Associating host galaxy candidates to massive black hole binaries resolved by pulsar timing arrays

We propose a novel methodology to select host galaxy candidates of future pulsar timing array (PTA) detections of resolved gravitational waves (GWs) from massive black hole binaries (MBHBs). The method exploits the physical dependence of the GW amplitude on the MBHB chirp mass and distance to the observer, together with empirical MBH mass-host galaxy correlations, to rank potential host galaxies in the mass-redshift plane. This is coupled to a null-stream-based likelihood evaluation of the GW amplitude and sky position in a Bayesian framework that assigns to each galaxy a probability of hosting the MBHB generating the GW signal. We test our algorithm on a set of realistic simulations coupling the likely properties of the first PTA resolved GW signal to synthetic all-sky galaxy maps. For a foreseeable PTA sky-localization precision of 100 deg2, we find that the GW source is hosted with 50 per cent (90 per cent) probability within a restricted number of ≤ 50(≤ 500) potential hosts. These figures are orders of magnitude smaller than the total number of galaxies within the PTA sky error-box, enabling extensive electromagnetic follow-up campaigns on a limited number of targets.