Exploring the evolution of gravitational-wave emitters with efficient emulation: Constraining the origins of binary black holes using normalising flows

Binary population synthesis simulations allow detailed modelling of gravitational-wave sources from a variety of formation channels. These population models can be compared to the observed catalogue of merging binaries to infer the uncertain astrophysical input parameters describing binary formation and evolution, as well as relative rates between various formation pathways. However, it is computationally infeasible to run population synthesis simulations for all variations of uncertain input physics. We demonstrate the use of normalising flows to emulate population synthesis results and interpolate between astrophysical input parameters. Using current gravitational-wave observations of binary black holes, we use our trained normalising flows to infer branching ratios between multiple formation channels, and simultaneously infer common-envelope efficiency and natal spins across a continuous parameter range. Given our set of formation channel models, we infer the natal spin to be $0.04^{+0.04}_{-0.01}$, and the common-envelope efficiency to be $>3.7$ at 90% credibility, with the majority of underlying mergers coming from the common-envelope channel. Our framework allows us to measure population synthesis inputs where we do not have simulations, and better constrain the astrophysics underlying current gravitational-wave populations.