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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. 

Abstract It is often assumed that electron backscatter and continuum (bremsstrahlung) productions emitted from electron-solid interactions during X-ray microanalysis in compounds can be extrapolated from pure element observations by means of the assumption of average atomic number, or Z-bar (Z¯). For pure elements the average Z is equal to the atomic number, but this direct approach fails for compounds. The use of simple atomic fractions yields completely spurious results, and while the commonly used mass fraction Z averaging produces fairly reasonable results, we know from physical considerations that the mass of the neutron plays only a negligible role in such interactions below ∼1 MeV. Therefore, including the mass or atomic weight in such calculations can only introduce further errors in these models. We present an expression utilizing atomic fractions of the atomic numbers of the elements in the compound (Z fraction), with an exponent to account for the variation in nuclear screening as a function of the element Z value.