Multi-wavelength properties of $z\gtrsim 6$ LISA detectable events

We investigate the intrinsic and observational properties of $z\gtrsim 6$ galaxies hosting coalescing massive black holes (MBHs) that gives rise to gravitational waves (GWs) detectable with the Laser Interferometer Space Antenna (LISA). We adopt a zoom-in cosmological hydrodynamical simulation of galaxy formation and black hole (BH) co-evolution, zoomed-in on a $M_h \sim 10^{12}~\rm M_{\odot}$ dark matter halo at z = 6, which hosts a fast accreting super-massive black hole (SMBH) and a star-forming galaxy. Following the SMBH formation backward in time, we identify the merging events that concurred to its formation and we pick up the ones that are detectable with LISA. Among these LISA detectable events (LDEs), we select those that, based on their intrinsic properties are expected to be bright in one or more electromagnetic (EM) bands. We post-process these events with dust radiative transfer calculations to make predictions about their spectral energy distributions and continuum maps in the JWST to ALMA wavelength range. We compare the spectra arising from galaxies hosting the merging MBHs with those arising from AGN powered by single accreting BHs. We find that it will be impossible to identify an LDE from the continuum SEDs because of the absence of specific imprints from the merging MBHs. We also compute the profile of the H$_{\rm \alpha}$ line arising from LDEs, considering the contribution from their star-forming regions and the accreting MBHs. We find that the presence of two accreting MBHs would be difficult to infer even if both MBHs accrete at super-Eddington rates. We conclude that the combined detection of GW and EM signals from $z\gtrsim 6$ MBHs is challenging not only because of the poor sky-localization provided by LISA, but also because the loudest GW emitters are not massive enough to leave significant signatures in the emission lines arising from the broad line region.