Supermassive black hole growth and merger rates from cosmological N-body simulations

Understanding how seed black holes (BHs) grow into intermediate-mass and supermassive black holes (IMBHs and SMBHs, respectively) has important implications for the duty cycle of active galactic nuclei (AGN), galaxy evolution and gravitational wave astronomy. Most studies of the cosmological growth and merger history of BHs have used semianalytic models and have concentrated on SMBH growth in luminous galaxies. We have developed a 'hybrid method' that combines high-resolution cosmological N-body simulations for the haloes' merger history, with semi-analytical recipes for BH pair dynamics and BH gas accretion. We track the assembly of BHs over a large range of final masses - from seed BHs to SMBHs - over widely varying dynamical histories. We used the dynamics of dark matter haloes to track the evolution of seed BHs in three different gas accretion scenarios. We have found that growth of a Sagittarius A* - size of SMBH reaches its maximum mass M_SMBH = ∼10 ⁶ M_⊙ at z ∼ 6 through early gaseous accretion episodes, after which it stays at near constant mass. At the same redshift, the duty cycle of the host AGN ends, hence redshift z = 6 marks the transition from an AGN to a starburst galaxy which eventually becomes the Milky Way. By tracking BH growth as a function of time and mass, we estimate that the IMBH merger rate reaches a maximum of R_max = 55 yr^-1 at z = 11. From IMBH merger rates we calculate N_ULX = 7 per Milky Way type galaxy per redshift in redshift range 2 ≲ z ≲ 6.