Mathematics
Scientific paper
Sep 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..43..411s&link_type=abstract
Astrophysics and Space Science, vol. 43, Sept. 1976, p. 411-424.
Mathematics
11
Coordinate Transformations, Polytropic Processes, Stellar Models, Stellar Rotation, Asymptotic Methods, Perturbation Theory, Singularity (Mathematics)
Scientific paper
The equilibrium structure of rotating polytropes is considered on the basis of the Poisson and Laplace equations. It is noted that if the method of solution involves an asymptotic expansion in terms of a small parameter, singularities will appear in the solution under certain circumstances. The breakdown of the regular expansion in the vicinity of the Emden sphere is analyzed, and an alternative method is outlined which involves the introduction of strained radial coordinates. It is shown that when strained coordinates are used in this problem, the Poisson and Laplace domains are defined explicitly in terms of the strained variable. Matching with the exterior solution is examined, and the straining functions are determined to third order. Numerical results for a polytrope with an index of 1.5 are presented and compared with those obtained by Smith (1975) through the method of matched asymptotic expansions. The two sets of results are found to be in excellent agreement.
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