  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.
