An Empirical Bayesian Approach Applied to the Globular Cluster Pulsar Population

• Activity Number: 135
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Consulting
• Author(s): Philip Turk*+ and Duncan Lorimer
• Companies: West Virginia University and West Virginia University
• Keywords: N-mixture model ; astrostatistics ; consulting ; empirical Bayesian ; globular clusters ; pulsars

Abstract

In this talk, we describe an empirical Bayesian approach to estimate the size of an astronomical population of sources of which only a small subset is observed above some limiting flux density threshold. The method is most naturally applied to astronomical source stellar populations at a common distance, even where a survey detects no objects. The model allows for the inclusion of physical parameters of the stellar population and the detection process. We apply this method to the current sample of radio pulsars in Galactic globular clusters. Using published flux density limits on surveys in 94 globular clusters, we examine a large number of models with different dependencies. We find that models which include the globular cluster two-body encounter rate are strongly selected for. The optimal model we fit agrees well with earlier published work and provides strong support to the idea that the two-body encounter rate directly impacts the number of neutron stars in a cluster. Our model predicts that the total number of potentially observable pulsars in all Galactic globular clusters, accounting for radio pulsar beaming, is 2280 (95\% CI: 790, 5000).