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 PsrPopPy software. We find that the E-P method cannot automatically reproduce the inverse-square scaling law for the radio pulsar flux, even though this scaling is built into the synthetic data by construction , 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 considerable 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 ± 1 σ depending on the chosen flux threshold. Therefore, the E-P method cannot be used to determine the correct scaling of radio pulsar flux with distance. Our results also demonstrate that the E-P method breaks down when the detection threshold scales non-linearly with flux along with scatter .