Gravitational Wave Duet by Resonating Binary Black Holes within Ultralight Dark Matter

TL;DR

The paper demonstrates that inspiralling binary black holes inside ultralight bosonic solitons induce resonant interactions when the orbital frequency sweeps through harmonics of the boson frequency, generating distinctive modulations in gravitational waves. By modeling ULDM as a real scalar field with mass $m$ and self-coupling $\lambda$ (negative $\lambda$ for attraction), they derive oscillatory metric perturbations $\Psi$ at frequencies $2\omega_a$ and $4\omega_a$ and show these drive a resonant force $F_{DM}=\ddot{\Psi} r$ on the binary. The authors perform orbit-averaged, Fourier-decomposed analysis to obtain evolution equations for the orbital elements and compute GW waveforms that exhibit residual oscillations at each harmonic, which can be probed by space-based detectors via a Fisher-matrix approach. They map detectable regions in the ULDM parameter space $(m,\hat{\lambda})$ for various binary masses and system densities, demonstrating that LISA-like observatories can constrain ULDM even when it is purely gravitational. The work highlights a gravity-only pathway to ULDM discovery, with implications for axion minicluster solitons and future multi-field scenarios, while noting limitations such as dynamical friction and halo feedback as avenues for further study.

Abstract

Gravitational wave observations have significantly broadened our capacity to explore fundamental physics beyond the Standard Model, providing crucial insights into dark matter that are inaccessible through conventional methods. Here, we investigate the resonant interactions between binary black hole systems and solitons, self-gravitating configurations of ultralight bosonic dark matter, which induce metric perturbations and generate distinct oscillatory patterns in gravitational waves. Upcoming experiments such as the Laser Interferometer Space Antenna could detect the oscillatory patterns in gravitational waveforms, providing an evidence for solitons. Because the effect relies solely on gravity, it does not assume any coupling of the dark sector to Standard Model particles, highlighting the capability of future gravitational-wave surveys to probe dark matter.

Figures (11)

• Figure 1: Illustration of binary black holes resonating with ULDM. The spacetime perturbations induced by ULDM introduce an additional force between the black holes, leading to distinctive patterns in the GWs emitted during their merger.
• Figure 2: Time evolution of the dimensionless semimajor axis $\alpha$ for an equal-mass binary system. The binary system is characterized by a total mass $M=10^{4}M_{\odot}$, an initial orbital frequency $\omega_{0}=10^{-3}\mathrm{Hz}$, and an initial eccentricity $e_{0}=0.5$. Benchmark ULDM parameters include $m = 10^{-17}$eV and $\hat{\lambda} = -10^{-4}$ with average ULDM densities (blue, green, and red lines) given by $\bar{\rho}_{\mathrm{DM}} = \{10^{18}, 10^{19}, 10^{20} \} M_{\odot} / \mathrm{pc}^3$ respectively.
• Figure 3: The amplitude spectral density of GWs with (red line) and without (black line) ULDM clouds around the binary system. The binary system has a total mass of $M = 10^{4}M_{\odot}$, an initial orbital frequency of $\omega_{0} = 10^{-3}\mathrm{Hz}$, and an initial eccentricity of $e_{0} = 0.5$. It is located at a distance of $d_{L} = 0.1\mathrm{Gpc}$ and has orbital inclinations of $\iota = \pi/4$ and $\beta = \pi/4$. The benchmark ULDM parameters are same as those presented in Fig. \ref{['fig:PlotGrid_alpha']}, except that the average ULDM density is fixed by $\bar{\rho}_{\mathrm{DM}} = 10^{20} M_{\odot} / \mathrm{pc}^3$. The gray line represents LISA's sensitivity curve Robson:2018ifk.
• Figure 4: The detectable regions in the parameter space of $\{ m, \lambda \}$ for binary systems under different conditions. The reference parameters (highlighted in light blue) involve a binary system with $M=10^{2}M_{\odot}$, an initial eccentricity $e_{0}=0.5$, and an average ULDM density $\bar{\rho}_{\mathrm{DM}} = 10^{18} M_{\odot} / \mathrm{pc}^3$. Additional scenarios shown include a system with a lower initial eccentricity $e_0 = 0.3$ (in green), another with a lower ULDM density $\bar{\rho}_{\mathrm{DM}} = 10^{16} M_{\odot} / \mathrm{pc}^3$ (in purple), and a binary system with an increased total mass of $M=10^{4}M_{\odot}$ (in dark blue). The dotted and dashed lines mark the soliton stability thresholds at $10^{16} M_{\odot} / \mathrm{pc}^3$ and $10^{18} M_{\odot} / \mathrm{pc}^3$ respectively.
• Figure 5: Variation of dimensionless pressure components of ULDM as functions of $\hat{\lambda}$. The frequency mode $\Lambda_{2}$ remains the dominant one throughout.