Unified view of scalar and vector dark matter solitons

Abstract

The existence of solitons -- stable, long-lived, and localized field configurations -- is a generic prediction for ultralight dark matter. These solitons, known by various names such as boson stars, axion stars, oscillons, and Q-balls depending on the context, are typically treated as distinct entities in the literature. This study aims to provide a unified perspective on these solitonic objects for real or complex, scalar or vector dark matter, considering self-interactions and nonminimal gravitational interactions. We demonstrate that these solitons share universal nonrelativistic properties, such as conserved charges, mass-radius relations, stability and profiles. Without accounting for alternative interactions or relativistic effects, distinguishing between real and complex scalar dark matter is challenging. However, self-interactions differentiate real and complex vector dark matter due to their different dependencies on the macroscopic spin density of dark matter waves. Furthermore, gradient-dependent nonminimal gravitational interactions impose an upper bound on soliton amplitudes, influencing their mass distribution and phenomenology in the present-day universe.

Figures (5)

• Figure 1: Fractional difference between the mass radius $\widetilde{R}_s$ and the particle radius $\widetilde{R}_s^{\xi=0}$, which enclose $95\%$ of the total mass or particle number of solitons.
• Figure 2: Mass-radius relation for solitons with SIs and negligible NGIs. Solid lines are obtained numerically and corresponding gray dashed lines are analytical approximations based on \ref{['soliton_mr_si']}.
• Figure 3: Mass-radius relation for solitons with NGIs. Solid lines are obtained numerically and corresponding gray dashed lines are predictions by \ref{['soliton_mr_ngi']}. Two dots represent solitons with the critical amplitude \ref{['critical_amp']}, beyond which no soliton solutions exist. For $\widetilde{\xi}<0$, the maximum mass and smallest radius of stable solitons correspond to the turnover point described by \ref{['soliton_turnover_ngi']}. For $\xi>0$, the maximum mass and smallest radius of solitons are given by \ref{['critical_point_ngi']}.
• Figure 4: Field (left) and density (right) profiles of solitons. The solid lines represent the critical solitons, characterized by central amplitudes approaching \ref{['critical_amp']} and central densities diverging to $\pm \infty$. The (blue) dashed lines correspond to the marginally stable soliton for $\widetilde{\xi}<0$, with the mass given by \ref{['soliton_turnover_ngi']}. The (orange) dotted lines represent the soliton with vanished density $\rho_\xi$ at the center.
• Figure 5: Mass-radius relation for solitons with gradient-dependent SIs. The notation follows that of figure \ref{['fig:mrrelationngi']}.