2025A&A...694A.194F

Recent observations by pulsar timing arrays (PTAs) suggest the presence of gravitational wave (GW) signals that potentially originate from supermassive black hole binaries (SMBHBs). These binaries can generate two kinds of signals: a stochastic gravitational wave background (GWB) or a deterministic continuous gravitational wave (CGW). The ability to correctly recognize and separate them is crucial for accurate signal recovery and astrophysical interpretation. This paper is aimed at investigating the interaction between stochastic GWB and deterministic CGW signals with the analysis pipelines currently available. We focus on understanding potential misinterpretations and biases in the parameter estimation when these signals are analysed separately or altogether. To this end, we performed several realistic simulations based on the European PTA 24.8 yr dataset. We first injected either a GWB or a CGW into five datasets (of three GWB realisations and two CGW realisations) with identical noise. We analysed each signal type independently and then we analysed data sets containing both a stochastic GWB and a single resolvable CGW. We compared the parameter estimations using different search models, including Earth term (ET) only or combined Earth and pulsar term (ET + PT) CGW templates, along with correlated or uncorrelated power law GWB templates. We show that when searched for independently, the GWB and CGW signals can be misinterpreted (i.e. they can be confused with each other) and only a combined search is able to recover the true signal present. For datasets containing both a GWB and a CGW, failure to account for the latter biases the recovery of the GWB; however, when we perform a combined search, both GWB and CGW parameters can be recovered without any strong bias. Care must be taken with the method used to perform combined searches on these multi-component datasets, as the CGW PT can be misinterpreted as a common uncorrelated red noise. However, this can be avoided by conducting direct searches for a correlated GWB plus a CGW (ET + PT). Our study underscores the importance of combined searches to ensure unbiased recovery of GWB parameters in the presence of strong CGWs. This is crucial to accurately interpreting the signal recently found in PTA data and it is a first step towards a robust framework for disentangling stochastic and deterministic GW components in more sensitive datasets in the future.