Rapidly rotating polytropes as a net of singular perturbation problems

Details Rapidly rotating polytropes as a net of singular perturbation problems Rapidly rotating polytropes as a net of singular perturbation problems

Jul 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..35..223s&link_type=abstract

Astrophysics and Space Science, vol. 35, July 1975, p. 223-240.

Mathematics

17

Astronomical Models, Asymptotic Series, Perturbation Theory, Singularity (Mathematics), Stellar Rotation, Angular Velocity, Boundary Conditions, Boundary Value Problems, Chandrasekhar Equation, Mathematical Models

Scientific paper

An analytical technique is presented which completely solves the problem of rotating polytropes. The singularity in the Chandrasekhar expansion is fully taken into account and successfully treated, 'impossible' nonlinear integrations are avoided, and the esthetically displeasing numerical-patching procedures are replaced by a more fundamental asymptotic-matching process. It is shown that the basic Chandrasekhar expansion is only locally valid and must be supplemented by additional locally valid expansions. It is found that an asymptotic-matching principle supplying the missing constraints is obtained despite the insufficient boundary conditions of the additional expansions for unique determination because each expansion is derived in principle from the same exact solution. The case of a 'convective polytrope' with n = 1.5 is analyzed in detail, and third-order results are given which seem to have a maximum error of 1/18%.

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