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Assessment of the Roche and the Darwin–Radau Approximations for Rotating Astrophysical Objects

Assessment of two of the frequently used approximations for rotating astrophysical objects, the Roche and the Darwin–Radau approximations, is performed by comparing the rotational frequencies computed by these approximations with those of self-consistent numerical hydrostatic solutions. Overall, the Darwin–Radau approximation performs better, though the error increases as the rotational oblateness increases. It should be also remarked that the Darwin–Radau approximation does not provide a closed-form formula of the frequency as a function of the oblateness.