Accretion Disk Perturbations and Their Effects on Kerr Black Hole Superradiance and Gravitational Atom Evolution

TL;DR

This paper models how accretion disk perturbations influence Kerr black hole superradiance and gravitational atom evolution, revealing environmental effects that impact the growth and detectability of ultralight bosons.

Contribution

It introduces a three-level Hamiltonian model incorporating disk-induced perturbations, highlighting how symmetries and static or dynamic disk features affect superradiance.

Findings

Quadrupolar tidal fields cause energy level shifts and mode mixing.

Transient spiral waves can suppress superradiance by populating decaying modes.

Static warps can create narrow growth gaps and enhance superradiance near degeneracies.

Abstract

Kerr black hole (BH) superradiance can form gravitational atoms and produce characteristic gravitational-wave signals, providing a probe of ultralight bosons and dark matter. In realistic systems, accretion-disk gravity can shift energy levels and mix states, modifying the effective superradiant growth. We model the disk as a weak external perturbation via a multipole expansion and derive an effective three-level Hamiltonian for the $n=2$ subspace $\{\ket{211},\ket{210},\ket{21-1}\}$ in the weak-coupling regime. The leading disk effect is the quadrupolar ($\ell_d=2$) tidal field, whose symmetries fix the selection rules: axisymmetry gives only diagonal shifts, equatorial nonaxisymmetry activates $\Delta m=\pm2$ mixing ($\ket{211}\leftrightarrow\ket{21-1}$), and breaking equatorial reflection opens $\Delta m=\pm1$ couplings involving $\ket{210}$. As illustrations, a transient equatorial $m=2$ spiral wave drives the resulting two-level system and can suppress or quench superradiance by populating a decaying mode, while a quasi-static warp produces full three-level mixing and can generate narrow ``growth gaps'' near accidental near-degeneracies, with the same static reshuffling also allowing enhancement when weight shifts toward the growing mode. These findings demonstrate that accretion disk perturbations are a crucial environmental factor in determining the dynamics of BH superradiance and the evolution of boson clouds, thereby providing a more reliable theoretical basis for assessing the detectability of ultralight bosons in realistic astrophysical settings.