The paper discusses the solution to the "final parsec problem" of supermassive black hole (SMBH) mergers, which is the challenge of how SMBHs can inspiral and merge over the final parsec of separation. The authors propose that dynamical friction from the dark matter (DM) spike surrounding the black holes can resolve this issue, provided the DM has a self-interaction cross section of order cm²/g. This effect also softens the gravitational wave (GW) spectrum at low frequencies, as suggested by current data. For collisionless cold DM, the friction deposits so much energy that the spike is disrupted and cannot bridge the final parsec. However, for self-interacting DM, the isothermal core of the halo can act as a reservoir for the energy liberated from the SMBH orbits. A realistic velocity dependence, such as generated by a massive mediator like a dark photon, is favored to fit the GW spectrum while providing a large enough core. The paper also explores the implications of these findings for small-scale structure problems in cold DM models.The paper discusses the solution to the "final parsec problem" of supermassive black hole (SMBH) mergers, which is the challenge of how SMBHs can inspiral and merge over the final parsec of separation. The authors propose that dynamical friction from the dark matter (DM) spike surrounding the black holes can resolve this issue, provided the DM has a self-interaction cross section of order cm²/g. This effect also softens the gravitational wave (GW) spectrum at low frequencies, as suggested by current data. For collisionless cold DM, the friction deposits so much energy that the spike is disrupted and cannot bridge the final parsec. However, for self-interacting DM, the isothermal core of the halo can act as a reservoir for the energy liberated from the SMBH orbits. A realistic velocity dependence, such as generated by a massive mediator like a dark photon, is favored to fit the GW spectrum while providing a large enough core. The paper also explores the implications of these findings for small-scale structure problems in cold DM models.