Imprints of massive black-hole binaries on neighbouring decihertz gravitational-wave sources

The most massive black holes in our Universe form binaries at the centre of merging galaxies. The recent evidence for a gravitational-wave (GW) background from pulsar timing may constitute the first observation that these supermassive black hole binaries (SMBHBs) merge. Yet, the most massive SMBHBs are out of reach of interferometric {GW} detectors and are exceedingly difficult to resolve individually with pulsar timing. These limitations call for unexplored strategies to detect individual SMBHBs in the uncharted frequency band $\lesssim10^{-5}\,\rm Hz$ in order to establish their abundance and decipher the coevolution with their host galaxies. Here we show that SMBHBs imprint detectable long-term modulations on GWs from stellar-mass binaries residing in the same galaxy. We determine that proposed deci-Hz GW interferometers sensitive to numerous stellar-mass binaries could uncover modulations from $\sim\mathscr{O}(10^{-1}$ - $10^4)$ SMBHBs with masses $\sim\mathscr{O}(10^7$ - $10^8)\,\rm M_\odot$ out to redshift $z\sim3.5$. This offers a unique opportunity to map the population of SMBHBs through cosmic time, which might remain inaccessible otherwise.