HI velocity fields and the shapes of dark matter halos

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A new method for measuring deviations from axisymmetry in the velocity fields of gas disks is presented. The method is an extension of the method that Franx, van Gorkom and de Zeeuw developed for a single orbit gas ring. The measurement is based upon a higher order harmonic expansion of the full velocity field. Epicyclic theory is used to calculate the effects of a perturbation in the potential on these harmonic terms. It is shown how the s₁ and s₃ harmonics can be used to measure epsilonᵣ sin(2 phiobs), where epsilonᵣ is the elongation of the potential and phiobs is an (unknown) viewing angle. As a demonstration, I applied this method to the HI velocity fields of two spiral galaxies, NGC 2403 and NGC 3198.