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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 (PTAs) 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 semianalytic SMBHB population model, fit to North American Nanohertz Observatory for Gravitational Waves (NANOGrav’s) 15 yr GWB amplitude, and with 1000 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 nHz, is below our GWB realizations with ap-value significancep= 0.05–0.06 (≈1.8σ–1.9σ). The second, at 16 nHz, is above our GWB realizations withp= 0.04–0.15 (≈1.4σ–2.1σ). We explore the properties of a loud SMBHB that could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by 3 orders of magnitude, from ∼10⁶to ∼10³, between 2 and 20 nHz. This causes a break in the strain spectrum as the stochasticity of the background breaks down at ${26}_{-19}^{+28}\mathrm{nHz}$, 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. 

Abstract The NANOGrav 15 yr data provide compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists of a simple power-law fit involving two parameters: an amplitudeAand a spectral indexγ. In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for arunning(i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{\mathrm{run}}\left(f\right)=\gamma +\beta \ln \left(f/f_{\mathrm{ref}}\right)$. We fit this running-power-law (RPL) model to the NANOGrav 15 yr data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameterβconsistent with no running, $\beta \in \left(-0.80,2.96\right)$, and an inconclusive Bayes factor, $B\left(\mathrm{RPL}\mathrm{versus}\mathrm{CPL}\right)=0.69\pm 0.01$. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzeroβ. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from Big Bang nucleosynthesis, the cosmic microwave background, and LIGO–Virgo–KAGRA.