The origin of the nano-Hertz stochastic gravitational wave background: the contribution from $z\gtrsim1$ supermassive black-hole binaries

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 binary SMBHs. The amplitude of the GWB, which is typically quantified in terms of the characteristic strain, $A_{\rm 1 yr}$, at a frequency $1\,{\rm yr}^{-1}$, encodes significant astrophysical information about the SMBH binary (SMBHB) population, including the mass and redshift distributions of SMBHBs. Recent results from a number of pulsar timing arrays have identified a common-spectrum noise process that is consistent with a loud GWB signal with amplitude $A_{\rm 1 yr}{\sim}2\times10^{-15}$, which is higher than typical predictions $A_{\rm 1 yr} \lesssim 10^{-15}$. These predictions usually assume theoretically-motivated but highly uncertain prescriptions for SMBH seeding and evolution. In this work, we use a simple, flexible model of SMBH evolution to explore the possible range of GWB amplitudes, given observational constraints. In particular, we focus on the possible contribution to the GWB from high redshift ($z\gtrsim 1$) SMBHBs, for which few robust observational constraints exist. We find that the GWB amplitude may be higher than fiducial predictions by as much as ${\sim}0.5$ dex if much of the SMBH mass density was established by $z\sim1$. Beyond pulsar timing constraints, 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 contribution of high-$z$ SMBHBs to the GWB.