Galaxy observations suggest there is about one merger of supermassive black hole binaries (SMBHB) throughout the observable universe in a year. Here, we introduce the methodology to search for gravitational waves from these events with Pulsar Timing Arrays (PTAs). Modelling the inspiral, the merger, the ringdown, and the gravitational wave memory components of the signal in simulated data, we demonstrate a proof of principle for detection and parameter estimation. We study a few representative SMBHB mergers with chirp masses spanning 10^8 - 10^10~M_ at distances from a few Mpc to 100~Mpc to asses their detectability in PTA observations. Assuming the fixed binary inclination angle of 90^ corresponding to the maximum displacement memory signal, these signals appear distinct for a PTA with 25 pulsars timed for 13 years with 100 ns precision. We demonstrate the capabilities of PTAs to constrain chirp masses and distances of detected merging binaries, as well as to place limits. The sky position uncertainties of the order of 1^, which we find in this optimistic example, could potentially enable electromagnetic follow-up and multi-messenger observations of SMBHB mergers. Finally, we 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.
Tomson et al. (Mon,) studied this question.