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

1. THE OBSERVATIONAL SITUATION

Galactic disks are thin; the stellar scale height is typically 200 pc, yet on survey plates the disk will often be visible beyond 10 kpc from its center. Gaseous disks are even thinner. So even small deviations from planarity can be obvious, especially when a disk is viewed edge on.

The nearest edge-on disk is that of the Milky Way, and as soon as 21-cm surveys made it possible to study this on a Galaxy-wide scale, it became apparent that it is warped beyond the solar circle (Burke, 1957; Kerr, 1957). The line of nodes lies within ~ 10° of the Sun-center line. In the North (l 90°) the HI disk curls steadily up to over 3 kpc above the plane at R 16 kpc. In the South (l 270°) the disk curves about a kiloparsec below the plane before turning back towards the plane at R 15 kpc, nearly reaching the plane again at R 20 kpc. (Henderson et al. 1982).

The HI disk of the Galaxy's nearest giant neighbour, M31, is similarly warped, though on a grander scale: within R 25 kpc the disk is flat, but then develops an ``integral-sign'' warp that by R 30 kpc has carried the disk more than 3 kpc from the plane of the inner disk (Newton & Emerson, 1977).

The HI disk of the third largest galaxy of the Local Group, M33, is so grotesquely warped that at many points our line of sight intersects the disk twice (Rogstad et al. 1976). In this case the warping starts at R 6 kpc and develops so rapidly that the last detected hydrogen at R 10 kpc appears to be rotating about an axis inclined at 40° to the axis of the inner disk.

By the late 1970's high-resolution 21-cm maps made by large aperture synthesis telescopes showed that warping is by no means confined to the Local Group. Sancisi (1976) found that four of a sample of five edge-on galaxies have warped HI disks. Bosma (1978) studied the 21-cm velocity fields of 25 objects and concluded that eight of them are warped. He analyzed these warps with the tilted-ring model of Rogstad et al. (1974). This assumes that the disk consists of a sequence of concentric rings, each of which rotates about its own axis. The angular velocity and orientation of each ring are chosen to optimize the model's representation of the observed line-of-sight velocities over the face of the galaxy.

Bosma's study emphasized the necessity of distinguishing between features in velocity contour maps that are induced by a warp, and those due to the streamlines being elliptical, though confined to a plane. The key discriminant is the behaviour of the kinematic axes. The kinematic minor axis is defined to be the curve along which the line-of-sight motion equals the systemic velocity, while the kinematic major axis is the curve along which it peaks as a function of angle about the galactic center. The tilted disk model always predicts that the kinematic axes are mutually perpendicular since the direction along which the line-of-sight velocity of a rotating ring peaks is always perpendicular to that at which the line-of-sight velocity becomes systemic. Bosma found that 8/25 of his objects have mutually perpendicular but curved kinematic axes, and concluded that these galaxies have warped disks.

Briggs (1990) studied a sample of 12 warped objects with high-quality 21-cm data and compiled a list of rules to which these warps conform. His key rules are:

• The warp develops between R₂₅ and the Holmberg radius R_H0 (where the surface brightness in B reaches 26.5 mag arcsec^-2).

• The line of nodes tends to be straight inside R_H0.

• Outside R_H0 the line of nodes curves so as to form a loosely-wound leading spiral.

Briggs' work emphasizes that HI disks are strongly warped only where they extend far beyond the ``optical image'', i.e., the portion of the galaxy that rises above the background sufficiently to be seen on survey plates. One of Bosma's important conclusions was that HI disks generally are very extended. In fact, the admittedly rather scattered information from absorption measurements in the optical (Petitjean & Bergeron 1990) as well as the 21-cm line indicate that giant galaxies are enveloped in sheets of gas that reach at least to 100 kpc.

Given that HI disks begin to warp only where the optical disk is becoming hard to trace, it is not surprising that the evidence for warped stellar disks is limited. Moreover, much of our knowledge of warped HI disks has been deduced from velocity contour plots of a type that are not generally available for stellar disks. Nevertheless examples of warped stellar disks do exist (van der Kruit, 1979; Sasaki, 1987). Recently Sánchez-Saavedra et al. (1990) have examined all northern, highly inclined spirals in the NGC catalogue on Palomar Sky Survey plates and report that in 42/86 some sort of warp is detectible. This finding is remarkable since for a warp to be optically detectible its line of nodes has to lie fairly close to the line of sight. Consequently, if half of all edge on spirals show a warp, virtually all spirals must be warped.

Interesting as it is, this finding of Sánchez-Saavedra must be treated with caution: not only are 23/42 of the warps described as ``barely perceptible'', but the detailed surface photometry of van der Kruit & Searle (1981, 1982a, b) found evidence for only one very marginal optical warp in seven edge-on galaxies.

Observations have thus amply demonstrated that HI disks are more often than not warped and that the warp becomes pronounced at the edge of the optical image. Why is this so?