Astrophysical Model Selection in Gravitational Wave Astronomy

Theoretical studies in gravitational wave astronomy have mostly focused on the information that can be extracted from individual detections, such as the mass of a binary system and its location in space. Here we consider how the information from multiple detections can be used to constrain astrophysical population models. This seemingly simple problem is made challenging by the high dimensionality and high degree of correlation in the parameter spaces that describe the signals, and by the complexity of the astrophysical models, which can also depend on a large number of parameters, some of which might not be directly constrained by the observations. We present a method for constraining population models using a hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We illustrate this approach by considering the constraints that can be placed on population models for galactic white dwarf binaries using a future space-based gravitational wave detector. We find that a mission that is able to resolve approximately 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%.