Finding supermassive black hole binary mergers in Pulsar Timing Array data

Galaxy observations suggest that mergers of supermassive black hole binaries (SMBHBs) are rare events on cosmological scales, with characteristic rates of order one per decade across the observable Universe. In this work, we present a framework to search for merging SMBHBs in pulsar timing array (PTA) data using a physically complete waveform model that includes the late inspiral, merger, ringdown, and gravitational-wave memory. This approach enables a unified treatment of continuous premerger emission and the nonoscillatory memory signal associated with coalescence. Using simulated PTA datasets, we demonstrate a proof of principle for parameter estimation of merging SMBHBs, focusing on representative systems with chirp masses of 10 8 and 10 10 M ⊙ at distances of 3 Mpc and 100 Mpc respectively. These signals are distinguishable for a PTA consisting of 25 pulsars observed over 13 years with 100 ns timing precision. For these sufficiently strong signals, we recover the simulated binaries with log Bayes factors exceeding 10, and show that chirp mass and luminosity distance can be jointly constrained with uncertainties governed by the characteristic mass-distance degeneracy of the signal. The sky position uncertainties are of the order of a few degrees, which could potentially enable electromagnetic follow-up and multimessenger observations of SMBHB mergers. We also show that the measurement uncertainties on the parameters of simulated merging binaries depend weakly on the presence of the gravitational wave background with Hellings-Downs correlations in our simulated data. We further demonstrate that commonly used memory burst approximations lead to biased strain amplitudes and inferred source parameters when compared to the full SMBHB waveform, even when optimally tuned. These results establish a pathway toward searching for SMBHB mergers and late-stage inspirals with PTAs using physically complete waveform models, complementing existing searches for continuous gravitational waves.