Constraining the selection corrected luminosity function and total pulse count for radio transients

TL;DR

This paper introduces LuNfit, a Bayesian algorithm that accurately estimates the intrinsic luminosity and nulling fractions of pulsar pulses, improving bias correction in radio transient studies.

Contribution

LuNfit is a novel Bayesian nested sampling algorithm that corrects selection biases and estimates pulsar pulse properties more reliably than traditional methods.

Findings

LuNfit accurately estimates nulling fractions for pulsars and RRATs.

A log-normal distribution fits the luminosity of some pulsars, while others favor an exponential model.

Traditional correction methods can be unreliable for faint sources.

Abstract

Studying transient phenomena, such as individual pulses from pulsars, has garnered considerable attention in the era of astronomical big data. Of specific interest to this study are Rotating Radio Transients (RRATs), nulling, and intermittent pulsars. This study introduces a new algorithm named LuNfit, tailored to correct the selection biases originating from the telescope and detection pipelines. Ultimately LuNfit estimates the intrinsic luminosity distribution and nulling fraction of the single pulses emitted by pulsars. LuNfit relies on Bayesian nested sampling so that the parameter space can be fully explored. Bayesian nested sampling also provides the additional benefit of simplifying model comparisons through the Bayes ratio. The robustness of LuNfit is shown through simulations and applying LuNfit onto pulsars with known nulling fractions. LuNfit is then applied to three RRATs, J0012+5431, J1538+1523, and J2355+1523, extracting their intrinsic luminosity distribution and burst rates. We find that their nulling fraction is 0.4(2), 0.749(5) and 0.995(2) respectively. We further find that a log-normal distribution likely describes the single pulse luminosity distribution of J0012+5431 and J1538+1523, while the Bayes ratio for J2355+1523 slightly favors an exponential distribution. We show the conventional method of correcting selection effects by "scaling up" the missed fraction of radio transients can be unreliable when the mean luminosity of the source is faint relative to the telescope sensitivity. Finally, we discuss the limitations of the current implementation of LuNfit while also delving into potential enhancements that would enable LuNfit to be applied to sources with complex pulse morphologies.