ELONGATED DISKS AND THE SCATTER IN THE TULLY-FISHER RELATION

It is often speculated that the dark halos of spiral galaxies are triaxial or prolate, with the long axis pointing in the plane of the disk. This would produce a potential that is elongated in the plane of the disk. We explore the signatures produced by such deviations from axisymmetry. We find observable effects in the photometry and kinematics of the stars and gas in the disk, if substructure like bars and spiral arms can be ignored. These effects include ellipticity gradients and position angle twists in disks, velocity gradients along the apparent minor axis of the disk, differences between kinematically determined inclinations and photometrically determined inclinations, and systematic residuals in circular orbit fits to the velocity field. Noncircular gas motions produce significant scatter in the Tully-Fisher relation, amounting to 0.46 mag if the ellipticity of the potential in the plane of the disk is 0.10. Thus, small deviations from axisymmetry are sufficient to produce all or most of the observed scatter in the Tully-Fisher relation. The ellipticity of the potential in the plane of the disk must be less than 0.10 and most likely lies in the range 0-0.06. This range corresponds to an ellipticity of the density distribution of the halo between 0 and 0.16, if halos are the dominant mass component. The constraint on the shape of the dark halo is less tight in "maximum disk" models for spiral galaxies, since in these models the disk material significantly circularizes the total potential. These results imply that use of detailed kinematic information may reduce the observed scatter in the Tully-Fisher relation by 0.1 mag or more.