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, $\varphi$ and $\chi$, with a coupling term $\frac{1}{2}\lambda \varphi {\chi }^2$, which is motivated by the multiple-axion framework. The ultralight scalar $\varphi$ forms a cloud that efficiently produces $\chi$ particles nonperturbatively via parametric resonance, with a large mass hierarchy, ${\mu }_{\chi }\gg {\mu }_{\varphi }$. Rather than escaping the system as investigated by previous studies, these $\chi$ particles remain bound, orbiting the black hole. Moreover, the particle production occurs primarily at the peak of the cloud's profile, allowing $\chi$ particles in quasicircular orbits to pass repeatedly through resonant regions, leading to cumulative amplification. This selective process naturally forms a dense ring of $\chi$ particles, with a mass ratio to the cloud fixed by $({\mu }_{\varphi }/{\mu }_{\chi }{)}^2$. 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

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