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, i.e., a cross-correlation search for single sources, or a deterministic template model. In Schult et al. [Expectations for the first supermassive black-hole binary resolved by PTAs. I. Model efficacy, Phys. Rev. D 114, 023034 (2026).], 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 ($\mathrm{S}/\mathrm{N}$) 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 $\mathrm{S}/\mathrm{N}$), closely followed by the sky location, and later the chirp mass (if the source is highly evolving) and inclination angle. At fixed $\mathrm{S}/\mathrm{N}$, sources at higher frequencies generally achieve better precision on the GW frequency, chirp mass, and sky location. The time (and $\mathrm{S}/\mathrm{N}$) 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.

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• Gravitational wave detection
• Gravitational wave sources
• Gravitational waves
• Astronomical black holes