Jayanth Chennamangalam, D. R. Lorimer, Ilya Mandel, Manjari Bagchi
Studies of the Galactic population of radio pulsars have shown that their luminosity distribution appears to be lognormal 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 95.45% credible intervals of $133^{+101}_{-58}$, $66^{+55}_{-31}$ and $109^{+125}_{-63}$, respectively. Beaming considerations would increase the true population size by approximately a factor of two. Future cluster pulsar discoveries would allow this method to be used to compare the luminosity function between different clusters.
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http://arxiv.org/abs/1207.5732
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