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 ≲10⁻⁵ Hz 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 at a distance d ≲ 1 kpc. We determine that proposed decihertz GW interferometers sensitive to numerous stellar-mass binaries could uncover modulations from ~O(10⁻¹–10⁴) SMBHBs with masses ~O(10⁷–10⁸) M_⊙out to redshift z ≈ 3.5. This offers a unique opportunity to map the population of SMBHBs through cosmic time, which might remain inaccessible otherwise.

宇宙中最大质量的黑洞在合并星系的中心形成双星。最近来自脉冲星定时的引力波（GW）背景的证据可能构成这些超大质量黑洞双星（SMBHB）合并的首次观测。然而，最大质量的 SMBHB 超出了干涉引力波探测器的范围，并且很难用脉冲星定时单独解析。这些限制需要未探索的策略来检测未知频段≲ 10 ^-5 Hz 中的单个 SMBHB，以确定它们的丰度并破译与其宿主星系的共同演化。在这里，我们表明，SMBHB 在距离d ≲ 1 kpc 的同一星系中的恒星质量双星的引力波上留下了可检测的长期调制。我们确定，所提出的对众多恒星质量双星敏感的分赫兹引力波干涉仪可以揭示从~ O (10 ⁻¹ –10 ⁴ ) SMBHBs（质量~ O (10 ⁷ –10 ⁸ ) M _⊙到红移z ≈ 3.5 的调制）。这提供了一个独特的机会来绘制宇宙时间范围内的 SMBHB 人口分布图，否则可能无法访问。