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

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.