The role of distant pulsars in the detectability of continuous gravitational waves

Context. One of the imminent science goals of pulsar timing arrays (PTAs) is the detection of a continuous gravitational wave (CGW) emitted by an individual supermassive black hole binary (SMBHB). SMBHBs that cause CGWs with GW frequencies fGW > 10 nHz (high-frequency end of the nano-Hertz GW spectrum) have undergone significant orbital evolution and hence a change in fGW over time. In PTA datasets with a sufficiently long observational time span, this means that the contributions of the Earth and the pulsar terms to the CGW signal signature can eventually become resolvable. Since the pulsar term is accumulated incoherently and thus often treated as an additional source of noise, this separation can prove to be beneficial for the detection of the CGW signal in the PTA dataset. Aims. We investigate to which extent resolvable Earth and pulsar terms affect currently used techniques for CGW searches with PTA datasets, which treat the pulsar term as an additional source noise. We focus on the dependence of the pulsar term frequencies on the pulsar distance. We aim to answer the question of whether adding more distant pulsars to a PTA dataset can mitigate biases and improve the detection of CGWs. Methods. We used simulated PTA datasets based on the EPTA DR2 and IPTA DR2 pulsars in order to study the performance of the Earth-term-only Bayesian parameter estimation of the circular SMBHB model parameters and the frequentist narrow-band optimal statistic in the light of resolved pulsar terms due to larger pulsar distances. Results. We show that under ideal conditions, more distant pulsars can facilitate the CGW search with PTA datasets. The Bayesian parameter estimation is yielding better parameter constraints, and the frequentist search becomes more stable. Based on realistic dataset simulations, however, we found that other configuration parameters of a PTA, such as the anisotropic distribution of pulsars and the effective number of pulsars in a PTA, can play a crucial role in the importance of this effect.