Abstract
Chandrasekhar's (1933) paper on rotational distortion of polytropes contained a perturbation term in the potential which was linear inv, the rotation parameter. The same paper, and subsequent papers by various authors, developed an analytic expression for the boundary also linear inv. The latter expression is equivalent to a two term Taylor series about the unperturbed boundary, and is in error by 12% near critical rotation, for a polytropic index 3.0. The boundary can be located directly from the functions representing density, potential, and the potential gradient. The boundary error by this procedure is 0.2% near critical rotation.
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Linnell, A.P. Rotational distortion of polytropes by analytic approximation, II. Astrophys Space Sci 48, 165–183 (1977). https://doi.org/10.1007/BF00643048
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DOI: https://doi.org/10.1007/BF00643048