Constraining Formation Models of Binary Black Holes with
  Gravitational-Wave Observations
  Gravitational waves (GWs) from binary black hole (BBH) mergers provide a new
probe of massive-star evolution and the formation channels of binary compact
objects. By coupling the growing sample of BBH systems with population
synthesis models, we can begin to constrain the parameters of such models and
glean unprecedented knowledge about the inherent physical processes that
underpin binary stellar evolution. In this study, we apply a hierarchical
Bayesian model to mass measurements from a synthetic GW sample to constrain the
physical prescriptions in population models and the relative fraction of
systems generated from various channels. We employ population models of two
canonical formation scenarios in our analysis --- isolated binary evolution
involving a common-envelope phase and dynamical formation within globular
clusters --- with model variations for different black hole natal kick
prescriptions. We show that solely with chirp mass measurements, it is possible
to constrain natal kick prescriptions and the relative fraction of systems
originating from each formation channel with $\mathcal{O}(100)$ of confident
detections. This framework can be extended to include additional formation
scenarios, model parameters, and measured properties of the compact binary.
