Where are NANOGrav's big black holes?

TL;DR

Recent PTA detections of nanohertz gravitational waves suggest the presence of supermassive black hole binaries more massive than previously predicted, indicating a need to revise models of black hole populations.

Contribution

This work shows that the observed GW background amplitude implies the existence of extremely massive SMBHs (~3×10^{10} M_sun), much larger than current models predict, highlighting the importance of rare, massive black holes.

Findings

Measured GW background exceeds theoretical predictions.

To match observations, SMBHs must be significantly more massive (~3×10^{10} M_sun).

PTA data provides unique insights into the rare, massive end of SMBH distribution.

Abstract

Multiple pulsar timing array (PTA) collaborations have recently reported the first detection of gravitational waves (GWs) of nanohertz frequencies. The signal is expected to be primarily sourced by inspiralling supermassive black hole binaries (SMBHBs) and these first results are broadly consistent with the expected GW spectrum from such a population. Curiously, the measured amplitude of the GW background in all announced results is a bit larger than theoretical predictions. In this work, we show that the amplitude of the stochastic gravitational wave background (SGWB) predicted from the present-day abundance of SMBHs derived from local scaling relations is significantly smaller than that measured by the PTAs. We demonstrate that this difference cannot be accounted for through changes in the merger history of SMBHs and that there is an upper limit to the boost to the characteristic strain from multiple merger events, due to the fact that they involve black holes of decreasing masses. If we require the current estimate of the black hole mass density -- equal to the integrated quasar luminosity function through the classic Soltan argument -- to be preserved, then the currently measured PTA result would imply that the typical total mass of SMBHs contributing to the background should be at least $\sim 3 \times 10^{10} M_\odot$, a factor of $\sim 10$ larger than previously predicted. The required space density of such massive black holes corresponds to order $10$ $3 \times 10^{10} M_\odot$ SMBHs within the volume accessible by stellar and gas dynamical SMBH measurements. By virtue of the GW signal being dominated by the massive end of the SMBH distribution, PTA measurements offer a unique window into such rare objects and complement existing electromagnetic observations.