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Large dark matter overdensities can form around black holes of astrophysicaland primordial origin as they form and grow. This "dark dress" inevitablyaffects the dynamical evolution of binary systems, and induces a dephasing inthe gravitational waveform that can be probed with future interferometers. Inthis paper, we introduce a new analytical model to rapidly computegravitational waveforms in presence of an evolving dark matter distribution. Wethen present a Bayesian analysis determining when dressed black hole binariescan be distinguished from GR-in-vacuum ones and how well their parameters canbe measured, along with how close they must be to be detectable by the plannedLaser Interferometer Space Antenna (LISA). We show that LISA can definitivelydistinguish dark dresses from standard binaries and characterize the darkmatter environments around astrophysical and primordial black holes for a widerange of model parameters. Our approach can be generalized to assess theprospects for detecting, classifying, and characterizing other environmentaleffects in gravitational wave physics.

Measuring the dark matter environments of black hole binaries with gravitational waves