The Origin of the Nano-Hertz Stochastic Gravitational-wave Background: The Contribution from <i>z</i> ≳ 1 Supermassive Black Hole Binaries

Abstract The nano-Hertz gravitational wave background (GWB) is a key probe of supermassive black hole (SMBH) formation and evolution if the background arises predominantly from SMBH binaries (SMBHBs). The GWB amplitude, which is typically quantified as the characteristic strain, A yr at a frequency 1 yr −1 , encodes significant astrophysical information about the SMBHB population, including the SMBHB mass and redshift distributions. Recent results from a number of pulsar timing arrays have identified a common-spectrum noise process, correlated between pulsars, that is consistent with a loud GWB signal with A yr ∼ 2 × 10 −15 , which is higher than most predictions A yr ≲ 10 −15 . These predictions usually assume theoretically motivated but highly uncertain prescriptions for SMBH seeding and evolution. Recent observations, largely by the James Webb Space Telescope, have uncovered a population of obscured, overmassive, accreting black holes in the early Universe that may suggest that the black hole mass density and net accretion were larger at high redshifts than previously thought. In this work, we use two simple, flexible models of SMBH evolution to explore the possible range of GWB amplitudes, given observational constraints. In particular, we explore enhanced contributions to the GWB from high redshift ( z ≳ 1) SMBHBs. We find that the GWB amplitude may be higher than fiducial predictions by as much as ∼1 dex if much of the SMBH mass density was established by z ∼ 1. Beyond pulsar timing constraints, further observations of the high redshift SMBH population from the James Webb Space Telescope and the Laser Interferometer Space Antenna will be key for constraining the GWB contribution of mid-high- z SMBHBs.