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, with rates of order one per decade across the observable Universe. We present a framework to search for merging SMBHBs in pulsar timing array (PTA) data using a physically complete waveform model including inspiral, merger, ringdown, and gravitational-wave memory. This enables a unified treatment of continuous emission and the non-oscillatory memory signal. Using simulated PTA datasets, we demonstrate parameter estimation for representative systems with chirp masses of $10^8$ and $10^{10}~M_\odot$ at distances of $3$ Mpc to $100$ Mpc respectively. For sufficiently strong signals, we recover binaries with log Bayes factors >10 and constrain chirp mass and luminosity distance, subject to their characteristic degeneracy. Sky localization uncertainties of a few degrees could potentially enable electromagnetic follow-up and multi-messenger observations of SMBHB mergers. 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 for searching for SMBHB mergers with PTAs using complete waveform models.