Subdominant Modes of Scalar Superradiant Instability and Gravitational Wave Beats

Ultralight scalars could extract energy and angular momentum from a Kerr black hole (BH) because of superradiant instability. Multiple modes labelled with $nlm$ grow while rotating around the BH, emitting continuous gravitational wave (GW). In this work, we carefully study the contribution of the subdominant modes with $n\geq 1$ in the evolution of the BH-condensate system. We find the BH still evolves along the Regge trajectory of the $n=0$ modes even with the presence of the subdominant modes. The interference of the dominant and the subdominant modes produces beats in the emitted GW, which could be used to distinguish the BH-condensate systems from other monochromatic GW sources, such as neutron stars.