Data span and frequency coverage requirements for robust detection and inference in PTAs: A case study with EPTA DR2

TL;DR

This paper investigates why the shorter DR2new data release sometimes yields higher GWB significance than the longer DR2full release in the EPTA DR2, attributing this to limited frequency coverage and noise degeneracies. By generating DR2-like simulations across varying timespans, the authors show that the first decade contributes little to GWB evidence, leading to overlapping HD S/N distributions and a ≈$2σ$ fluctuation in significance; spectral leakage further biases DR2new’s parameter estimates unless properly modeled. They demonstrate that incorporating IPTA-frequency coverage markedly improves detection and parameter accuracy, and that long-baseline data mitigate degeneracies and leakage effects. The results support the view that the DR2 behavior is consistent with current analysis pipelines and underscore the need for leakage-aware modeling and broadband data combinations to achieve robust GWB inference. Overall, the work provides a practical framework for interpreting GWB searches with heterogeneous PTA datasets and informs strategies for future IPTA-era analyses.

Abstract

Pulsar Timing Arrays (PTAs) are approaching the sensitivity required for a $5σ$ detection of the nanohertz stochastic gravitational-wave background (GWB). This makes it crucial to deeply understand the behaviour of our analysis pipelines. A counterintuitive feature of the European Pulsar Timing Array (EPTA) second data release is that restricting the dataset to the last 10.3 years (DR2new) increases the inferred GWB significance from $\leq2σ$ for the full 25-year dataset (DR2full) to $\geq3.5σ$. We investigate whether this behaviour indicates an anomaly or is a possible outcome of the pipeline. Using realistic, DR2-like simulations with varying timespans, we find that the first 10 years contribute little to the GWB evidence due to their limited frequency coverage. This produces substantial overlap between the HD S/N distributions of DR2full and DR2new. Random noise fluctuations therefore yield a higher GWB evidence in DR2new than in DR2full in $15\%$ of cases. Furthermore, $5\%$ of simulations match the HD S/N of the real data, indicating that the observed behaviour is consistent with being a $\sim2σ$ outcome due to noise fluctuations. Regardless of significance, DR2new simulations introduce biases in the GWB parameter estimation due to spectral leakage effects that are ignored in standard analyses and which flatten the inferred spectrum. Including leakage removes these biases, demonstrating the reliability of DR2new when the signal is properly modelled. Furthermore, we demonstrate that combining EPTA DR2full with long-baseline data from NANOGrav and PPTA, as well as low-frequency data from LOFAR and NenuFAR, significantly enhances GWB evidence and parameter accuracy. Finally, we examine the impact of the observation timespan and find that short-baseline datasets introduce strong amplitude biases and are ineffective at constraining the GWB.

Figures (11)

• Figure 1: Characteristic strain spectrum of the injected GWB. Purple stars are the contributions to the spectrum of all the SMBHBs in the populations. The black solid line is the total power spectrum in each frequency bin, where the frequency bins start at $f = 1/T_{\rm obs}$ and have width $\Delta f = 1/T_{\rm obs}$ with $T_{\rm obs}$ = 24.8yr. The power law approximation of the spectrum is also shown.
• Figure 2: Top: Distribution of the SNR computed from the 100 realizations of DR2 (orange) and DR2FC (green). Bottom: Difference in frequency coverage between the two kinds of datasets. The TOAs from all the pulsars are plotted together to highlight the drop in the frequency coverage occurring in DR2 at 15yr from now, which corresponds to the plateau of its SNR.
• Figure 3: 2-d distributions of the noise marginalised HD S/N and the degeneracy coefficient (weighted average JSD)
• Figure 4: Comparison of the precision and accuracy of the GWB parameter estimation performed with DR2full (orange) and DR2new (purple).
• Figure 5: Median of the marginalised posterior distributions of $\gamma_{\rm GWB}$ and $\log_{10}A_{\rm GWB}$ of the 100 realisations of DR2full and DR2new (shaded regions, 95$\%$C.I.) and of the 5 realisations selected on the HD S/N (solid lines, 68 and 95$\%$C.I.). As a reference, the median values and 2$\sigma$ covariance principal axis obtained from the real data are displayed.