Mass-redshift dependency of supermassive black hole binaries for the gravitational wave background

Studying how the black hole (BH)-(galaxy) bulge mass relation evolves with redshift provides valuable insights into the co-evolution of supermassive black holes and their host galaxies. However, obtaining accurate measurement of BH masses is challenging due to the bias towards the most massive and luminous galaxies. Instead, we focus on the BH and bulge masses as they vary with redshift using the EAGLE, Illustris, TNG100, TNG300, Horizon-AGN, and SIMBA large-scale cosmological simulations. We use an analytical astrophysical model with galaxy stellar mass function, pair fraction, merger time-scale and BH-bulge mass relation extended to include redshift evolution. The model can predict the intensity of the gravitational wave background (GWB) produced by a population of supermassive black hole binary (SMBHB) as a function of the frequency. This allows us to compare the predictions of this model with the constraints of pulsar timing array observations. Here, we employ Bayesian analysis for the parameter inference. We find that all six simulations are consistent with a range of simulated GWB spectra. By fixing the BH-bulge mass parameters to the simulations we analyse the changes in the constraints on the other astrophysical parameters. Furthermore, we also examine the variation in SMBHB merger rate with mass and redshift between these large-scale simulations.