We discussed in the foregoing section that in a number of galaxies the position angle of the major axis changes with radius. In that section we concentrated on those cases where an oval distortion seemed to be present in the disk of the galaxy. Now we will discuss the cases for which we suspect that the outer parts of the disk, or at least the HI distribution there, are warped. Since we infer the warp from the kinematics we can speak of a kinematical warp, in contrast to warps seen in the HI distribution of edge-on galaxies which we call direct warps. The major difference between a galaxy with a kinematical warp and one with an oval distortion appears to be the alignment in the inner parts of the kinematical major axis with the one of the optical picture. Moreover, the HI distribution in a kinematical warp sometimes extends far beyond the optically visible disk. We first present a brief summary of the observations, then we investigate whether the simple tilted ring models, which can describe a kinematical warp, can also describe a direct warp, and finally we comment on the general problems of warps.
The following galaxies are thought to have a kinematical warp:
M83. The HI distribution of this galaxy extends to about 2.5 times the Holmberg diameter. The kinematical major axis changes its position angle in the outer parts with more than 60°. Rogstad et al. (1974) were the first to present a tilted ring model, it fitted the observations rather well. The rings are concentric and are progressively changing their orientation away from the main plane, the line of nodes changes as well. The inner parts are not well resolved. In the optical picture, a bar is present. It cannot be excluded that this bar causes some deviations from axial symmetry too.
M33. Rogstad et al. (1976) found that most of the profiles have two peaks, a strong one and a weak one. They showed that this behaviour can again be explained in terms of a tilted ring model, with the outermost rings crossing the face of the galaxy. Earlier investigations, see e.g. Warner et al. (1973), showed already a variation in the position angle of the major axis at large distances from the centre.
M31. Roberts and Whitehurst (1975) have presented evidence for a warp in the southern part. Recently, Newton and Emerson (1977) have shown that also the northern part is slightly warped. The orientation of the HI contours changes in the outer parts; in the inner parts the contours are well aligned with the optical disk. The kinematical major axis also changes in the outer parts, consistent with the orientation of the HI contours. Note that both studies have been performed with moderate resolution (R / B ~ 10).
NGC 5033. In this galaxy the change with radius in the orientation of the HI contours is followed by that of the kinematical major axis. Both start already at 0.6 times the Holmberg radius, nevertheless, a tilted ring model can describe the observations rather well.
NGC 5055. The extent of the HI emission in this galaxy is very large: about two times the Holmberg size. The kinematical major axis changes first from 99° to about 95°, and then turns back to about 115°. The contours of the HI distribution follow this trend. On deep photographs some faint optical emission has been found which does not correspond closely to HI emission.
NGC 2841. The HI extent of this galaxy is about 2.5 times the Holmberg diameter. The kinematical major axis changes with radius; the HI distribution follows the same trend.
NGC 7331. In this galaxy the HI distribution by itself shows that the outer HI layer does not lie in the main plane of the galaxy. The velocity field indicates a changing kinematical major axis, first turning within the optical image to one side and turning back through the main plane towards the other side farther out.
NGC 300. The velocity field of this galaxy has been included in Fig. 1, although the data from Shobbrook and Robinson (1967) have a ratio R/B of about 3. The HI extends to about twice the Holmberg diameter, and the kinematical major axis is changing with about 20°. Rogstad mentions in his M33 paper that this galaxy shows a kinematical warp at higher resolution (R/B about 10)
For each of these galaxies (except NGC 300) models have been made to describe the geometry. This has been done in the following way: The galaxy is divided into concentric rings with an appropriate width of say one beamwidth. Each of the rings has its own orientation in the sky, independent of the others. For each ring the orientation is derived from the velocity field by calculating, for a given set of orientation parameters, the mean circular velocity and the dispersion around this mean. As best fitting parameters we select those for which the dispersion is the smallest. For highly inclined galaxies the determination of the inclination is usually difficult because of the small number of independent beams along the minor axis; in those cases fits can be found by trial and error using the individual profiles or position velocity profiles as a guide. In this way we arrive at a series of radial distributions for the rotation velocity, Vc(R), the position angle of the line of nodes, (R), the inclination, i(R), and the mean projected surface density of neutral hydrogen in each ring, H(R). A general feature of these models is that the orientation of the rings in the inner parts of the galaxy agrees well with that inferred from the optical photograph, while the orientation in the outer parts is different.
The tilted-ring-models describe the observations of the galaxies discussed above rather well. We have investigated whether this model can also describe the observations in warped disks in edge-on galaxies. As already discussed, NGC 7331 is just enough edge-on to see the warp directly in the HI-distribution, and just enough face-on to allow the inference of the warp from the kinematics; they are consistent with each other. It remains to be seen whether warps in edge-on galaxies have a similar geometry.
Sancisi (1976, 1977) reported warped HI disks in the following edge-on galaxies:
NGC 5907. In this galaxy the warp at the extreme radial velocities starts at the point where the optical disk seems to terminate. There is a rather regular behaviour as function of radial velocity: channel maps at velocities closer to the systemic velocity start their bending at shorter projected distances to the centre (see Fig. 2 of Sancisi, 1977).
NGC 4565. In this galaxy a warp has been found similar to, but of smaller amplitude than the one in NGC 5907. In both cases the contours of the HI distribution tend to be aligned with the bright optical picture, but at low column density level this is uncertain (Sancisi, priv. comm.).
NGC 4244. In this galaxy a warp has been observed, but of much smaller amplitude than the foregoing cases.
NGC 4631. This galaxy is warped too (Weliachew et al., 1978), but there is a companion, NGC 4656, which is in tidal interaction with it (see section 6).
Finally we mention the warp in our Galaxy (Burke, 1957; Kerr, 1957) and call attention to the small deviations from the principal plane in the inner parts (see Fig. 6 of Gum et al., 1960).
We have tried to fit a tilted ring model to the observations of NGC 5907 by calculating channel maps at the appropriate radial velocities and smoothing them to a 1' beam. As input parameters we took the rotation curve derived by Sancisi (priv:comm.) and estimated radial distributions of H(R), (R), and i(R). A few trials are shown in Fig. 4. Note that the channel maps close to the turnover velocity are not very different, but at lower radial velocities they differ significantly, and model c can be excluded. Higher sensitivity and higher resolution observations might show which of the two curves of i(R) is the best one, but we favour model a. For the moment we conclude that a tilted ring model might apply for edge-on galaxies as well, but we emphasize that a precise fit is not trivial.
Figure 4. Tilted ring models for the galaxy NGC 5907. In the left panels we show two observed channel maps at radial velocities Vrad 460 and 820 km s-1. Since the systemic velocity Vsys = 670 km s-1 this corresponds to V = (Vrad - Vsys) = 210 km s-1 and V = 150 km s-1. Only the channel map at 820 km s-1 shows the split up in the outer contours clearly; the channels with V = 170 and 190 km s-1 do not show this (cf. Sancisi, 1976). We show three models with the same radial run of position angles, but with different inclinations. Model c shows the split up at V = 150, 170 and 190 km s-1 and does not agree with the observations. Model a is capable of producing a hint of a split up and predicts the low contours in the total HI distribution to be parallel to the bright optical disk. Model b does not produce a split up and predicts the low contours in the HI distribution to have a sandglass-like shape.
The fact that we observe so many galaxies to be warped poses an interesting dynamical problem. Kahn and Woltjer (1959) suggested that for any aspherical galaxy warps cannot be long lived because of the following argument: The frequency of oscillation of a star perpendicular to the plane of a galaxy differs from the circular frequency in the plane,resulting in a precession motion. This difference is a function of radius: at each radius the rate of precession is different. Thus an "organized" warp will after some time decay into a corrugated disk. Various suggestions have been made to meet this objection; most of them invoke a forcing mechanism. We will review them briefly and especially discuss what our new observations can tell us about them.
The following suggestions or models have been made to explain the warp phenomenon:
a. Movement of the galaxy with respect to intergalactic gas (Kahn and Woltjer, 1959).
b. Free precession of the disk (Lynden-Bell, 1965).
c. Tidal interactions (Hunter and Toomre, 1969, and references therein)
d. Infalling gas (Rogstad et a1., 1976; also Larson, 1976)
e. Precession of a disk in a massive aspherical halo (Binney, 1978).
ad a. The basis of this idea is that intergalactic gas exists in groups of galaxies, like the Local Group, to make them gravitationally bound. Further, a galaxy is assumed to have a halo of cosmic rays and magnetic fields which is confined by the intergalactic gas pressure. A movement of the galaxy with respect to the intergalactic gas creates pressure gradients around.the halo, which are then thought to be transferred to the edges of the disk. In this way integral sign shapes are formed. As also pointed out by Binney (1978), this scenario is questionable, especially the transfer of the pressure gradients into a deflection of the disk is unclear. Moreover, the complex warps of NGC 5055 and NGC 7331, where, if seen edge-on, the main plane is crossed twice at either side of the centre of the galaxy, cannot be explained easily in this picture.
ad b. Lynden-Bell (1965) suggested that forced oscillations might prevent the smearing out of the warp; he specifically showed that if in a MacLaurin spheroid the symmetry axis deviates from the direction of the angular momentum vector a wobble occurs, which causes a systematic bending of the disk. This possibility for explaining warps has been rejected by Hunter and Toomre (1969), see below.
ad c. Hunter and Toomre (1969) showed, that for thin disks, with a realistic mass distribution within the disk, stable modes of warping do not exist. Because of this, they argued that tidal interactions could be responsible for the forcing of the warp. Since warps decay rapidly,the tidal interaction must have occurred recently, e.g. one or two revolutions ago, which in practice means 2 × 109 years ago at most. Moreover, the companion that causes the warp should pass rather closely to provide a sufficient pull. This idea has been put forward for the warps in our Galaxy (by the Magellanic Clouds, cf. Hunter and Toomre, 1969), M31 (by M32, Byrd, 1977), M81 (by M82, Kilian and Gottesman, 1977) and NGC 4631 (by NGC 4656, Weliachew et al., 1978). For small galaxies like M33, NGC 300 and NGC 4244 big brothers can be found close enough to have caused the damage (M31, NGC 55 and NGC 4214 resp.; all within 200 kpc projected distance). Also for NGC 5033 a massive companion, NGC 5005, is at 170 kpc. projected distance. For the large galaxies M83, NGC 5907, NGC 4565, NGC 5055, NGC 2841, and NGC 7331 no nearby massive companions can be found. Therefore it is unlikely that tidal forcing is a general explanation of the warp phenomenon.
ad d. The suggestion of infalling gas is motivated by the occurrence of the warp in the outer parts of galaxies, beyond the Holmberg radius. Around several galaxies HI clouds have been found (see section 7 for a discussion); capture of such clouds might lead to a warped HI disk in the outer parts. Larson (1976) suggested that the gas in the outer parts of galaxies has not yet settled itself into a disk. The idea of warps having to do with capture or infall of HI gas seems ad hoc; furthermore the warps in NGC 5033, NGC 5055 and NGC 7331 start within the Holmberg radius and therefore rule out this suggestion as a general explanation.
ad e. Recent considerations suggest that spiral galaxies might be surrounded by a dynamically hot component, usually called massive halo (Ostriker and Peebles, 1973). If this component dominates the gravitational field the forces perpendicular to the main plane on a tilted ring are less than in the case of a pure disk, and a tidally excited warp might not disappear so rapidly. Binney (1978) has argued that the hot component might be triaxial in form, analogous to normal ellipticals. In that case the hot component provides an efficient internal driving force for the oscillations. He suggests that triaxial haloes reveal themselves. in the velocity fields of spirals by showing a misalignment of the optical minor axis and the kinematical minor axis. This prediction is in direct conflict with the character of the tilted ring models described above. In those cases there is alignment in the inner parts between the kinematical axes and the axes of the optical disk. This suggests that, at least in the inner parts, the asphericity of the assumed hot component does not dominate the potential field of the disk in such a manner that the disk assumes an oval shape. It cannot be excluded, however, that in the outer parts the disk is deformed into an oval: it is not well possible to discriminate between projected circular orbits and projected elliptical orbits if the orientation of the plane is unknown. We emphasize that oval distortions in the disk can produce elliptical orbits too. This greatly complicates the comparison of Binney's predictions with the observational data. The galaxies quoted by him as suggestive evidence for the presence of the observable consequences of triaxial haloes are galaxies with either peculiar motions associated with spiral arms (M31, M81) or with a mild oval distortion in the disk (NGC 4258, IC 342 (?)). Nevertheless, the ambiguity between oval distortions and kinematical warps prevents us to rule out triaxial haloes completely.
From the foregoing discussion we conclude that none of the proposed solutions to the warp problem is very satisfactory. Tidal interactions are not excluded in some cases; capture of HI clouds or infall (especially in small late type galaxies) remains also a possibility. For the relatively isolated giant spirals a scenario like tidal pulling of the warp a long time ago, by a neighbouring giant, and subsequent slow evolution might be envisaged. The slowness of the evolution of the warp could then be related to the presence of a hot, perhaps triaxial, component in the mass distribution which dominates the potential field in the outer parts. Note that the large variety in the amplitude of the warp, and their complexity in the galaxies described above, suggests that they evolve, rather than retain their shape indefinitely.
Several questions can be raised on the observational side. There is as yet little evidence that warps in the relatively isolated galaxies occur in components other than the population I component (gas and young stars: the low velocity dispersion component in the disk). The sky-limited IIIaJ-plates, taken by Van der Kruit and Bosma for a number of galaxies listed above, do not reveal a significant warping at a level of 27m arcsec-2. Surface photometry of more galaxies, especially in the red, might reveal whether there is any deviation from the main plane in the old disk population. Furthermore, it would be interesting to know the fraction of warped galaxies for a sample of several tens of edge-on galaxies. It is also remarkable that we can indeed distinguish kinematical warps from at least large scale oval distortions in early type spirals. In-spirals with relatively small bars (M83, NGC 3198), where the optical appearance is dominated by the arms, the HI distribution extends beyond the optically visible disk and is warped there (although very mildly in the case of NGC 3198), but in spirals with large scale oval distortions the (detectable) HI is strictly confined to the optical disk. In that connection the difference between NGC 4736 and NGC 2841 is striking. Perhaps this is related to the way the disk of a spiral galaxy "solves its stability problem"?