  When two galaxies merge, they often produce a supermassive black hole binary
(SMBHB) at their center. Numerical simulations with stars and cold dark matter
show that SMBHBs typically stall out at a distance of a few parsecs apart and
take billions of years to coalesce. This is known as the final parsec problem.
We suggest that ultralight dark matter (ULDM) halos around SMBHBs can generate
dark matter waves due to dynamical friction. These waves can effectively carry
away orbital energy from the black holes, rapidly driving them together. To
test this hypothesis, we performed numerical simulations of black hole binaries
inside ULDM halos.
  Due to gravitational cooling and quasi-normal modes, the loss-cone problem
can be avoided. The decay time scale gives lower bounds on masses of the ULDM
particles and SMBHBs comparable to observational data. Our results imply that
ULDM waves can lead to the rapid orbital decay of black hole binaries.
