Clustering of binary black hole mergers: a detailed analysis of the eagle + mobse simulation

We perform a detailed study of the cosmological bias of gravitational wave (GW) events produced by stellar binary black hole mergers (BBHM). We start from a BBHM distribution modelled inside the eagle hydrodynamical simulation using the population synthesis code mobse. We then compare our findings with predictions from different halo occupation distribution (HOD) prescriptions and find overall agreement, provided that the modelled properties of host galaxies and haloes in the semi-analytical treatment match those in the simulations. By highlighting the sources of these discrepancies, we provide the stepping stone to build future more robust models that prevent the shortcoming of both simulation-based and analytical models. Finally, we train a neural network to build a simulation-based HOD and perform feature importance analysis to gain intuition on which host halo/galaxy parameters are the most relevant in determining the actual distribution and power spectrum of BBHM. We find that the distribution of BBHM in a galaxy does not only depend on its size, star formation rate and metallicity, but also by its kinetic state, namely its total energy and velocity dispersion.