Observability of the galaxies hosting LISA MBHBs. Left panel: median r-band magnitude of the galaxies hosting LISA MBHBs (red) and single MBHs (blue). Shaded areas represent the percentile 16th–84th. Dashed grey lines correspond to the r band limiting magnitude of SDSS (r = 25.1) and LSST (r = 27.5). Right panel: fraction of galaxies hosting LISA MBHBs (red) and single MBHs (blue) whose r-band magnitude is smaller than rth = 25.1 (solid line) and 27.5 (dashed line), i.e. those that are detectable. Top, middle, and bottom panels correspond to different mass bins: 10⁴ − 10⁵ M_⊙, 10⁵ − 10⁶ M_⊙, and 10⁶ − 10⁷ M_⊙, respectively. Overall, the figure shows that LISA MBHBs are hosted in dim galaxies; indeed, half of them are fainter than the detection limit of current photometric surveys.