Big Galaxies and Big Black Holes: The Massive Ends of the Local Stellar and Black Hole Mass Functions and the Implications for Nanohertz Gravitational Waves

We construct the $z=0$ galaxy stellar mass function (GSMF) by combining the GSMF at stellar masses $M_* \lesssim 10^{11.3} M_\odot$ from the census study of Leja et al. (2020) and the GSMF of massive galaxies at $M_* \gtrsim 10^{11.5} M_\odot$ from the volume-limited MASSIVE galaxy survey. To obtain a robust estimate of $M_*$ for local massive galaxies, we use MASSIVE galaxies with $M_*$ measured from detailed dynamical modeling or stellar population synthesis modeling (incorporating a bottom-heavy initial mass function) with high-quality spatially-resolved spectroscopy. These two independent sets of $M_*$ agree to within ${\sim}7$%. Our new $z=0$ GSMF has a higher amplitude at $M_* \gtrsim 10^{11.5} M_\odot$ than previous studies, alleviating prior concerns of a lack of mass growth in massive galaxies between $z\sim 1$ and 0. We derive a local black hole mass function (BHMF) from this GSMF and the scaling relation of SMBH and galaxy masses. The inferred abundance of local SMBHs above $\sim 10^{10}M_\odot$ is consistent with the number of currently known systems. The predicted amplitude of the nanohertz stochastic gravitational wave background is also consistent with the levels reported by Pulsar Timing Array teams. Our $z = 0$ GSMF therefore leads to concordant results in the high-mass regime of the local galaxy and SMBH populations and the gravitational wave amplitude from merging SMBHs. An exception is our BHMF yields a $z=0$ SMBH mass density that is notably higher than the value estimated from quasars at higher redshifts.