The ellipticity of the disks of spiral galaxies

The disks of spiral galaxies are generally elliptical rather than circular. The distribution of ellipticities can be fitted with a lognormal distribution. For a sample of 12,764 galaxies from the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), the distribution of apparent axis ratios in the i band is best fit by a lognormal distribution of intrinsic ellipticities with ln epsilon = -1.85 +/- 0.89. For a sample of nearly face-on spiral galaxies analyzed by Andersen & Bershady using both photometric and spectroscopic data, the best-fitting distribution of ellipticities has ln epsilon = -2.29 +/- 1.04. Given the small size of the Andersen & Bershady sample, the two distributions are not necessarily inconsistent with each other. If the ellipticity of the potential were equal to that of the light distribution of the SDSS DR1 galaxies, it would produce 1.0 mag of scatter in the Tully-Fisher relation, greater than is observed. The Andersen & Bershady results, however, are consistent with a scatter as small as 0.25 mag in the Tully-Fisher relation.