Stellar-mass binaries evolving in the vicinity of supermassive black holes (SMBHs) may be common in the universe, either in active galactic nuclei or in other astrophysical environments. Here, we study in detail the resonant excitation of SMBH modes driven by a nearby stellar-mass binary. The resulting resonant energy fluxes vary with the orbital location and frequency of the binary, exhibiting a rich and complex structure. In particular, we find that the total energy flux radiated to infinity is maximized at a gravitational-wave frequency that is close, but not exactly equal to, the real part of the corresponding quasi-normal-mode frequency. Moreover, as the binary is moved farther away from the SMBH, this offset from the mode frequency becomes increasingly pronounced. In addition, for suitable orientations, the binary can effectively “feed” the light ring of the SMBH, selectively exciting particular oscillation modes. For rotating (Kerr) black holes, the mode spectrum is significantly more intricate; however, individual modes are also less strongly damped, leading to an enhanced—but more difficult to interpret—resonant response.

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• Classical black holes
• Gravitational wave sources
• Astronomical black holes
• Galactic nuclei & quasars