Echoes of Self-Interacting Dark Matter from Binary Black Hole Mergers

TL;DR

This work addresses how DM environments around intermediate-mass black-hole binaries imprint GW dephasing during inspiral, with SIDM spikes sustained by a mediator capable of producing observable effects. The authors build density-profile models (CDM spikes with $\gamma_{\rm sp}=7/3$ and SIDM cores connected to spikes via velocity-dependent cross-sections) and simulate binary inspirals using the $N$-body code KETJU to capture the DM response and BH feedback. They show that velocity-dependent SIDM can sustain dense spikes that generate measurable dephasing in LISA, characterized by a chirp-mass shift $\delta M_{\rm ch}$ and a dephasing relation $\frac{\Delta N_{\rm cyc}}{N^{acc}_{\rm cyc, vac}} \approx \frac{5}{3}\frac{\delta M_{\rm ch}}{M_{\rm ch}}$, and they forecast LISA’s ability to distinguish CDM vs SIDM and to constrain SIDM parameters, noting a notable dependence on the mass-ratio $q$ and mediator velocity scale $v_M$. The results indicate SIDM spikes can imprint observable GW signatures on sub-parsec scales, offering a novel gravitational probe of SIDM structure complementary to traditional astrophysical constraints, while emphasizing the role of DM halo feedback in accurate GW waveform modeling.

Abstract

Dark matter (DM) environments around black holes (BHs) can influence their mergers through dynamical friction, causing gravitational wave (GW) dephasing during the inspiral phase. While this effect is well studied for collisionless dark matter (CDM), it remains unexplored for self-interacting dark matter (SIDM) due to the typically low DM density in SIDM halo cores. In this work, by considering BH mergers within SIDM spikes, which can arise from models with a massive force mediator, we show that the GWs emitted are dephased in a distinct manner. To incorporate the feedback of the BH orbital motion that can significantly modify the DM profiles, we use $N$-body simulations to analyze GW dephasing in binary BH inspirals within CDM and SIDM spikes. By tracking the binary's motion in different SIDM environments, we show that the Laser Interferometer Space Antenna (LISA) can distinguish DM profiles shaped by varying DM interaction strengths, revealing detailed properties of SIDM.

Figures (9)

• Figure 1: Examples of SIDM density profiles with different $\sigma_0/m$ (colored lines) and $v_M$ (solid and dashed lines) around a black hole binary with $M_1 = 10^4\,M_{\odot}$ and $q=10^{-4}$. We have here $r_s \sim 10^{-9}$ pc. The solid black curve shows the corresponding CDM profile for comparison, while the dashed red curve highlights different regions of the SIDM profile. For numerical study, we use the CDM (solid black), solid blue, and solid red curves, with the binary inspiraling from $r\approx 30\,r_s$ and merging at $r \approx 10\,r_s$.
• Figure 2: The evolution of the SIDM density profiles around a BH of mass $10^4\,M_{\odot}$ over the binary merger time of $\sim 4$ years, for binary mass ratios $q = 10^{-4}$ (top row) and $10^{-2}$ (lower row). Purple-shaded regions refer to the inspiralling region for the respective binary.
• Figure 3: The dephasing obtained for the SIDM environment from our simulation, for various $\sigma_0/m_\chi$, $v_M = 3$ km/s (blue squares) and 4 km/s (red triangles), and BH mass ratios $q = 10^{-4}$ (upper panel) and $10^{-2}$ (lower panel). We show the dephasing obtained assuming no feedback on the DM halo from the secondary BH (blue and red dashed lines). The error bars on the bullets are based on $1/\sqrt{N}$ analysis of the 5 simulations per case we performed.
• Figure 4: The shifts in the chirp mass for $N_{\rm cyc}$ measurements for $q = 10^{-4}$ with SIDM environments. Gray lines mark the uncertainties on the measurement of the chirp mass by LISA for various SNRs, as calculated using , assuming luminosity distances of 125 (solid), 60 (dashed) and 20 (dotted) Mpc. Top: The shifts shown against a combination of the SIDM parameters $\sigma_0/m_{\chi}$ and $v_M$. The mass shift is expected to be universal for the combination of SIDM parameters. Bottom: We compare the mass shifts of one SIDM model parameter, labeled by different values of $(\sigma_0/m_{\chi})_a$ as indicated by the color code in the bottom right, with those of another parameter, denoted by the superscript $b$ on the $y$-axis. Squares (triangles) show the averaged results from the 5 simulations we performed, for $v_M = 3\,(4)$ km/s, with the error bars obtained using the method of error propagation from \ref{['eq:dephasing_analytic']}. Some markers are offset from the exact values of $\left(\sigma/m_{\chi}\right)_b$ for clarity in the presentation.
• Figure 5: Snapshots of our $N$-body simulation in the projected 2D plane, with the trajectories traced by the smaller BH (smaller black dot) around the central BH (larger black dot) in DM environments (blue lines) shown as gray lines, with opacity indicating increasing time. We show inspirals with $q = 10^{-4}$ in a CDM spike (top) and an SIDM spike (bottom) with $\sigma_0/m_\chi = 2\,\rm{cm^2/g}$ and $v_M = 3$ km/s. The masses of the DM clumps are different for CDM and SIDM to account for the different density profiles, leading to more DM trajectories for SIDM than CDM.