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We demonstrate that rapidly rotating bipolytropic (composite polytropic) stars and toroidal discs can be obtained using Hachisu's self-consistent field technique. The core and the envelope in such a structure can have different polytropic indices and also different average molecular weights. The models converge for high T/|W| cases, where T is the kinetic energy and W is the gravitational energy of the system. The agreement between our numerical solutions with known analytical as well as previously calculated numerical results is excellent. We show that the uniform rotation lowers the maximum coremass fraction or the Schönberg-Chandrasekhar limit for a bipolytropic sequence. We also discuss the applications of this method to magnetic braking in low-mass stars with convective envelopes.

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Monthly Notices of the Royal Astronomical Society

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