Supermassive Black Hole Binary Environments: Effects on the Scaling Laws and Time to Detection for the Stochastic Background

TL;DR

This paper analyzes how the environments of supermassive black hole binaries influence the gravitational wave background detection by pulsar timing arrays, deriving scaling laws and assessing delays caused by environmental effects.

Contribution

It introduces new scaling laws for the SNR of PTA signals considering environmental effects and quantifies how gas and stars impact detection timelines.

Findings

Environmental interactions can delay detection by several years.

Gas and stellar surroundings accelerate SMBHB mergers at large distances.

Depletion of low-frequency GW background affects PTA sensitivity.

Abstract

One of the primary gravitational wave (GW) sources for pulsar timing arrays (PTAs) is the stochastic background formed by supermassive black holes binaries (SMBHBs). In this paper, we investigate how the environments of SMBHBs will effect the sensitivity of PTAs by deriving scaling laws for the signal-to-noise ratio (SNR) of the optimal cross-correlation statistic. The presence of gas and stars around SMBHBs will accelerate the merger at large distances, depleting the GW stochastic background at low frequencies. We show that environmental interactions may delay detection by a few years or more, depending on the PTA configuration and the frequency at which the dynamical evolution transitions from being dominated by environmental effects to GW-dominated.