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 a galactic tidal encounter and also during the galaxy formation process. The self-gravitational potential corresponding to the self-consistent, non-axisymmetric density response of the disk is obtained by inversion of 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 0.75 - 0.9 for a wide range of galaxy parameters. The reduction is negligible at all radii for higher harmonics (m > or = 3) of the halo potential. (abridged).