  When particle dark matter is bound gravitationally around a massive black
hole in sufficiently high densities, the dark matter will affect the rate of
inspiral of a secondary compact object that forms a binary with the massive
black hole. In this paper, we revisit previous estimates of the impact of
dark-matter accretion by black-hole secondaries on the emitted gravitational
waves. We identify a region of parameter space of binaries for which estimates
of the accretion were too large (specifically, because the dark-matter
distribution was assumed to be unchanging throughout the process, and the
secondary black hole accreted more mass in dark matter than that enclosed
within the orbit of the secondary). To restore consistency in these scenarios,
we propose and implement a method to remove dark-matter particles from the
distribution function when they are accreted by the secondary. This new
feedback procedure then satisfies mass conservation, and when evolved with
physically reasonable initial data, the mass accreted by the secondary no
longer exceeds the mass enclosed within its orbital radius. Comparing the
simulations with accretion feedback to those without this feedback, including
feedback leads to a smaller gravitational-wave dephasing from binaries in which
only the effects of dynamical friction are being modeled. Nevertheless, the
dephasing can be hundreds to almost a thousand gravitational-wave cycles, an
amount that should allow the effects of accretion to be inferred from
gravitational-wave measurements of these systems.
