The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background

We search for an isotropic stochastic gravitational-wave background (GWB) in the 12.5 yr pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. Our analysis finds strong evidence of a stochastic process, modeled as a power law, with common amplitude and spectral slope across pulsars. Under our fiducial model, the Bayesian posterior of the amplitude for an f^-2/3 power-law spectrum, expressed as the characteristic GW strain, has median 1.92 × 10^-15 and 5%-95% quantiles of 1.37-2.67 × 10^-15 at a reference frequency of ${f}_{\mathrm{yr}}=1\,{\mathrm{yr}}^{-1};$ the Bayes factor in favor of the common-spectrum process versus independent red-noise processes in each pulsar exceeds 10,000. However, we find no statistically significant evidence that this process has quadrupolar spatial correlations, which we would consider necessary to claim a GWB detection consistent with general relativity. We find that the process has neither monopolar nor dipolar correlations, which may arise from, for example, reference clock or solar system ephemeris systematics, respectively. The amplitude posterior has significant support above previously reported upper limits; we explain this in terms of the Bayesian priors assumed for intrinsic pulsar red noise. We examine potential implications for the supermassive black hole binary population under the hypothesis that the signal is indeed astrophysical in nature.