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

Abstract

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 $f_\mathrm{GW} > 10 \text{nHz}$ have undergone significant orbital evolution, hence a change of $f_\mathrm{GW}$ over time. In PTA data sets with sufficiently long observational time span, this means that the Earth and pulsar terms' contributions 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 data set. We aim to investigate to what extent resolvable Earth and pulsar terms affect currently used techniques for CGW searches with PTA data sets, that treat the pulsar term as an additional source noise. We focus on the dependency of the pulsar term frequencies on the pulsar's distance. We aim to answer the question of whether adding more distant pulsars to a PTA data set can mitigate biases and improve the detection of CGWs. We show that under ideal conditions, more distant pulsars can facilitate the CGW search with PTA data sets. Bayesian parameter estimation is yielding better parameter constraints and the frequentist per-frequentist optimal statistic search becomes more stable. However, using the realistic data set simulations, it was 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 to the importance of this effect.