My results indicate that the tidal force from a satellite similar to the LMC produces a significant tilt in the galactic disk. Over two orbital times, a massive ~1010 Mu satellite (Schommer et al. 1992) tilts the disk by roughly 2, corresponding to ~900 pc at R = ~25 kpc (Figures 17, 18, and 19). The amplitude increases with radius; the outer edge of the disk tilts to ~1.5 kpc at R = 32 kpc (Figure 16). In agreement with the geometry of the Galaxy's warp, the tilt occurs primarily along the orbital plane of the satellite with the near disk edge tilted towards the location of perigalacticon (Figure 19). The lighter ~109 Mu satellite tilts the disk by only 0.5; closer determination of the LMC's mass is critical.
In concordance with Weinberg's (1995) attempt to link the LMC with the Galaxy's warp, the satellite influences the disk too weakly to fully account for the warp's observed magnitude. However, the response found here (0.9 kpc) is half again that found by Weinberg (0.6 kpc), falling short of the warp's observed magnitude (1.5 kpc) by roughly a third.
This shortfall may occur because the simulations follow only 2 orbits. The LMC's orbital period is between 1 and 2 Gyr, permitting 4 or 5 orbits since the formation of the disk 8 Gyr ago. Successive satellite passages may reinforce a tilt if damping forces require greater than 2 Gyr, allowing a gradual enhancement of the warp over the past 8 Gyr. The simulations show the dominant tidal response to occur in the gaseous material at the edge of the disk, thus the warp may be enhanced or sustained by gas infalling along tilted planes.
In general, these simulations show that a massive orbiting satellite generates a small warp in its primary. Larger warps (Figure 1) might result from satellite infall, both from direct tidal force as the satellite draws close to the galaxy, and from orbital coupling as the satellite's orbit approaches the galactic plane.
On the results of the simulations presented herein, I conclude that the Large Magellanic Cloud is a partial, if not the primary, contributor to the Milky Way's warp. The massive halo amplifies the tidal force far beyond Hunter and Toomre's (1969) predictions. Further simulations of several orbital periods should settle this 40 year old contention.
While the most luminous satellite, the LMC is not the only source of tidal force. Static force calculations (Appendix E) indicate that the ~108 Mudwarf spheroidal in Sagittarius exerts a direct tidal force equivalent to that of the LMC due to the dwarf's proximity and low orbital inclination. Perigalacticon passage of this satellite at ~15 kpc will strongly perturb the disk, punching a hole through the gaseous disk. While its low mass only weakly perturbs the halo, the satellite's low inclination orbit may permit disk resonances, enhancing the tidal effects.
Is it a coincidence that the strong asymmetry of the Galaxy's warp occurs around the distance of this satellite's perigalacticon? Could the direct passage of this low-luminosity satellite through the disk account for the warp's asymmetry?
There is no need to maintain warps for the entire age of the universe, as coherent disks formed only ~8 Gyr ago. Still, this period appears oppressively long for primordial warps considering the constraints imposed by the winding time presented by Binney (1992), the halo/disk settling time computed by Dubinski and Kujiken (1995), and the frictional damping time calculated by Nelson and Tremaine (1995). Warps are seemingly transitory, lasting only a few Gyr at best. Evidently, ongoing galactic processes routinely induce warps.
Some warped galaxies lack a satellite equivalent to the LMC, therefore the tidal force of a massive satellite is not a necessary condition. My results indicate that the LMC is barely capable of exciting the Milky Way's small warp, confirming the inability of a distant massive satellite to induce a sizable warp as that in NGC-5907 (Figure 1). This suggests that large warps occur in response to more direct interactions, such as gaseous infall or satellite accretion. Halo infall might also be responsible for altering the fundamental axes of a triaxial halo (Binney 1992).
It is likely that warps are a generic response to minor perturbations: tidal effects from satellites, kinetic effects from accreted matter, slewing halo axes - all fundamentally related to the complex interactions between the disk and halo. These mechanisms misalign the disk from the halo and warps form naturally as a result of realignment.
The simulations presented herein make a number of potentially incorrect assumptions. Of primary concern is the very limited parameter space, in which I varied only the LMC satellite mass. Further research should explore a larger area of parameter space, both satellite parameters and halo density and distribution. New simulations could improve the model in the following ways.
The following questions arose in the course of my research and appear to be largely unexplored topics. Most relate to the evolutionary effects of the numerous low mass satellites upon their primaries.