Dephasing in binary black hole mergers surrounded by scalar wave dark matter clouds

TL;DR

The paper demonstrates that a massive scalar field surrounding a binary black hole system can produce measurable dephasing in gravitational waves, with the effect strongly dependent on the scalar mass parameter $M\mu_{\rm S}$ and the binary mass ratio $q$. Using constraint-satisfying initial data via an extended TwoPunctures solver and high-order numerical relativity with the Einstein Toolkit and Canuda, the authors simulate quasi-circular binaries ($q=1$ and $q=1/2$) in scalar clouds across $M\mu_{\rm S}\in\{0,0.2,0.4,0.6,0.8,1\}$. They observe scalar radiation and accretion that form overdensities around each BH, minor mass growth ($\lesssim 0.04\%$) and a final spin around $\chi_f\sim 0.62$, while gravitational-wave signals exhibit phase shifts up to several tenths of a cycle and shifts in the peak frequency, possibly accelerating or delaying mergers depending on the configuration. The results establish a path toward environmental waveform templates for next-generation detectors and highlight the potential to probe ultralight scalar fields and dark matter structures with strong-gravity probes.

Abstract

Scalar fields of masses between $10^{-21}\rm{eV}/c^2$ and $10^{-11} \rm{eV}/c^2$ can exhibit enhanced gravitational interactions with black holes, and form scalar clouds around them. Such a cloud modifies the dynamics of a coalescing black-hole binary, and the resulting gravitational waves may provide a new channel to detect light scalar fields, such as axion-like particles or wave-like dark matter candidates. In this work we simulate a series of black-hole mergers with mass ratios $q=1$ and $q=1/2$, immersed in an scalar field overdensity with masses in the range $Mμ_{\rm{S}} \in[0,1.0]$. To do so, we implemented a constraint-satisfying initial data solver based on the puncture method, we improved the accuracy of our open-source software Canuda to eighth order finite differences, and we reduced the initial orbital eccentricity. We investigate the impact of the scalar mass on the gravitational and scalar radiation. We find that binaries can undergo a delayed or an accelerated merger with respect to the vacuum. Our study highlights the challenge and importance of accurately modeling black-hole binaries in dark matter environments.

Figures (19)

• Figure 1: Sketch of an unequal-mass BH binary interacting with a massive scalar cloud. Solid black circles indicating the BHs, their trajectories as dotted and dashed lines, and the oscillating scalar field represented by color. Left panel: Initial configuration of the binary and scalar cloud that is set up as spherically symmetric Gaussian profile at the BHs' center-of-mass. Right panel: The system one orbit into the inspiral. Around the BHs, the scalar field forms a pair of scalar overdensities that generate scalar radiation.
• Figure 2: Convergence plot for TwoPunctures_BBHSF , computing the initial solution of a binary BH with mass ratio $q=1/2$ immersed in a scalar cloud with mass parameter $M\mu_{\rm S}=0.4$; run q12mu04 in Table \ref{['tab:simulations_list']}. We show the relative error $\Delta_{N,160}$ between a solution $u_{N}$ obtained with $N$ collocation points and the reference solution $u_{160}$, as a function of the number of collocation points $N$.
• Figure 3: Two-dimensional snapshots of the simulation q12mu04. From left to right, the pseudocolor plots show the scalar's energy density $\rho$ normalized by the initial maximum value $\rho_{0,\max}=1.6\times 10^{-7} M^{-2}$ (left), the scalar field $\Phi$ (middle), and real part of the Newman-Penrose scalar $\Psi_4$ (right). The green circles in the left column indicate the locations and radii of the BHs' apparent horizons. From top to bottom we display these quantities at different stages of the binary's coalescence: (1) shortly after initial data settles and a burst junk radiation is emitted, (2) $1.5$ orbits after the beginning of the simulation, (3) $0.5$ orbit before merger, and (4) $\sim130$M after the merger. Note the difference in the displayed spatial domain, chosen to highlight features of the quantities.
• Figure 4: Evolution of the Christodoulou mass, Eq. \ref{['eq:christodouloumass']}, for a BH binary with $q=1$ and scalar mass parameters $M\mu_{\rm S}$. The reference simulation in vacuum is indicated by the solid black line. Left: Percent change of the individual BHs' masses compared to their initial values. Right: Mass of the final BH.
• Figure 5: Same as Fig. \ref{['fig:q1_ah_mass_bh']} but for mass ratio $q=1/2$. Left: Percent change of the mass of BH 1 (top) and BH 2 (bottom) relative to their initial masses. Right: Mass of the final BH.