Radial linear stability of nonrelativistic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>ℓ</mml:mo></mml:math>-boson stars
Armando A. Roque, Emmanuel Chávez Nambo, Olivier Sarbach
Abstract
We study the linear stability of nonrelativistic $\ensuremath{\ell}$-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 $\ensuremath{\ell}$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ensuremath{\ell}+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ensuremath{\ell}$, 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.