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

TL;DR

This work investigates how resolvable Earth-term and pulsar-term signatures in continuous gravitational waves from SMBHBs affect pulsar timing array analyses. By simulating PTA data with realistic EPTA/IPTA configurations and varying pulsar distances, the authors assess the benefits of including distant, PT-resolved pulsars for ET-only Bayesian searches and for the Per-Frequency Optimal Statistic. Under ideal conditions, distant pulsars improve parameter constraints (notably sky location, $f_{GW}$, and $h_0$) and stabilize frequentist estimates, but realistic PTA geometry and noise properties can limit these gains. The study also shows that separating ET and PT frequencies reduces PFOS estimator variance in the ET bin, enhancing CGW detectability at higher frequencies and lower S/N, with practical implications for future PTA design and target strategies.

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.

Figures (9)

• Figure 1: Sky map indicating the positions of the pulsars (stars) used in this work, and the CGW positions used for the investigations in this wok. The size of the pulsar position markers is inverse proportional to the residual root-mean-square of each pulsar.
• Figure 2: $f_\mathrm{GW}$-$\log_{10}\mathcal{M}_\mathrm{c}$ p$f_\mathrm{GW}$-$\log_{10}\mathcal{M}_\mathrm{c}$ parameter space. The shaded areas indicate the region of resolved PTs, for a PTA timing baseline of 10 years. The gray areas correspond to an angular separation between the pulsar and the CGW source of 90°, the blue areas correspond to 22.5°. The darker and lighter shades refer to a pulsar distance of 1k and 4k, respectively. The red symbols indicate the positions of two exemplary SMBHB candidates in that parameter space, with $f_\mathrm{GW}$ estimates and upper limits of $\log_{10}\mathcal{M}_\mathrm{c}$ from electromagnetic models or PTA analyses (OJ287: Titarchuk_2023Komossa_2023, 3C66B: CardinalTremblay_2025).
• Figure 3: Cornerplot of the CGW parameter posteriors (excluding $\log_{10}\mathcal{M}_\mathrm{c}$, $\Phi_0$, $\psi$) created from the joint MCMC chain of 500 realisations of each data set. It shows the result from the data set containing a CGW signal with $\log_{10}\mathcal{M}_\mathrm{c}=9.1$. The darker contours correspond to the PTA with pulsars at 1k, the lighter contours correspond to the PTA with pulsars at 4k
• Figure 4: Cornerplot of the CGW parameter posteriors (excluding $\log_{10}\mathcal{M}_\mathrm{c}$, $\Phi_0$, $\psi$) created from the joint MCMC chain of 500 realisations of each data set. The darker contours correspond to the PTA with pulsars at 1k, the lighter contours correspond to the PTA with pulsars at 4k
• Figure 5: Distribution of PT frequencies versus S/N contribution in the EPTA20 data set for three different CGW source positions and pulsars at both 1k (dark blue squares) and 4k (light blue dots). The CGW frequency (ET frequency) is indicated as the dark blue vertical line. The fundamental frequencies of the PTA with $T_\mathrm{obs}=10\yr$ are indicated with the gray vertical lines and labels. Top: Virgo cluster. Middle: $P_1 =$(RA 18h, DEC-22.5deg). Bottom: $P_2 =$(RA 3h, DEC-45deg). Due to the dependence of the strain on the angular distance between the pulsar and the source (cf. Eq. \ref{['eq:CGW_residuals']}), the $S/N$ varies across the three positions.