A nanohertz-frequency stochastic gravitational-wave background can potentially be detected through the precise timing of an array of millisecond pulsars. This background produces low-frequency noise in the pulse arrival times that would have a characteristic spectrum common to all pulsars and a well-defined spatial correlation. Recently the North American Nanohertz Observatory for Gravitational Waves collaboration (NANOGrav) found evidence for the common-spectrum component in their 12.5 yr data set. Here we report on a search for the background using the second data release of the Parkes Pulsar Timing Array. If we are forced to choose between the two NANOGrav models—one with a common-spectrum process and one without—we find strong support for the common-spectrum process. However, in this paper, we consider the possibility that the analysis suffers from model misspecification. In particular, we present simulated data sets that contain noise with distinctive spectra but show strong evidence for a common-spectrum process under the standard assumptions. The Parkes data show no significant evidence for, or against, the spatially correlated Hellings–Downs signature of the gravitational-wave background. Assuming we did observe the process underlying the spatially uncorrelated component of the background, we infer its amplitude to be A = 2.2 − 0.3 + 0.4 × 10 − 15 in units of gravitational-wave strain at a frequency of 1 yr−1. Extensions and combinations of existing and new data sets will improve the prospects of identifying spatial correlations that are necessary to claim a detection of the gravitational-wave background.

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 yr. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum h c = A ( f / 1 yr − 1 ) α , we measure A = 3.1 − 0.9 + 1.3 × 10 − 15 and α = −0.45 ± 0.20, respectively (median and 68% credible interval). For a spectral index of α = −2/3, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of A = 2.04 − 0.22 + 0.25 × 10 − 15 . However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on A that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with α = −2/3, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of p ≲ 0.02 (approx. 2σ). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array.