Inferring Binary Pulsar Population Statistics Using the NANOGrav 11 YearData Set

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) monitors a set of millisecond pulsars to search for the effects of gravitational waves on pulsar signals. The NANOGrav 11 Year Data Set offers a unique opportunity to explore the statistics of binary pulsar populations. Containing the timing solutions for 31 millisecond pulsars in binary orbits with white dwarf companions, this data set provides us with access to a large number of binary pulsars which have been observed with a unique level of consistency over multi-year time scales. We have used this data set to examine the binary pulsar orbital inclination angle distribution to see if the results are consistent with the standard assumption that the angles are uniformly distributed over the cosine of the inclination. This assumption could be violated if, for example, coupling between a pulsar's spin and its binary orbit causes preferential beaming in certain directions relative to the orbital plane. We will present multiple approaches and statistical tests that we have used to check this assumption. We will discuss our results for each when applied to the binary pulsars in the NANOGrav 11 Year Data Set. While only applied to orbital inclinations, the statistical analysis tools we develop are quite powerful and can be used to infer and test the population statistics of any of the parameters present in a pulsar's timing solution.