Common Envelope Evolution of Ultralight Boson Clouds

TL;DR

This work addresses how ultralight boson clouds bound to spinning black holes in comparable-mass binaries evolve as the orbital separation approaches the cloud size, potentially forming a common envelope. It develops a gravitational-molecule description in which cloud states are treated as molecular eigenstates and analyzes adiabatic evolution, resonant level transitions, and eccentricity pumping using Landau–Zener formalisms with couplings $\eta_{ij}$ and energy gaps $\epsilon_{ij}$. Key findings show that clouds largely evolve adiabatically, but secular and resonant transitions can transfer population between states and pump the binary eccentricity up to ${\cal O}(0.1)$ in the LVK band, with a characteristic GW frequency $f_B \sim 18\, (\alpha/0.1)^3 (5 M_\odot / M)$ Hz at $a\sim r_B$. For equal-mass binaries the clouds survive to form a common envelope, suggesting observable gravitational-wave signatures and providing a framework for probing ultralight bosons via binary dynamics.

Abstract

Ultralight bosons can be excited around spinning black holes via black hole superradiance. These boson clouds may play an important role in the orbital evolution of binary black holes. In this work, we investigate the formation and evolution of common envelopes of ultralight boson clouds in comparable mass-ratio black hole binaries. We describe the cloud evolution using gravitational molecular eigenstates and analyze the possible level transitions during orbital decay, as well as the impact on orbital dynamics. We find that the cloud can generally lead to eccentricity growth. In particular, the eccentricity may vary significantly during level transition, leaving an eccentricity of ${\cal O}(0.1)$ within the detection band of ground-based gravitational wave detectors.

Figures (10)

• Figure 1: Cloud common envelope formation. For comparable mass-ratio binaries, a cloud is expected to be bounded by its own host black holes when the orbital separation is much larger compared to the cloud. As the orbit decays, the clouds may undergo mass transfer and eventually form a common envelope surrounding the binary.
• Figure 2: Energy levels of the molecular eigenstates. The vertical and horizontal axes show the dimensionless energy $\tilde{\epsilon} \equiv \epsilon_{n \ell m}/\mu\alpha^2$ and dimensionless orbital semimajor axis $\tilde{a} \equiv a/r_B$. The upper and the lower plots show the energy levels with $q=1$ and $q=2/3$ respectively. For $q=1$, the system is symmetric under reflection, which breaks when $q \neq 1$. As a result, each energy level in the upper plot splits into two levels in the lower plot.
• Figure 3: Couplings between molecular eigenstates. The vertical axis shows $\tilde{\eta}_{ij}/\tilde{a}$, where $\tilde{\eta}_{ij} = \eta_{ij}/\Omega$ which scales with $\tilde{a}$ at large separation limit.
• Figure 4: Semimajor axis of orbits at eccentricity-induced resonant transitions. In these plots, the colored lines show the energy difference between the considered states ($\ket{100}$, $\ket{210}$, $\ket{200}$, $\ket{320}$, and $\ket{21\pm1}$) and their coupling states with $n \le 4$. The black lines show the averaged orbital frequency. The eccentricity-induced resonant transitions are expected to happen near the intersects of the colored lines and black dashed lines.
• Figure 5: Integrals in Eqs. \ref{['depconq']} and \ref{['depcon']}. The vertical axis shows ${\rm I}_x (a) = \left(\frac{a}{r_B}\right)^x G^2M^2 \eta^2/\alpha^6$, where colors of curves represent conditions for various mass ratios ($q=0.5$, $0.75$, $1$, $1.25$ and $1.5$ ) with corresponding powers.