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. We use an analytical astrophysical model with galaxy stellar mass
function, pair fraction, merger timescale and BH-bulge mass relation extended
to include redshift evolution. The model can predict the intensity of the
gravitational wave background produced by a population of supermassive black
hole binary (SMBHB) as a function of the frequency. We focus on the BH-bulge
mass relation and its variation with redshift using the EAGLE, Illustris,
TNG100, TNG300, Horizon-AGN and SIMBA large-scale cosmological simulations. By
understanding the processes and relationships concerning the formation and
co-evolution of galaxies and their central BHs we can make theoretical and
analytical expressions in order to refine current astrophysical models. 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. By fitting the BH-bulge mass parameters to the Illustris
and SIMBA simulations we analyze 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.Comment: 17 pages, 13 figures, 5 tables, 23 appendix figure