A few galaxies in Fig. 1 have very asymmetric velocity fields: the differences in projected circular velocities between a certain point and its corresponding mirror point at the opposite side of the galaxy are in the order of 50 km s-1 or more. The optical pictures of these galaxies look distorted as well, but in the inner parts axial symmetry is usually maintained. In most cases a companion galaxy is found nearby, which could have distorted the outer parts of the disk by tidal interaction. We first describe the galaxies individually and then discuss some related topics.
Galaxies with large scale asymmetries:
M101. This galaxy has a very asymmetric HI distribution, the NE side being about twice as large as the SW side. The HII-regions are also asymmetrically distributed, but here the SW side is larger (cf. Allen, 1975). The HI coincides with the faint optical arms in the outer parts. The velocity field is symmetric in the inner parts, out to 7' radius. Beyond this radius the radial velocities remain more or less constant on the NE side, but decrease strongly on the approaching SW side. At the NW side the lines of equal radial velocity show kinks, but these are not related to the spiral structure. Perhaps the outer parts are irregularly warped. All the large HII-regions lie in the asymmetric part. Two nearby companions are present: NGC 5477 at about 22', and NGC 5474 at about 46' distance. Both are small and distorted, and they differ in systemic velocity with M101 only by 30 km s-1. It has been suggested that the outer parts of M101 are distorted by these companions (Beale and Davies, 1969), though no detailed model exists. The filamentary outer arms might be interpreted as wavelets (Julian and Toomre, 1966) formed under influence of a point mass (most likely NGC 5477).
M81. The outer parts of this galaxy, outside a radius of 10'; are not symmetric. The southern side is connected to NGC 3077 (Van der Hulst, 1977) and the velocity field there has the characteristics of a kinematical warp. At the east side a small dwarf, Ho IX, is present, and at the northern side the Arp ring (Arp, 1965) is found. The rotation curves of the northern and southern parts differ considerably outside 10' radius (Rots, 1974). Tidal interactions with both M82 and NGC 3077 might be responsible for the asymmetry, although no convincing model has been constructed (see Van der Hulst, 1977).
M51. This galaxy is seen rather face-on, and has a companion NGC 5195 at 6' distance. The velocity field of the eastern half differs from that of the western half, especially at larger distances from the centre. The HI distribution by itself is rather symmetric (see Shane, 1975), but the optical picture is asymmetric. Toomre and Toomre (1972) constructed a model for this system based on tidal interaction during a close passage.
M31. Emerson (1976) and also Roberts and Whitehurst (1975) report double or multiple profiles in the outer parts. Byrd (1976, 1977) suggests that tidal interaction with M32, during its passage through the disk of M31, can account for the observed features which differ in radial velocity from the value expected for normal rotation. The inclination of the galaxy is so large, however, that arms at different radii might still be observed within one beam.
NGC 2805. This galaxy, which resembles M101, is a member of a group of galaxies studied by Bosma et al. (1978). The optical picture is highly asymmetric, except in the very inner parts. The HI distribution has an unresolved ridge in the north and is oriented roughly east-west. This orientation does not correspond to either that of the optical picture or that indicated by the velocity field. As in the case of M101 the HI-HII antisymmetry is present. Note that R/B is about 5, similar to that of Rogstad and Shostak's (1971) picture of M101. Perhaps the outer parts are warped.
NGC 4631. This galaxy, which is listed in table 2.1, is not illustrated in Fig. 1 because it is seen edge-on. Weliachew et al. report the existence of four tail-like features out of the plane, one pointing towards the companion NGC 4656. Combes (1978) proposes a tidal interaction model involving NGC 4631, NGC 4656, and NGC 4627.
Of course more galaxies than those discussed above are known to have a large scale asymmetry, and in most cases a companion galaxy can be found in the neighbourhood (not always cf. Toomre, 1977). Following Toomre and Toomre (1972), most observers prefer to interpret their data in terms of a gravitational interaction model. Toomre and Toomre have produced very convincing fits for 4 interacting systems by comparing the computed distribution of test particles, originally rotating in disks around two point masses, with the observed light distribution as seen on photographs. For the galaxies listed above similar models have been proposed or suggestions have been made that they could be described with such a model. Besides M51, fits for NGC 4631 and M31 look promising, a fit for M81 is dubious, and for NGC 2805 and M101 no model construction has yet been published). This rather poor state of affairs is perhaps related to the fact that in most cases more than two galaxies have to be considered, while in some cases (M101) the candidate-perturbers have only a few percent of the mass of the victim. Note that most of the galaxies appear to be irregularly warped; the warp might be directly related to the tidal interaction.
From the successful fits of the Toomre and Toomre models we can infer an interesting point about the mass distributions of the galaxies involved. In their model of M51 / NGC 5195 the shortest distance between the galaxies is about 20 kpc. If these galaxies had massive haloes, in the sense of Ostriker et al. (1974), with a radius of typically 50 kpc, a passage at 20 kpc distance results in a dynamical friction which is probably large enough to cause the galaxies to merge. In any case it seems unlikely that encounters of galaxies with 80% or more mass in a halo will produce the same tidal effects as do encounters of simple disk galaxies. Therefore the success of tidal interaction models using simple disks must place a constraint on the ratio halo mass to disk mass. (A similar conclusion from a slightly different line of argument has recently been reached by White and Sharp (1977)).