On the radial linear stability of nonrelativistic $\ell$-boson stars

TL;DR

This paper investigates the linear stability of nonrelativistic $ ext{l}$-boson stars, revealing that ground states are stable while excited states have multiple unstable modes, using combined analytical and numerical methods.

Contribution

It provides the first detailed stability analysis of $ ext{l}$-boson stars, identifying stability properties of ground and excited states within the Schrödinger-Poisson framework.

Findings

Ground states are linearly stable.

Excited states have $2n$ unstable modes.

All excited states are saddle points of the energy functional.

Abstract

We study the linear stability of nonrelativistic $\ell$-boson stars, describing static, spherically symmetric configurations of the Schr\"odinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ell$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ell+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ell$, the ground state is linearly stable, whereas the $n$'th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.