Abstract
The cosmic merger history of supermassive black hole binaries (SMBHBs) is
expected to produce a low-frequency gravitational wave background (GWB). Here
we investigate how signs of the discrete nature of this GWB can manifest in
pulsar timing arrays through excursions from, and breaks in, the expected
$f_{\mathrm{GW}}^{-2/3}$ power-law of the GWB strain spectrum. To do this, we
create a semi-analytic SMBHB population model, fit to NANOGrav's 15 yr GWB
amplitude, and with 1,000 realizations we study the populations' characteristic
strain and residual spectra. Comparing our models to the NANOGrav 15 yr
spectrum, we find two interesting excursions from the power-law. The first, at
$2 \; \mathrm{nHz}$, is below our GWB realizations with $p$-value significance
$p = 0.05$ to $0.06$ ($\approx 1.8 \sigma - 1.9 \sigma$). The second, at $16 \;
\mathrm{nHz}$, is above our GWB realizations with $p = 0.04$ to $0.15$
($\approx 1.4 \sigma - 2.1 \sigma$). We explore the properties of a loud SMBHB
which could cause such an excursion. Our simulations also show that the
expected number of SMBHBs decreases by three orders of magnitude, from $\sim
10^6$ to $\sim 10^3$, between $2\; \mathrm{nHz}$ and $20 \; \mathrm{nHz}$. This
causes a break in the strain spectrum as the stochasticity of the background
breaks down at $26^{+28}_{-19} \; \mathrm{nHz}$, consistent with predictions
pre-dating GWB measurements. The diminished GWB signal from SMBHBs at
frequencies above the $26$~nHz break opens a window for PTAs to detect
continuous GWs from individual SMBHBs or GWs from the early universe.