$Q$-ball superradiance: Analytical approach

TL;DR

This paper develops an analytical method to study superradiance in $Q$-balls, revealing how wave amplification depends on $Q$-ball properties and providing insights into the spectrum's structure.

Contribution

It introduces a perturbative analytical approach using Bessel functions to analyze wave scattering and superradiance in $Q$-balls, improving understanding and computational efficiency.

Findings

Amplification factors for thin-wall $Q$-balls are sinusoidal functions.

Peak spacing at high frequencies equals the inverse of $Q$-ball size.

The analytical method clarifies the spectrum's multi-peak structure.

Abstract

It was recently discovered that waves scattering off a $Q$-ball can extract energy from it. We present an analytical treatment of this process by adopting a multi-step function approximation for the background field, which yields perturbative solutions expressed in terms of Bessel functions. For thin-wall $Q$-balls, the amplification factors reduce to simple sinusoidal functions, which explains the multi-peak structure of the spectrum and identifies the physical quantities that determine it. For instance, at high frequencies, the peak spacing is simply the inverse of the $Q$-ball size. The analytical solution further enables us to delineate the full range of possible amplification factors. For general $Q$-balls, this analytical framework also substantially improves the efficiency of evaluating the amplification factors.