Annu. Rev. Astron. Astrophys. 1992. 30: 51-74 Copyright © 1992 by Annual Reviews. All rights reserved

9. CONCLUSIONS

Warps continue to be a fascinating puzzle. There seems little doubt that they are trying to tell us something about the halos which dominate their dynamics, and about the later stages of galaxy formation. But there is still no consensus as to what exactly their message is.

The key to understanding warps is a knowledge of how a self-gravitating disk evolves from an initially warped configuration. This is fundamentally an initial-value problem, but most theoretical work in the field has focused on determining the low-order normal modes of centrifugally supported disks. This is unfortunate since the connection between normal modes and the initial-value problem of a stellar system is complex and by no means fully understood. Though the jury is still out, it is unlikely that real galaxies have discrete warping modes. If these existed, they would ensure that warps could be immortal. But their non-existence by no means rules out the possibility that the disks of galaxies have long-lived collective oscillations that resemble warps. These would eventually die away if galaxies were island universes. But galaxies are neither dynamically old nor isolated, and their oscillations may be excited often enough to remain conspicuous most of the time.

The question of what the long-lived collective oscillations of galaxies might be becomes considerably more complex when one bears in mind that the disk is presumably embedded in a more massive and extensive halo. Conceptually the simplest potentially long-lived oscillation of a disk/halo system is a simple misalignment of the symmetry planes of the visible galaxy and the enveloping halo. In such a case the inner galaxy precesses with respect to the halo, and the warp arises at the interface between these two units. If this precession were unaffected by Landau damping, it would consitute a normal mode. Actually the motion is almost certain to damp, and the status of existing normal mode calculations, which treat the halo as a rigid object, must be considered doubtful. It should be possible to obtain a very much better understanding of this problem than we currently have by studying suitable n-body simulations.

Is it reasonable to picture the halo as made up of inner and outer bits in steady mutual precession? What about the more complex irregularities and time-dependencies that are inevitable if the Universe is flat and galaxies are perpetually growing and merging?

The question here is one of scale. Far enough from visible galaxies, halos must be chaotically time-dependent and full of moving lumps of every size. Do these disturbances propagate in to the radii R₂₅ at which warps begin?

The overall scale of an L halo is certainly enormous: 1 Mpc. On the other hand infall places material on deeply plunging orbits which typically penetrate to within ~ 100 kpc of the center. Also infalling gas will dissipate most of its potential energy and settle to orbits of radius ~ 150 kpc even if it surrenders none of its original angular momentum. In the likely event that it does surrender angular momentum to the halo, the orbits of freshly accreted gas may well be at radii typical of warps. So it is by no means inconceivable that warps are in direct physical contact with material that is only now joining the galactic system.

An intriguing feature of infall is the speed with which it reorientates the net angular momentum vectors of galaxies; there is every indication that a typical overall spin vector swings through a full 180° with each doubling of the Hubble time. Does the spin axis of the visible galaxy follow the fluctuations of the overall spin vector, or does it get out of step and now point in a direction unrelated to the direction of the current overall spin vector? In either case it must be subject to a torque which will warp the disk such that the line of nodes is parallel to the applied torque. In the first case the direction of the applied torque is directly related to the current infall pattern. In the second case it may be better to think in terms of perpetually excited, damped precession.

Over the next few years large n-body simulations of cosmic clustering and galaxy formation such as are now under way in a number of places should greatly clarify these issues. These simulations have already demonstrated that the infall process is very far from spherically symmetric, being concentrated into filaments that behave rather like cosmic rivers. The gravitational field which drives matter into and then down these filaments is by no means locally generated, and in these circumstances it is unclear how useful the predictions of the spherical infall model will prove to be. So the final picture of the relation between warps and disturbed halos may well differ considerably from that outlined here. But one's best guess must be that warps will in the end prove to be valuable probes of cosmic infall and galaxy formation.