Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays

TL;DR

This paper shows that accounting for selection bias in supermassive black hole-host galaxy relations significantly reduces the expected gravitational wave background in pulsar timing arrays, impacting detection prospects.

Contribution

It quantifies how selection bias lowers GWB estimates, providing revised predictions that align better with recent PTA limits.

Findings

Expected GWB amplitude is about three times smaller when bias is considered.

Median GWB amplitude at 1/year frequency drops from 1.3e-15 to 4e-16.

Bias correction resolves tension between predictions and PTA limits without additional effects.

Abstract

Supermassive black hole -- host galaxy relations are key to the computation of the expected gravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. It has been recently pointed out that standard relations adopted in GWB computations are in fact biased-high. We show that when this selection bias is taken into account, the expected GWB in the PTA band is a factor of about three smaller than previously estimated. Compared to other scaling relations recently published in the literature, the median amplitude of the signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to $4\times10^{-16}$. Although this solves any potential tension between theoretical predictions and recent PTA limits without invoking other dynamical effects (such as stalling, eccentricity or strong coupling with the galactic environment), it also makes the GWB detection more challenging.