Imperfect draining vortex as analogue extreme compact object

TL;DR

This paper models scalar wave interactions with an imperfect draining vortex as an analogue for extreme compact objects, revealing bound states, spectral lines, and superradiant instabilities that could be observed in future experiments.

Contribution

It introduces a novel effective boundary model for analogue ECOs, analyzing wave absorption, bound states, and superradiance with numerical and analytical methods.

Findings

Bound states cause enhanced absorption at specific frequencies.

Superradiant amplification leads to instabilities in rotating cases.

Spectral lines can characterize the effective field theory near the vortex core.

Abstract

Motivated by recent experimental progress, we study scalar wave propagation over an imperfect draining vortex, which can serve as an analogue for rotating and non-rotating extreme compact objects (ECOs). We encapsulate the absorbing properties of the analogue ECO by means of an effective boundary located around the analogue horizon. The presence of reflection at the effective boundary, characterised by a single parameter $\mathcal{K}$, allows for the existence of bound states located between the effective vortex core and the angular momentum barrier. The existence of these bound states leads to an enhanced absorption when the frequency of the incoming wave matches bound state frequencies, which result in Breit-Wigner type spectral lines in the absorption spectra. We also investigate the case of rotating analogue ECOs. In this scenario, some of the bound states undergo superradiant amplification and become unstable. In both the rotating and non-rotating case, we calculate numerically transmission/reflection spectra exhibiting the enhanced absorption/amplification. We complement our numerical study with WKB estimates as well as an extension of the P\"oschl-Teller toy model which we solve analytically. Our simple model exhibits distinctive properties which could be observed in future analogue gravity experiments. We further argue that the observation of the spectral lines could be a way to characterise the effective field theory at play in the vicinity of the vortex core.