Stability and collisions of excited spherical boson stars: glimpses of chains and rings

TL;DR

This work demonstrates that excited spherical boson stars in the Einstein-scalar system exhibit a non-spherical instability under generic 3+1D perturbations, with stronger self-interactions ($\Lambda$) generally accelerating the instability rather than stabilizing it. By performing 3+1D evolutions, the authors show that fundamental stars remain robust, whereas excited states can decay to a ground-state configuration or fragment into non-spherical remnants. In head-on collisions, the remnant outcome depends on the total mass: above the maximum ADM mass leads to black holes, while sub-threshold cases yield either a fundamental boson star or a non-spherical chain/ring remnant for excited stars, the latter connecting dynamically to equilibrium chains/rings found in Liang:2025myf. The findings imply limited astrophysical viability for long-lived excited states and highlight rich non-spherical dynamics and GW signatures that depend on excitation and self-interaction strength, enriching the phenomenology of compact scalar objects.

Abstract

Scalar, spherically symmetric, radially excited boson stars were previously shown to be stabilized, against spherical dynamics, by sufficiently strong self-interactions. Here, we further test their stability now in a full 3+1D evolution. We show that the stable stars in the former case become afflicted by a non-spherical instability. Then, we perform head-on collisions of both (stable) fundamental and (sufficiently long-lived) excited boson stars. Depending on the stars chosen, either a black hole or a bosonic remnant are possible. In particular, collisions of excited stars result in a bosonic bound state which resembles a dynamical superposition of chains and rings, akin to the ones found as equilibrium solutions in Liang:2025myf. These evolutions emphasize a key difference concerning the dynamical robustness of fundamental vs. excited spherical boson stars, when generic (beyond spherical) dynamics is considered.

Figures (22)

• Figure 1: ADM mass $vs.$ the frequency for boson star solutions with four different values of $\Lambda$ and different values of the radial excitation number $n$. Solid curves correspond to fundamental boson stars, dashed curves to $n=1$ and dotted curves to $n=2$. The vertical lines indicate the frequencies of the solutions we considered.
• Figure 2: Grid structure, in units of $\mu$, for a head-on collision of stars with $n=2,\ \omega=0.98,\ \Lambda=100$ (solutions IX), and the energy density of the scalar field ($\mu^{-2}\rho_K$).
• Figure 3: Initial and final state (during the time evolution) of solution II (see \ref{['solutions']}), with $n=0,\ \omega=0.90,\ \Lambda=125$. The snapshots show the $xy$ plane (in units of $\mu$) and the colour code is assigned to the energy density of the scalar field ($\mu^{-2}\rho_K$).
• Figure 4: Evolution of the scalar field energy $E_\Phi$ of the stable star shown in \ref{['ground-stable']}.
• Figure 5: Violation of the L2-norm of the Hamiltonian (left) and of the Hamiltonian constraint along $x$ in a constant $t$ hypersurface (right) for the same star shown in Figures \ref{['ground-stable']} and \ref{['komar-mass']}.