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

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The essence of a warp is that the angular momentum vector of the outer disk is not aligned with that of the inner disk. If galaxies are endowed with their angular momentum by tidal torques, such misalignments arise naturally in any cosmogony such as the popular cold dark matter theory (CDM), in which the primordial fluctuation spectrum has lots of power on small scales. To see this, follow Gunn (1977) in imagining that the galaxy is formed by the infall of successive shells of material. The tidal torque on each shell comes predominantly from shells of about twice as big (e.g., Quinn & Binney, 1991). So the angular momenta acquired by shells significantly different in size are determined by the irregularities of independent shells, and are consequently largely independent (Ryden 1988).

Since the angular momentum vectors of galaxies are generally moderately well aligned over more than a decade in radius, substantial angular momentum exchange must take place as the galaxy forms. The classical wind-up problem is a reflection of the fact that the time-scale for such exchange is less than the Hubble time out to radii of several x 10 kpc: an inclined ring exchanges and re-exchanges its skew component of angular momentum with the embedding potential every precession period. Dissipation, which is enhanced as the winding-up of a warp increases the relative motion of neighboring rings, taxes this commerce, so that it eventually dies out, and all rings relapse into a fundamental plane.

However, since the halo dominates the overall mass and angular momentum budgets, angular momentum exchange between the different shells of the halo is fundamentally more important than the angular-momentum exchanges of proto-disk material. Quinn & Zurek (1988) have studied such exchanges in n-body simulations of galaxy formation from power-spectrum fluctuations, and have shown that they are efficient, probably because a typical halo particle moves on a deeply plunging orbit, and thus contributes to the angular momentum density in many radial bins. So the existing evidence suggests that halos are well coordinated throughout the region populated by luminous material.

By contrast, both in simulations and in the real Universe, baryonic material is often found to circulate around an axis other than the spin axis of the embedding background population. For example, warped disks whose outer rings are misaligned with the surrounding halo have been seen to form in simulations of galaxy merging (Hernquist, 1989) and galaxy formation (Katz & Gunn, 1991). In the real Universe early-type galaxies are frequently found to possess rings of gas whose angular momentum vectors are highly inclined to that of the underlying stellar distribution (e.g., Bettoni & Galletta, 1991).

So it is natural that parts of any disk should form somewhat inclined to the spin axis of an embedding halo. What is surprising is that in the face of wind-up and gaseous dissipation (if the disk is not in a discrete normal mode), and of the inevitable Landau damping, such misaligned portions of a disk can remain tipped for something like the Hubble time. One is thus led to ask whether warping is not continuously regenerated as galaxies grow.

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