A sine-Gordon soliton star model with a mix of dark energy and Fermi matter is studied in the two-dimensional Brans-Dicke gravity model. The phase structure is analysed for a strong-coupling Thirring model. Subsequently, a soliton star model with cool Fermi matter coupling is constructed. We found that the soliton state and the mass of a star can change the density and pressure of matter at certain temperatures. Moreover, the stability of dark energy in the center of a star is proved when the coupling coefficient of the scalar field and Fermi matter satisfies some constraint conditions.
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