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In this paper we report the structure of solitonic quark stars, based on current hadron models. The fields include a particle field, a background field and a complex field. Relativistic Tolman- Oppenheimer-Volkoff equatiions have been obtained. This set of equations provides a convenient framework to study the structure of solitonic quark stars, which consist of quark matter confined within a false vacuum. This false vacuum phase is separated from the ground state (a true vacuum phase and the neutron matter) by both a volume energy and a surface energy. Similar descriptions of false vacuum states have been successfully applied to hadron models (the standard model). In this work we have demonstrated that solitonic stars which are dominated by a volume energy reduce to quark stars while those dominated by a volume energy reduce to soliton stars. In a solitonic quark star, the limiting mass (such as the Chandrasekhar mass limit) is dependent on the contribution from the surface energy and can vary over a wide range, from a few to over $10^9$ solar masses.
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