Mass-redshift dependency of Supermassive Black Hole Binaries for the Gravitational Wave Background

Abstract

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