Estimate of the superradiance spectrum in dispersive media

In 2016, the Nottingham group detected the rotational superradiance effect. While this experiment demonstrated the robustness of the superradiance process, it still lacks a complete theoretical description due to the many effects at stage in the experiment. In this paper, we shine new light on this experiment by deriving an estimate of the reflection coefficient in the dispersive regime by means of a Wentzel-Kramers-Brillouin analysis. This estimate is used to evaluate the reflection coefficient spectrum of counter-rotating modes in the Nottingham experiment. Our finding suggests that the vortex flow in the superradiance experiment was not purely absorbing, contrary to the event horizon of a rotating black hole. While this result increases the gap between this experimental vortex flow and a rotating black hole, it is argued that it is in fact this gap that is the source of novel ideas. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.