The frequency function of elliptical galaxy intrinsic shapes

We present fully nonparametric estimates of the frequency function of elliptical galaxy intrinsic shapes under the axisymmetric and triaxial hypotheses. If elliptical galaxies are assumed to be oblate or prolate, the frequency function of intrinsic shapes is negative for axis ratios near unity due to the lack of apparently round galaxies. Both axisymmetric hypotheses are found to be inconsistent at the 99 percent level with the data. Triaxial intrinsic shapes are fully consistent with the data; a number of possible triaxial frequency functions are presented, some of which exhibit strong bimodality. We also compute the ``maximum entropy'' distribution of intrinsic shapes under the triaxial hypothesis