Expectations for the first supermassive black-hole binary resolved by PTAs I: Model efficacy

Abstract

One of the most promising targets for Pulsar Timing Arrays (PTAs) is identifying an individual supermassive black hole binary (SMBHB) out of the population of binaries theorized to produce a gravitational wave background (GWB). In this work, we emulate realistic PTA datasets, complete with an increasing number of pulsars and timing baseline, in which we inject a single binary on top of a Gaussian GWB. We vary the binary's source parameters, including sky position and frequency, and create ten noise realizations for each source/PTA combination to synthesize an ensemble of datasets to assess current Bayesian binary search techniques. We develop a novel, cross-correlation based model, Spike Pixel (SP), tuned for the frequency-specific anisotropy induced by an individual SMBHB and compare its binary detection and characterization capabilities to two waveform-based template models. We find that a template-based search including the full gravitational-wave signal structure (i.e., both the Earth and pulsar effects of an incident GW) returns the highest Bayes Factors (BF) and the most robust parameter estimation. SP attains a realization-median BF>10 at source strengths (S/N)~7-15. Interestingly, despite being a deterministic model, the Earth-term template struggles to identify and characterize low-frequency binaries (i.e., 5 nHz). These binaries require higher source strengths (S/N)~16-19 to reach the same BF threshold. This is likely due to neglected confusion effects between the pulsar and Earth terms. By contrast, SP shows promise for parameter estimation despite treating a binary's GW signal as excess directional GW power without phase modeling. Sky location and frequency parameter constraints returned by SP are only surpassed by the Earth term template model at (S/N)~12-13. Milestones for a first detection using the full-signal GW model are included in a companion paper Petrov et al. 2026.