Exploring the local black hole mass function below $10^6$ solar masses

The local black hole mass function (BHMF) is of great interest to a variety of astrophysical problems, ranging from black hole binary merger rates to an indirect census of the dominant seeding mechanism of supermassive black holes. In this Letter, we combine the latest galaxy stellar mass function from the Galaxy And Mass Assembly survey with X-ray-based constraints to the local black hole occupation fraction to probe the BHMF below $10^6$ $M_{odot}$. Notwithstanding the large uncertainties inherent to the choice of a reliable observational proxy for black hole mass, the resulting range of BHMFs yields a combined normalization uncertainty of $lesssim$1 dex over the $[10^5-10^6]$ $M_{odot}$ range, where upcoming, space-based gravitational wave detectors are designed to be most sensitive.