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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 willeffect the sensitivity of PTAs by deriving scaling laws for the signal-to-noiseratio (SNR) of the optimal cross-correlation statistic. The presence of gas andstars around SMBHBs will accelerate the merger at large distances, depletingthe GW stochastic background at low frequencies. We show that environmentalinteractions may delay detection by a few years or more, depending on the PTAconfiguration and the frequency at which the dynamical evolution transitionsfrom being dominated by environmental effects to GW-dominated.

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