for S09 (data obtained from Fig. 2 of Singleton et al (2009)). The value of for n = 2 is approximately the same as n = 1 for Method 1 and about ten times larger in Method 2.…”

“…Like most other astrophysical phenomenon, it is implicitly assumed that the pulsar fluxes obey the inversesquare law. However, this ansatz has been recently challenged by Singleton et al (2009) (hereafter, S09). Their conclusions were based on computing the convergence of a maximum likelihood technique used to reconstruct the flux distribution (at 1400 MHz) of pulsars from the Parkes multi-beam survey.…”

“…

Singleton et al (2009) have argued that the flux of pulsars measured at 1400 MHz shows an apparent violation of the inverse-square law with distance (r), and instead the flux scales as 1/r. They deduced this from the fact that the convergence error obtained in reconstructing the luminosity function of pulsars using an iterative maximum likelihood procedure is about 10 5 times larger for a distance exponent of two (corresponding to the inverse-square law) compared to an exponent of one.

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