Pulsar current revisited

TL;DR

This paper critically examines the use of the pulsar current in the $P$--$ {ar P}$ plane to estimate pulsar birthrates, revealing its model dependence and proposing an alternative approach that avoids pseudo source terms.

Contribution

It revisits the derivation of the pulsar current, highlighting its sensitivity to the assumed pulsar evolution law, and introduces a potential law framework that circumvents pseudo source complications.

Findings

The pulsar current interpretation depends on the assumed evolution law.

Pseudo source terms are necessary for certain evolution models to estimate birthrates.

Potential law models eliminate the pseudo source issue, providing a more robust birthrate estimate.

Abstract

The pulsar current, in the $P$--$ {\dot P}$ plane where $P$ is the pulsar period and ${\dot P}$ is the period derivative, is used as a supposedly ``model free'' way to estimate the pulsar birthrate from statistical data on pulsars. We reconsider the derivation of the kinetic equation on which this is based, and argue that the interpretation of the pulsar current is strongly model dependent, being sensitive to the form of the assumed evolution law for pulsars. We discuss the case where the trajectory of a pulsar is assumed to be of the form ${\dot P}=KP^{2-n}$ with $K$ and $n$ constant, and show that (except for $n=2$) one needs to introduce a pseudo source term in order to infer the birthrate from the pulsar current. We illustrate the effect of this pseudo source term using pulsar data to estimate the birthrate for different choices of $n$. We define and discuss an alternative ``potential'' class of evolution laws for which this complication is avoided due to the pseudo source term being identically zero.