Extracting Properties of Dark Dense Environments around Black Holes from Gravitational Waves

Dark matter (DM) can form dense condensates around black holes (BHs), such as superradiant clouds and ultracompact mini halos, which can significantly affect the orbital evolution of their companion objects through dynamical friction (DF). In this work, we define a novel quantity to quantify such effects in the emitted gravitational waves (GWs) in terms of GW amplitude, frequency, and their time derivatives. The information about the density profile can be extracted from this quantity, which characterizes the type of condensate and, therefore, the corresponding DM property. This quantity allows us to probe the dark dense environment by multi-wavelength GW observation with existing ground-based and future space-based GW detectors, potentially revealing the properties of the dark sector and shedding light on the primordial origin of the stellar mass BHs. A null detection can place strong constraints on the relevant DM parameters.