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

TL;DR

The paper addresses how dark dense environments around black holes modify gravitational-wave inspirals and proposes a novel observable, $D$, defined from GW observables $h$, $f$, and $df/dt$, to quantify dynamical-friction–driven energy loss. By analyzing the evolution of $D$ with GW frequency, the authors show that different environments—a superradiant GA boson cloud, a soliton-like ultralight DM halo, or a spike-like CDM halo—imprint distinct $D$–$f$ morphologies that allow inference of boson masses or halo density-profile indices. They derive practical detectability criteria, map parameter spaces to LISA/DECIGO frequency bands, and demonstrate how measurements or null detections can constrain or reveal the properties of the dark sector and possible primordial origins of stellar-mass black holes. This work provides a new, observationally accessible pathway to probe DM and BSM physics in the strong-gravity regime using gravitational waves.

Abstract

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.

Figures (8)

• Figure 1: [Top] The GW waveform with and without the impacts from a superradiant boson cloud. We choose a $|211\rangle$ state boson cloud with $\alpha = 0.1$. [Bottom] The GW waveform with and without the impacts from a spike-like DM halo. We choose DM halo power index as $\gamma = -9/4$. The parameters of BH binary is set as $M = 30 \, M_\odot$, $q = 1$. The initial frequency is set as $f_{\rm ini} = 0.04 \, \text{Hz}$.
• Figure 2: The $D-f$ diagram for a GA boson cloud with $\alpha = 0.1,\, 0.11,\, 0.12$, respectively. The solid curves represent the numerical results obtained using $C_\Lambda$ calculated from Eq. \ref{['Eq.ULBCLambda']}. The dashed curves show the best-fit analytical approximation of $D$, derived by assuming $C_\Lambda \propto f^{-2/3}$ in Eq. \ref{['eq:D_boson_cloud']}. The parameters of the BH binary are set to $M = 30\,M_\odot$ and $q = 1$, with the corresponding redshift fixed at $z = 0.5$.
• Figure 3: The $D-f$ diagram for a soliton with $\alpha = 0.04, 0.045,0.049$ that corresponds to boson mass $\mu = 1.8, 2,2.2 \times10^{-13} \, \text{eV}$, respectively. The solid curves represent the numerical results obtained using $C_\Lambda$ calculated from Eq. \ref{['Eq.ULBCLambda']}. The dashed curves are the best-fit analytical approximation of $D$ by assuming $C_\Lambda \sim f^{-2/3}$. We set the mass ratio of solition and the BH is $\varepsilon = 10^{-3}$, parameters of the BH binary as $M = 30 \, M_\odot$ and $q = 1$, its corresponding redshift is set as $z = 0.5$.
• Figure 4: The $D-f$ diagram for a dark matter halo with power index $\gamma = -9/4$. We set the parameters of the BH binary as $M = 30 \, M_\odot$ and $q = 1$, the corresponding redshift is set as $z = 0.5$.
• Figure 5: The illustration of the parameter space where the power loss due to DF dominates over that from GW by a factor of 10 for $q=1,\,0.1$. We take $\mu = 5 \times 10^{-15}$ eV as our benchmark bosonic mass and fix the redshift at $z = 0.5$. The region with $\xi > 1$ is excluded to ensure the validity of our analysis. The yellow region indicates where the superradiant growth rate of the $211$ cloud exceeds the inverse age of the universe, implying that the cloud can form within the age of the universe. The shaded region on the right denotes $\alpha > 0.3$. The cyan shadow regions correspond to the detectable parameter regions in LISA bender1998lisa with an observation time of one month. The solid cyan curve corresponds to the case $q=1$, while the dashed one corresponds to the case $q=0.1$.