Galaxy fields of LISA massive black hole mergers in a simulated universe

Laser Interferometer Space Antenna (LISA) will extend the search for gravitational waves (GWs) at $0.1\, {-}\, 100$ mHz where loud signals from coalescing binary black holes of $10^4 \, {-}\, 10^7\, \, \rm {M}_{\odot }$ are expected. Depending on their mass and luminosity distance, the uncertainty in the LISA sky-localization decreases from hundreds of deg² during the inspiral phase to fractions of a deg² after the merger. By using the semi-analytical model L-Galaxies applied to the Millennium-I merger trees, we generate a simulated universe to identify the hosts of $z\, {\le }\, 3$ coalescing binaries with total mass of $3\, {\times }\, 10^{5}$, $3\, {\times }\, 10^6$, and $3\, {\times }\, 10^7\, \rm {M}_{\odot }$, and varying mass ratio. We find that, even at the time of merger, the number of galaxies around the LISA sources is too large (${\gtrsim }\, 10^2$) to allow direct host identification. However, if an X-ray counterpart is associated to the GW sources at $z\, {< }\, 1$, all LISA fields at merger are populated by ${\lesssim }\, 10$ active galactic nuclei (AGNs) emitting above ${\sim }\, 10^{-17} \, \rm erg\, cm^{-2}\, s^{-1}$. For sources at higher redshifts, the poorer sky-localization causes this number to increase up to ${\sim }\, 10^3$. Archival data from eRosita will allow discarding ${\sim }\, 10{{\ \rm per\ cent}}$ of these AGNs, being too shallow to detect the dim X-ray luminosity of the GW sources. Inspiralling binaries in an active phase with masses ${\lesssim }\, 10^6\, \rm {M}_{\odot }$ at $z\, {\le }\, 0.3$ can be detected, as early as 10 h before the merger, by future X-ray observatories in less than a few minutes. For these systems, ${\lesssim }\, 10$ AGNs are within the LISA sky-localization area. Finally, the LISA-Taiji network would guarantee the identification of an X-ray counterpart 10 h before merger for all binaries at $z\, {\lesssim }\, 1$.