Understanding the Quantized Angular Momentum of Rotating Q-balls

Abstract

Non-topological solitons, such as Q-balls, may contribute to the cosmological dark matter. The formation and evolution of Q-balls in the early universe requires an understanding of solitons with nonzero angular momentum. We derive (rather than assume) the schematic form of the scalar field configurations that produce rotating Q-balls, which produce their well known quantized angular momentum. This analysis leads to additional insight into the properties of these rotating solitons, including a method for computing their characteristic angular velocity. By considering rotating solitons in two spatial dimensions, we investigate these attributes concretely. We develop analytical approximations for the solitons and their defining quantities. We show that they agree with numerical results and exhibit the general properties of rotating solitons.

Figures (12)

• Figure 1: Left: Plot of the effective potential $V(f)$ for several values of $\kappa$ and the particle trajectory related to the soliton solution. Right: Q-disk profiles for the corresponding $\kappa$ values.
• Figure 2: Comparison of the numerical solution (blue), transition function (orange), and full analytic approximation (dashed green) for $\kappa=0.5$ (left) and $\kappa=0.7$ (right).
• Figure 3: Comparison of the numerical solution (blue), transition function (orange), and full analytic approximation (dashed green) for $\kappa=0.1$ (left) and $\kappa=0.3$ (right).
• Figure 4: Left: Plot of the potential $V_N(f,\overline{r})$ at various values of $\overline{r}$ for $\kappa = 0.2$ and $N = 2$. Right: Soliton profile for the same parameter values. The black dots denote the value of the soliton profile at steps of integer $\overline{r}$.
• Figure 5: Numerical Q-ring profiles $f$ computed for various $N$ and $\kappa$. Horizontal and vertical scales of each plot differ. The horizontal gray line marks the analytical approximation for the Q-ring profile height.