Can the Efron-Petrosian Method Recover the Inverse-Square Distance Law for Simulated Radio Pulsar Fluxes?

Abstract

We test whether the Efron-Petrosian (E-P) method can recover the inverse-square law dependence of the radio pulsar flux, using a synthetic catalog generated according to the specifications of the Parkes multi-beam survey using the {\tt PsrPopPy} software. We find that the E-P method cannot reproduce the inverse-square law, except over a narrow range of flux thresholds and even here we don't get pristine agreement. The main reason for the deviation is that the synthetic radio pulsar catalog is truncated based on a cut on the pulsar signal to noise ratio (SNR), which has a non-linear dependence on the flux along with plenty of scatter. We show that the disagreement is exacerbated as we raise the SNR threshold. We then demonstrate that if we create a synthetic catalog based on a flux cut (instead of an SNR-based threshold), we can recover the true distance exponent, with an accuracy ranging from pristine agreement to within $\pm 1 \sigma$ depending on the chosen flux threshold.