The Impact of Black Hole Scaling Relation Assumptions on the Mass Density of Black Holes

TL;DR

This study investigates how different assumptions about supermassive black hole scaling relations affect the inferred black hole mass distribution over cosmic time, impacting gravitational wave background predictions.

Contribution

It compares SMBH mass functions derived from two scaling relations across redshifts, highlighting their impact on gravitational wave background estimates and emphasizing the need to understand their evolution.

Findings

Velocity dispersion predicts more SMBHs >10^9 M_sun at high redshift.

Different scaling relations lead to substantial variations in SMBH demographics at z > 1.

Discrepancies may explain the mismatch between observed and predicted gravitational wave signals.

Abstract

We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift $z \sim 3$. 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: $\mathrm{M_{BH}}$-$\mathrm{M_{bulge}}$ and $\mathrm{M_{BH}}$-$\sigma$. Our SMBH mass functions come directly from stellar mass measurements for $\mathrm{M_{BH}}$-$\mathrm{M_{bulge}}$, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for $\mathrm{M_{BH}}$-$\sigma$. 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 $10^9 \mathrm{M}_\odot$. 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 $z > 1$