Properties and merger signatures of galaxies hosting LISA coalescing massive black hole binaries

The gravitational wave (GW) antenna LISA will detect the signal from coalescing massive black hole binaries (MBHBs) of $\rm 10^4\,{-}\,10^7\, M_{\odot}$, providing clues on their formation and growth along cosmic history. Some of these events will be localized with a precision of several to less than a deg$^2$, enabling the possible identification of their host galaxy. This work explores the properties of the host galaxies of LISA MBHBs below $z\,{\lesssim}\,3$. We generate a simulated lightcone by using the semi-analytical model $\mathrm{\texttt{L-Galaxies}}$ applied on the merger trees of the high-resolution N-body cosmological simulation $\mathrm{\texttt{Millennium-II}}$. The model shows that LISA MBHBs are expected to be found in optically dim ($r\,{>}\,20$), star-forming ($\rm sSFR\,{>}\,10^{-10}\, \rm yr^{-1}$), gas-rich ($f_{\rm gas}\,{>}\,0.6$) and disc-dominated ($\rm B/T\,{<}\,0.7$) \textit{low-mass galaxies} of stellar masses $10^8\,{-}\,10^9 M_{\odot}$. However, these properties are indistinguishable from those of galaxies harboring single massive black holes with comparable mass, making difficult the selection of LISA hosts among the whole population of low-mass galaxies. Motivated by this, we explore the possibility of using merger signatures to select LISA hosts. We find that 40-80% of the galaxies housing LISA MBHBs display merger features related to the interaction which brought the secondary MBH to the galaxy. Despite this, around 60% of dwarf galaxies placed in the surroundings of the LISA hosts will show such kind of features as well, challenging the unequivocal detection of LISA hosts through the search of merger signatures. Consequently, the detection of an electromagnetic transient associated with the MBHB merger will be vital to pinpoint the star-forming dwarf galaxy where these binary systems evolve and coalesce.