Data span and frequency coverage requirements for robust detection and inference in pulsar timing arrays

A case study with EPTA DR2

¹ Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
² INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
³ INAF – Osservatorio Astronomico di Brera, Via Brera 20, I-20121 Milano, Italy
⁴ INAF – Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius (CA), Italy
⁵ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 26 November 2025
Accepted: 4 March 2026

Abstract

Pulsar timing arrays (PTAs) are approaching the level of sensitivity required to make a 5-σ detection of the nanohertz stochastic gravitational-wave background (GWB). Thus, it is now crucial to develop a comprehensive understanding of our data and of the outcomes of our analysis pipelines. It is also essential to understand a counterintuitive feature revealed in the recent results from the European Pulsar Timing Array (EPTA) second data release (DR2). When restricting the dataset to its ultimate ∼10.3 years (DR2new), the inferred GWB significance increases from ≲2σ for the full 25-year dataset (DR2full), to ≳3.5σ for DR2new. In this work, we investigate whether this behaviour reflects an anomaly in the data or whether it is a possible outcome of the analysis pipeline. Using realistic DR2-like simulations, we generated multiple realisations with varying observation time spans and analysed their impact on GWB evidence and parameter estimations. We quantified the evidence using the signal-to-noise ratio (S/N) of a common process with Hellings-Downs spatial correlations (HD S/N). We find that the first ∼10 years of DR2 contribute little to the GWB evidence due to the limited bandwidth of the observation frequency, leading to a significant overlap between the DR2full and DR2new HD S/N distributions. As a consequence, random noise fluctuations result in DR2new producing a higher GWB significance than DR2full in ∼15% of the cases and 5% of the realisations are compatible with the HD S/N of the real DR2full and DR2new. This suggests that the picture observed in the data, while unlikely, remains consistent with a ∼2σ outcome due to noise fluctuations. We also find that regardless of the significance, the DR2new simulated data yielded biased GWB parameter estimates, primarily due to spectral leakage effects that are disregarded in the analysis and tend to flatten the inferred power-law spectrum. Including leakage in the model returns unbiased parameter estimates, demonstrating that DR2new is reliable when the signal is appropriately modelled. Furthermore, we show that combining EPTA DR2full data with complementary long-baseline observations from NANOGrav and PPTA and with low-frequency observations from LOFAR and NenuFAR significantly bolsters the GWB evidence, along with improved precision and accuracy in the parameter estimation. This outcome supports the case of integrating DR2full within the IPTA framework. Finally, we explored the impact of the observation time span on parameter estimations in greater detail, focusing on long-baseline (25 yr) and short-baseline (5 yr) datasets. We find that short-baseline datasets tend to introduce significant bias towards high amplitudes in the estimation of GWB parameters, while the short time span makes them very ineffective at constraining the GWB slope.