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Two types of boson stars in $U(1)$ gauged $3+1$-dimensional $O(3)$ sigma-model

We investigate boson stars in an $O(3)$ scalar field theory with a symmetry-breaking potential. By constructing numerically spherically symmetric solutions, we demonstrate that the model gives rise to a rich set of field configurations. The negative coupling constant of the scalar self-interactions allows for two types of boson stars: Type I solutions represent the usual boson stars, that emerge from the vacuum as the boson frequency is decreased below the boson mass, whereas type II boson stars emerge from a set of static soliton solutions. Depending on the strengths of the gravitational and the electric coupling constants, both types or only one type is present. At a critical set of coupling constants, both types undergo a bifurcation. There the spirals of both types disconnect from their branches and reconnect with each other, while the remaining branches of both types also reconnect with each other.