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

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 $147_{-65}^{+112}$, $83_{-35}^{+54}$ and $100_{-52}^{+91}$, 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.

9 pages, 4 figures, Accepted for publication in MNRAS

References in corpus (17)

• A Radio Pulsar Spinning at 716 Hz
• Birth and Evolution of Isolated Radio Pulsars
• A Radio Pulsar/X-ray Binary Link
• Internal Dynamics of Globular Clusters
• The characteristics of millisecond pulsar emission: I. Spectra, pulse shapes and the beaming fraction
• Twenty-One Millisecond Pulsars in Terzan 5 Using the Green Bank Telescope
• Observations of 20 millisecond pulsars in 47 Tucanae at 20 cm
• Chandra Study of a Complete Sample of Millisecond Pulsars in 47Tuc and NGC6397
• A 1.4-GHz Arecibo Survey for Pulsars in Globular Clusters
• Distances of the bulge globular clusters Terzan 5, Liller 1, UKS 1 and Terzan 4 based on HST NICMOS photometry
• Young Radio Pulsars in Galactic Globular Clusters
• Luminosities of recycled radio pulsars in globular clusters
• The Spectral Energy Distributions of White Dwarfs in 47 Tucanae: The Distance to the Cluster
• Deep Radio Imaging of Globular Clusters and the Cluster Pulsar Population
• Neutron star atmosphere composition: the quiescent, low-mass X-ray binary in the globular cluster M28
• Isolated pulsar spin evolution on the P-Pdot Diagram
• The radio luminosity distribution of pulsars in 47 Tucanae

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