2023MNRAS.524.4403M

We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift z ∼ 3. To make robust predictions for the gravitational wave background (GWB), we must have a solid understanding of the underlying SMBH demographics. Using the SDSS and 3D-HST + CANDELS surveys for 0 < z < 3, we evaluate the inferred SMBH masses from two SMBH-galaxy scaling relations: M_BH-M_bulge and M_BH-σ. Our SMBH mass functions come directly from stellar mass measurements for M_BH-M_bulge, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for M_BH-σ. We find that there is a substantial difference in predictions especially for z > 1, and this difference increases out to z = 3. In particular, we find that using velocity dispersion predicts a greater number of SMBHs with masses greater than 10⁹ M_⊙. The GWB that pulsar timing arrays find evidence for is higher in amplitude than expected from GWB predictions which rely on high-redshift extrapolations of local SMBH mass-galaxy scaling relations. The difference in SMBH demographics resulting from different scaling relations may be the origin for the mismatch between the signal amplitude and predictions. Generally, our results suggest that a deeper understanding of the potential redshift evolution of these relations is needed if we are to draw significant insight from their predictions at z > 1.