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Abstract

State-of-the-art searches for gravitational waves (GWs) in pulsar timing
array (PTA) datasets model the signal as an isotropic, Gaussian and stationary
process described by a power-law. In practice, none of these properties are
expected to hold for an incoherent superposition of GWs generated by a cosmic
ensemble of supermassive black hole binaries (SMBHBs), which is expected to be
the primary signal in the PTA band. We perform a systematic investigation of
the performance of current search algorithms, using a simple power law model to
characterize GW signals in realistic datasets. We use, as the baseline dataset,
synthetic realisations of timing residuals mimicking the European PTA (EPTA)
second data release (DR2). Thus, we include in the dataset uneven time stamps,
achromatic and chromatic red noise and multi-frequency observations. We then
inject timing residuals from an ideal isotropic, Gaussian, single power-law
stochastic process and from a realistic population of SMBHBs, performing a
methodical investigation of the recovered signal. We find that current search
models are efficient at recovering the GW signal, but several biases can be
identified due to the signal-template mismatch, which we identify via
probability-probability (P-P) plots and quantify using Kolmogorov-Smirnov (KS)
statistics. We discuss our findings in light of the signal observed in the EPTA
DR2 and corroborate its consistency with an SMBHB origin.