Ring formation from black hole superradiance through repeated particle production on bound orbits

Abstract

Ultralight bosonic fields around a rotating black hole can extract energy and angular momentum through the superradiant instability and form a dense cloud. We investigate the scenario involving two scalar fields, $\ddot{I}•$ and $\ddot{I}‡$, with a coupling term $\frac{1}{2}\hat{I}»\ddot{I}•\ddot{I}{‡}^2$, which is motivated by the multiple-axion framework. The ultralight scalar $\ddot{I}•$ forms a cloud that efficiently produces $\ddot{I}‡$ particles nonperturbatively via parametric resonance, with a large mass hierarchy, $\hat{I}{¼}_{\ddot{I}}‡\gg \hat{I}{¼}_{\ddot{I}}•$. Rather than escaping the system as investigated by previous studies, these $\ddot{I}‡$ particles remain bound, orbiting the black hole. Moreover, the particle production occurs primarily at the peak of the cloud's profile, allowing $\ddot{I}‡$ particles in quasicircular orbits to pass repeatedly through resonant regions, leading to cumulative amplification. This selective process naturally forms a dense ring of $\ddot{I}‡$ particles, with a mass ratio to the cloud fixed by $(\hat{I}{¼}_{\ddot{I}}•/\hat{I}{¼}_{\ddot{I}}‡{)}^2$. Our findings reveal a novel mechanism for generating bound-state particles via parametric resonance, which also impacts the evolution of the cloud. This process can be probed through its imprint on binary dynamics and its gravitational-wave signatures.

13 pages, 5 figures. Added minor corrections. Version accepted for publication in PRD