A Numerical Method for Generating Rapidly Rotating Bipolytropic Structures in Equilibrium

TL;DR

This paper presents a numerical method using Hachisu's technique to generate equilibrium models of rapidly rotating bipolytropic stars and disks with different core and envelope properties, with applications to stellar magnetic braking.

Contribution

It introduces a novel application of Hachisu's self-consistent field method to bipolytropic structures with varying polytropic indices and molecular weights, including high rotation cases.

Findings

Models agree well with analytical and previous numerical results.

Uniform rotation reduces the maximum core mass fraction.

The method applies to magnetic braking in low mass stars.

Abstract

We demonstrate that rapidly rotating bipolytropic (composite polytropic) stars and toroidal disks 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 core mass fraction or the Sch$\ddot{\rm{o}}$nberg-Chandrasekhar limit for a bipolytropic sequence. We also discuss the applications of this method to magnetic braking in low mass stars with convective envelopes.