Constraining the luminosity function parameters and population size of radio pulsars in globular clusters

TL;DR

This study uses Bayesian methods to constrain the luminosity function parameters and estimate the total population of radio pulsars in globular clusters, based on observed data and flux measurements.

Contribution

It introduces a Bayesian framework for estimating pulsar luminosity function parameters and population sizes in globular clusters, incorporating flux density data and diffuse emission.

Findings

Estimated pulsar populations: Terzan 5 (~147), 47 Tucanae (~83), M 28 (~100).

Population size estimates could double when considering beaming effects.

Constraints are limited with current data but will improve with future measurements.

Abstract

Studies of the Galactic population of radio pulsars have shown that their luminosity distribution appears to be log-normal in form. We investigate some of the consequences that occur when one applies this functional form to populations of pulsars in globular clusters. We use Bayesian methods to explore constraints on the mean and standard deviation of the luminosity function, as well as the total number of pulsars, given an observed sample of pulsars down to some limiting flux density, accounting for measurements of flux densities of individual pulsars as well as diffuse emission from the direction of the cluster. We apply our analysis to Terzan 5, 47 Tucanae and M 28, and demonstrate, under reasonable assumptions, that the number of potentially observable pulsars should be within 95% credible intervals of $147^{+112}_{-65}$, $83^{+54}_{-35}$ and $100^{+91}_{-52}$, respectively. Beaming considerations would increase the true population size by approximately a factor of two. Using non-informative priors, however, the constraints are not tight due to the paucity and quality of flux density measurements. Future cluster pulsar discoveries and improved flux density measurements would allow this method to be used to more accurately constrain the luminosity function, and to compare the luminosity function between different clusters.