3.4 Shape of dark matter halos
3.4.1 Polar ring galaxies
A special class of galaxies are the polar ring galaxies. These are small S0 galaxies seen edge-on, and have an additional ring (annulus) of matter orbiting over the poles. A first study of one of them, A0136 - 0801 (Schweizer et al. 1983), indicated that the material over the pole had roughly the same rotation speed as the stellar disk. From this, it was concluded that the dark halo must be nearly spherical. However, later studies using more accurate data, and including proper modelling of the self gravity of the polar ring, changed this conclusion. Sackett et al. (1994) show that for NGC 4650A the dark matter halo is quite flattened, but new data for this galaxy by Arnaboldi et al. (1997) and modelling by Combes & Arnaboldi (1996) shows that the situation is even more complicated yet.
3.4.2 Axisymmetry of the disks
Since the natural shape of dark matter is triaxial (Binney 1978), as is confirmed as well from the cosmologicial N-body simulations, it is surprising at first sight that disk galaxies are roughly axisymmetric in the outer parts. Yet this is borne out even for very high quality HI data. Schoenmakers (1998) analyzed data for several well studied spiral galaxies, and find a very high degree of axisymmetry. The same conclusion can be drawn from the work of Rix & Zaritsky (1995) on face-on spirals. This means that the process of disk galaxy formation is such that the original triaxial dark matter halo shape is modified by the formation of the disk, e.g. due to dissipation (cf. Dubinski 1994). In any case the shape of the dark matter halo close to the disk should be either oblate or prolate.
3.4.3 Flaring gas layers
A direct way to study the vertical shape of the dark halo is using the variation of the thickness of the gas layer with radius in edge-on galaxies. Predictions for this can be modelled quite straightforwardly from multicomponent disk/halo mass models (e.g. Athanassoula & Bosma 1988, Bosma 1994), but in practice the effects of angular resolution and sensitivity, small warps, lopsidedness, residual inclination effects, etc. may make the observational determination difficult. Moreover, the problem is directly dependent on the assumed value of the velocity dispersion of the gas. Even so, Olling (1996a, b) determined for the edge-on galaxy NGC 4244 that its dark matter halo must be quite flattened, like an E5-E9 shape. This result contrasts with the results of Hofner & Sparke (1994), who found much rounder halos, based on their interpretation of the warping behavior of the HI disks of several inclined galaxies.