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% 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. 1. INTRODUCTION Information about the three-dimensional shape of a galaxy is lost when the galaxy is projected onto the plane of the sky. This loss of information is acute in the case of elliptical galaxies, whose apparent shapes are elliptical but whose intrinsic shapes could be oblate, prolate or fully triaxial. Beginning with Hubble (1926), many attempts have been made to deduce the distribution of intrinsic shapes of elliptical galaxies from the distribution of their apparent shapes, under the assumption of random orientations. This inverse problem has a formally unique solution if galaxies belong to a one-parameter family of shapes, e.g. oblate or prolate, but is degenerate if galaxies are triaxial. Thus a statistical approach is limited in what it can tell us about elliptical galaxy intrinsic shapes. More recently, the emphasis has been directed toward increasing the quality of the data and the uniformity of the samples. Binney & de Vaucouleurs (1981) analyzed the ellipticities of 1750 galaxies in the Second Reference Catalogue. They found satisfactory agreement with the oblate, prolate and triaxial hypotheses. Ryden (1992) used CCD surface photometry of a sample of 171 bright ellipticals from Djorgovski (1985) to derive accurate, luminosity-weighted axis ratios. She then explored the degree to which these data could be described by a family of Gaussian frequency functions for the intrinsic shapes. In her best-t model, the mode of the distribution lay near oblate