Self-consistent response of a galactic disk to an elliptical perturbation halo potential

We calculate the self-consistent response of an axisymmetric galactic disk perturbed by an elliptical halo potential of harmonic number m = 2 and obtain the net disk ellipticity. Such a potential is commonly expected to arise due to galactic tidal encounter and also during the galaxy formation process. The self-gravitational potential corresponding to the self-consistent, nonaxisymmetric density response of the disk is obtained by inversion of the Poisson equation for a thin disk. This response potential is shown to oppose the perturbation potential because physically the disk self-gravity resists the imposed potential. This results in a reduction in the net ellipticity of the perturbation halo potential in the disk plane. The reduction factor denoting this decrease is independent of the strength of the perturbation potential and has a typical minimum value of similar to0.75-0.9 for a wide range of galaxy parameters. The reduction is most important at 1.4 exponential disk scale lengths and is progressively less so at higher radii. For the solar neighborhood region of the Galaxy, the reduction factor is 0.8. Beyond twice the Holmberg radius, the reduction is negligible, and there the disk asymmetry in the atomic hydrogen gas traces the true ellipticity of the halo potential. The reduction is negligible at all radii for higher harmonics (m greater than or equal to 3) of the halo potential. On correcting for the negative disk response, the true ellipticity of the halo potential for a typical spiral galaxy is shown to be higher by similar to 20% than the typical halo ellipticity of less than or equal to0.1. deduced in the literature from observations of isophotal or kinematical asymmetry of disks.