MEASURING NON-AXISYMMETRY IN SPIRAL GALAXIES

We present a method for measuring small deviations from axisymmetry of the potential of a filled gas disc. The method is based on a higher o rder harmonic expansion of the full velocity field of the disc. This e xpansion is made by first fitting a tilted-ring model to the velocity field of the gas disc and subsequently expanding the velocity field al ong each ring into its harmonic terms, We use epicycle theory to deriv e equations for the harmonic terms in a distorted potential. The phase of each component of the distortion can vary with radius. We show tha t if the potential has a distortion of harmonic number m, the velocity field as seen on the sky exhibits an m - 1 and m + 1 distortion. As i s to be expected, the effects of a global elongation of the halo are s imilar to an m = 2 spiral arm. The main difference is that the phase o f the spiral arm can vary with radius, Our method allows a measurement of epsilon(pot) sin 2 phi(2), where epsilon(pot) is the elongation of the potential and phi(2) is one of the viewing angles. The advantage of this method over previous approaches to measure the elongations of disc galaxies is that, by using H I data, one can probe the potential at radii beyond the stellar disc, into the regime where dark matter is thought to be the dominant dynamical component. The method is applied to the spiral galaxies NGC 2403 and 3198 and the harmonic terms are m easured up to ninth order. The residual velocity field of NGC 2403 sho ws some spiral-like structures. The harmonic analysis indicates that t he m = 3 term is dominant, with an average value of similar to 0.02v(c ). This is consistent with an average ellipticity of the potential of epsilon(pot) sin 2 phi(2) = 0.064 +/- 0.003, but spiral arms may coupl e significantly to this result. In the harmonic analysis of the kinema tics of NGC 3198 the m = 2 and m = 3 terms are strongest (similar to 0 .01v(c)), The inferred average elongation of the potential is 0.019 +/ - 0.003. Since the amplitude of the elongation is coupled to the viewi ng angles and may be influenced by spiral arms, more galaxies should b e examined to separate these effects from true elongation in a statist ical way.