The Host Galaxies of Pulsar Timing Array Sources: Converting Supermassive Black Hole Binary Parameters into Electromagnetic Observables

Abstract Pulsar timing arrays (PTAs) are approaching the sensitivity required to resolve gravitational waves (GWs) from individual supermassive black hole (SMBH) binaries. However, the large uncertainty in source localization will make the identification of its host environment challenging. We show how to convert the posterior probability function of binary parameters inferred by GW analyses into distributions of apparent magnitudes of the host galaxy. We do so for a scenario in which the host environment is a regular early-type galaxy, and one in which it is an active galactic nucleus. We estimate the reach of PTAs in the near and intermediate future, and estimate whether the binary hosts will be detectable in all-sky electromagnetic (EM) surveys. A PTA with a baseline of 20 yr and 116 pulsars, resembling the upcoming data release of the International Pulsar Timing Array, can detect binaries out to a luminosity distance of 2 Gpc (corresponding to a redshift of z ∼ 0.36), while a PTA with a baseline of 30 yr and 200 pulsars can reach out to distances slightly greater than 3 Gpc ( z ∼ 0.53). We find that the host galaxies of all binaries detectable with a baseline of 20 yr are expected to be present in the Wide-field Infrared Survey Explorer and SuperCOSMOS surveys, if they lie outside the plane of the Milky Way. The Two Micron All Sky Survey becomes incomplete for hosts of binaries more massive than 10 9.8 M ⊙ at a luminosity distance greater than 1 Gpc. The EM surveys become slightly more incomplete when PTAs with longer baselines and therefore improved sensitivities are considered.