Mass distribution of ultralight boson in binary black hole systems

TL;DR

The paper analyzes ultralight boson clouds around binary black holes, focusing on mass transfer and depletion mechanisms in unequal-mass systems with arbitrary spin orientations. By modeling the bosons as forming two-center, molecular-like orbitals (Born-Oppenheimer framework) and treating tidal perturbations as resonant mixing and ionization processes, it quantifies how scalar and vector clouds deplete differently as a function of mass ratio $q$ and fine-structure-like constant $\alpha$. Key results show scalar depletion is often dominated by hyperfine mixing into the primary, while vector depletion is driven by transfer to the companion, with strong orientation dependence for the vector case; ionization becomes dominant at small $q$. The work further connects cloud dynamics to gravitational-wave signatures, predicting GW-power offsets $\Delta P$ that reflect time-dependent mass redistribution within the binary. Overall, the study provides a detailed, semi-analytic framework for predicting boson-cloud depletion and its observable GW consequences in realistic binary configurations.

Abstract

Ultralight bosons are compelling dark-matter candidates. Both scalar and vector bosons can be produced through black hole superradiance, forming a boson cloud surrounding a rotating black hole. Self-interaction of bosons, together with transition mixing in binary black hole systems, give rise to dynamical phenomena that could be potentially observable with future gravitational wave observations. In this work, we investigate the dynamics of bosons in binary black hole systems. In particular, we focus on boson mass transfer in unequal-mass binary black hole systems with arbitrary spin-orientation of the companion. Our results show that the mass ratio between the companion and the primary black holes significantly affects cloud absorption through mass transfer. Moreover, when the companion's spin is not aligned with that of the primary, the efficiency of cloud depletion is further modified.

Figures (23)

• Figure 1: Fraction of the initial vector cloud mass that depletes into the primary black hole via Bohr mixing. It is assumed that the inspiral of the binary black hole begins at an orbital separation of $R_*=1000 r_b$ and evolves down to $R_*=3r_b$, where the ionization process starts to dominate.
• Figure 2: Illustration of a binary black hole system: The central black hole is surrounded by a scalar boson cloud occupying the states $\ket{\psi^1_{2p_x}}$ and $\ket{\psi^1_{2p_y}}$. The companion black hole depletes the cloud through its $s$- and $p$-states. Pink regions indicate positive components of the wavefunction, blue regions indicate negative components, and the gray sphere represents the $s$-state. As the companion black hole approaches, the $\ket{\psi^1_{2p_x}}$ state begins to overlap with both the companion's $s$- and $p_x$-state. In contrast, $\ket{\psi^1_{2p_y}}$ overlaps effectively only with the companion's $p_y$-state; it positive and negative components calcel out when interacting with companion's $s$-state, resulting in no net depletion from that channel.
• Figure 3: Coefficients of the molecular orbitals corresponding to $E_1$, where we choose $q=0.9$ and fine-structure-like constant $\alpha=0.1$.
• Figure 4: Occupation probabilities of the companion black hole's decaying modes, evaluated for $q=0.9$ and $\alpha=0.1$.
• Figure 5: Scalar cloud depletion via molecular orbitals and dominant separations of ionization. The green region indicates no cloud depletion, the blue region represents sharp cloud depletion, and the red curve corresponds to ionization removing approximately $10\%$ of the cloud, another blue curve represent $90\%$ ionization of the cloud. Here, we use the fine-structure-like constant $\alpha=0.1$.