  Evidence for a stochastic gravitational wave (GW) background, plausibly
originating from the merger of supermassive black holes (SMBHs), is
accumulating with observations from pulsar timing arrays. An outstanding
question is how inspiraling SMBHs get past the "final parsec" of separation,
where they have a tendency to stall before GW emission alone can make the
binary coalesce. We argue that dynamical friction from the dark matter (DM)
spike surrounding the black holes is sufficient to resolve this puzzle, if the
DM has a self-interaction cross section of order $\,$cm$^2$/g. The same effect
leads to a softening of the GW spectrum at low frequencies as suggested by the
current data. For collisionless cold DM, the friction deposits so much energy
that the spike is disrupted and cannot bridge the final parsec, while 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 the exchange of a massive mediator like a dark photon, is
favored to give a good fit to the GW spectrum while providing a large enough
core. A similar velocity dependence has been advocated for solving the
small-scale structure problems of cold DM.
