Dynamics in a Lopsided Spiral Galaxy: Negative Disk Response to Perturbation Halo Potential

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Abstract
We study the self-consistent response of an axisymmetric galactic disk perturbed by a constant lopsided (m = 1) halo potential and show that the disk self-gravity plays a crucial role in the determination of the net lopsided distribution in the disk. First, the self-gravitational potential corresponding to the nonaxisymmetric density response of the disk to the lopsided potential is calculated, by inversion of the Poisson equation for a thin disk, and this is shown to be negative, that is, it opposes the lopsided halo potential. Next, the net stellar disk response is obtained self-consistently so as to take account of the effect of both the imposed lopsided potential and also the disk response potential. The magnitude of the net lopsided potential in the galactic disk plane is shown to be always smaller than that of the perturbation lopsided potential. The perturbation potential is reduced by a factor that is independent of the strength of the perturbation potential. This factor has a minimum value of ~0.5-0.7, which is insensitive to the morphological type and size of the galaxy. The net lopsided distribution in the disk is shown to be important only beyond a radius of 1.4 disk scale lengths, and its magnitude increases with radius, indicating the increasing dynamical importance of the halo over the disk at larger radii. This is a robust dynamical result and is independent of the logarithmic slope of the rotation curve. This result is in exact agreement with the observations of stellar disks by Rix & Zaritsky (1995). It also provides a natural explanation as to why lopsidedness in the atomic hydrogen gas is observed mainly in the outer disk.