Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array

TL;DR

This study uses the Parkes PPTA-DR3 dataset (30 pulsars over ~18 years) to search for an isotropic nanohertz gravitational-wave background with a Bayesian PTA framework. It analyzes common red-noise processes and spatial correlations, employing both full HD-based and hierarchical pairwise approaches, and examines the impact of solar-system ephemeris uncertainties. The results reveal a strong common-spectrum process consistent with a GWB amplitude near A ≈ 2×10^-15 for γ = 13/3, but HD cross-correlations are only marginally supported (p ~ 0.014–0.018 via sky-scrambling), with notable time-dependence and pulsar-specific discrepancies. Overall, the evidence for a definitive GWB detection remains inconclusive, highlighting the value of longer baselines and IPTA-scale analyses to achieve a robust, cross-validated detection.

Abstract

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 years. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum $h_c = A(f/1 {\rm yr}^{-1})^α$, we measure $A=3.1^{+1.3}_{-0.9} \times 10^{-15}$ and $α=-0.45 \pm 0.20$ 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 $A=2.04^{+0.25}_{-0.22} \times 10^{-15}$. 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 $p \lesssim 0.02$ (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.

Figures (10)

• Figure 1: Factorized-likelihood analysis on the $\log_{10} A_{13/3}$ from the PPTA-DR3 pulsars. We highlight the three pulsars showing the highest (PSRs J1909$-$3744, J0437$-$4715, and J2145$-$0750) and lowest (PSRs J1744$-$1134, J1603$-$7202, and J1713$+$0747) consistency with the inferred common process with colored histograms. Other pulsars are presented as light-gray histograms. The prior density is shown with the green dashed line, and the total factorized-likelihood constraint for $\log_{10} A^{\mathrm{CRN}}_{13/3}$ (the product of all other histograms) is shown by the black line.
• Figure 2: Statistics assessing the support for a noise process with $\gamma=13/3$ for each pulsar in PPTA-DR3. Top: posterior probability density ratio for a $\gamma=13/3$ process, at $\log_{10} A_{13/3} = -14.69$, relative to $\log_{10} A_{13/3} < -16.5$ (where the data are insensitive to a $\gamma=13/3$ process) in blue, and the prior density in orange. Bottom: The Savage--Dickey Bayes factor $\mathcal{B}$ for a $\gamma=13/3$ process at any amplitude, which is also the ratio of the orange to blue points in the top panel. Filled and hollow circles correspond to prior range lower bounds on $\log_{10} A_{13/3}$ of $-20$ and $-18$, respectively.
• Figure 3: Marginal posterior probability distributions for the measured logarithmic amplitude and spectral index ($\gamma$) of a common uncorrelated process assuming different solar system ephemerides (SSE). Using DE440 (green) we measure $\gamma = 3.87 \pm 0.36$ and $\log_{10} A^{\mathrm{CRN}} = -14.50^{+0.14}_{-0.16}$ (median and 68% credible interval; shaded regions in one-dimensional histograms). The contours on the two-dimensional marginal distribution show the 1$\sigma$, 2$\sigma$, and 3$\sigma$ credible intervals for each of the SSEs.
• Figure 4: Marginal posterior probability distributions for the logarithmic amplitude and spectral index ($\gamma$) of a common uncorrelated process, under our tailored single-pulsar priors (blue) and broader equal priors (orange).
• Figure 5: Posterior probability density violins for the uncorrelated common-spectrum noise amplitude as a function of time, using a 6 yr (top) and 9 yr (bottom) sliding window (slices) over the data set. The spectral index is fixed at $-13/3$. Slices with unconstrained (log) amplitude posteriors have been reweighted to have linear priors in $A^{\mathrm{CRN}}_{13/3}$ (orange), and the 95% confidence upper limits are denoted with vertical arrows. Slices with constrained measurements of $\log_{10}A^{\mathrm{CRN}}_{13/3}$ are colored in blue. For reference, the dashed horizontal line indicates the $1.2\times10^{-15}$ upper limit set by our first 9 yr slice. The solid horizontal line and gray band indicate the measured $\log_{10 }A^{\mathrm{CRN}}_{13/3}$ of $-14.69$ and its 68% credible interval from our full PPTA-DR3 analysis. Here and elsewhere, the violins represent the probability density of a parameter, with broader segments of a violin corresponding to higher probability density.