Franx, M., van Gorkom, J., & de Zeeuw, T., 1994, Ap. J. 436, 642.
We present a new method to derive the shape of the potential from the velocity field of a gas ring, or a gas disk with a flat rotation curve. The method is an extension of previous work by Binney and Teuben, and it can detect deviations from axisymmetry at the level of a few percent. The velocity field of the ring or disk is expanded into harmonics, and we present analytic expressions which relate these harmonic terms to the intrinsic parameters, and the viewing angles. We show that both the velocity field and the geometry of the ring are necessary to give complete information on the shape of the potential in the plane of the ring. The velocity field alone gives incomplete information for small ellipticities. We present new neutral hydrogen data on the H I ring around the early-type galaxy IC 2006, which was discovered by Schweizer, van Gorkom, & Seitzer (1989). The new data show that the ring is filled and has a remarkably regular velocity field. Application of our method to this gas ring shows that the halo must be close to perfectly axisymmetric. We detect a nonsignificant ellipticity of the potential of 0.012 +/- 0.026. The 95% confidence limit on the ellipticity is 0.05. This implies that the potential is nearly circular in the plane of the ring. The analysis indicates that the circular velocity is nearly constant from 0.5 R(sub e) to 6.5 R(sub e). We confirm that the M/L ration in the outer parts increases (Schweizer et al. 1989). The stellar component probably has a strong disk. The data demonstrate that galaxies other than spiral galaxies have massive halos. The inferred shape of the halo can be contrasted to the strongly triaxial halos found in simulations of dissipationless halo formation. As suggested by Katz & Gunn (1991), the inclusion of baryonic matter in the simulations may be necessary to resolve this issue.