Expectations for the first supermassive black-hole binary resolved by PTAs II: Milestones for binary characterization

TL;DR

This paper investigates how a single resolving SMBHB signal can be characterized by pulsar timing arrays as data accumulate, using a full-deterministic CW model and IPTA-inspired simulations. The authors show that the GW frequency $f_{\rm GW}$ and strain $h_0$ are constrained first, with sky localization following, and the chirp mass $\mathcal{M}$ and inclination $\iota$ constrained later, with higher $f_{\rm GW}$ yielding sharper measurements due to pulsar-term information. They demonstrate that sky location and PTA geometry strongly shape early milestones, while pulsar-term contributions become more influential at higher S/N, and they compare full CW+GWB analyses to Earth-term-only cases to isolate pulsar-term effects. The findings inform strategies for host-galaxy identification and multi-messenger campaigns, and highlight the need for HD correlations in realistic GW background modeling as PTA datasets grow. Overall, the work provides a detailed roadmap of how CW parameters evolve with data, guiding expectations for the first resolvable SMBHB detections by PTAs.

Abstract

Following the recent evidence for a gravitational wave (GW) background found by pulsar timing array (PTA) experiments, the next major science milestone is resolving individual supermassive black hole binaries (SMBHBs). The detection of these systems could arise via searches using a power-based GW anisotropy model or a deterministic template model. In Schult et al. 2025, we compared the efficacy of these models in constraining the GW signal from a single SMBHB using realistic, near-future PTA datasets, and found that the full-signal deterministic continuous wave (CW) search may achieve detection and characterization first. Here, we continue our analyses using only the CW model given its better performance, focusing now on characterization milestones. We examine the order in which CW parameters are constrained as PTA data are accumulated and the signal-to-noise ratio (S/N) grows. We also study how these parameter constraints vary across sources of different sky locations and GW frequencies. We find that the GW frequency and strain are generally constrained at the same time (or S/N), closely followed by the sky location, and later the chirp mass (if the source is highly evolving) and inclination angle. At fixed S/N, sources at higher frequencies generally achieve better precision on the GW frequency, chirp mass, and sky location. The time (and S/N) at which the signal becomes constrained is dependent on the sky location and frequency of the source, with the effects of pulsar terms and PTA geometry playing crucial roles in source detection and localization.

Figures (10)

• Figure 1: Sky map of our simulated PTA configuration (yellow stars) and the two sky locations A and B where we inject a CW signal.
• Figure 2: Parameter constraints a function of time slice and (S/N)$_\Lambda$ for all four simulation sets. For each simulation set, the constraints and (S/N)$_\Lambda$ shown are the median values across all noise realizations. The constraints are plotted as $\Delta X_{68}/\Delta X_{100}$, where $\Delta X_{68}$ is the 68% credible interval of a given parameter $X$, and $\Delta X_{100}$ is the parameter's prior range. The sky location parameters $\cos\theta$ and $\phi$ are shown with dark and light blue circles, respectively. The GW frequency $\log_{10}f_{\rm{GW}}$ in shown with pink triangles, GW strain amplitude $\log_{10}h_0$ with gold squares, binary inclination angle $\cos\iota$ with orange squares, and chirp mass $\log_{10}\mathcal{M}$ with teal diamonds. The horizontal gray dashed, dash-dotted, and dotted lines indicate where the parameter is constrained to 10%, 1%, and 0.1% of its prior, respectively.
• Figure 3: 90% credible area as a function of (S/N)$_{\Lambda}$. Solid lines show the median value of both (S/N)$_{\Lambda}$ and $\Delta\Omega_{90}$, while the shaded regions show the full range of values across all 10 realizations. Light and dark blue (orange) curves correspond to the A5 and A20 (B5 and B20) injections, respectively. The dashed gray line indicates the (S/N)$^{-2}$ scaling relation.
• Figure 4: Distributions of pulsar term frequencies for all four injections. Sources with an Earth term frequency of 5 nHz are shown in the top panel, and those with an Earth term frequency of 20 nHz are shown in the bottom panel. The vertical dashed black line at the rightmost edge of each panel indicates the injected Earth term frequency. Pulsar term frequency distributions for locations A and B are shown with blue and orange curves, respectively. Lighter-colored curves show distributions for earlier time slices, while progressively darker-colored curves show distributions for later time slices. Note that the first (5-year) and last (22-year) time slices are excluded here; in the first slice the array contains only 5 pulsars, and the last slice contains the same number of pulsars as the 20-year slice.
• Figure 5: 90% credible areas for noiseless CW injections, keeping noise parameters fixed in the covariance matrix of the analyses. Areas are shown as a function of (S/N)$_{\rm{opt}}$ calculated with a CURN model. Color scheme is the same as in \ref{['fig:qcw_loc90']}, with full-signal injection+model shown in the left panel (solid lines) and Earth-term-only injection+model shown in the right panel (dashed lines). The binary parameters in the Earth-term-only injections are identical to those used in the full-signal injections.