9.2 Warped and Flaring Disks
Constraining the shape of the halos of ellipticals using gas disks was briefly mentioned in Section 7. Lees (1991) has argued that the twisted disk in the elliptical galaxy IC 2006 is indicative of a triaxial halo. Warps in spirals have also been used to constrain the concentration of their dark halos (Section 6). However, further techniques have also been pursued which yield shape information. Sparke and Casertano (1988) showed that both the concentration and oblateness of spiral galaxy halos could be constrained by modelling the shape of the warp. This work has been extended to include time evolution of the gas disk by Hofner and Sparke (1991). Their results indicate moderate flattening in the galaxies they have studied. In NGC 2903, for instance, the halo must be flatter than E2.
Dynamical arguments further suggest that concentrated dark halos should inhibit warps in disk galaxies (Sparke and Casertano 1988). This prediction has gained support from spiral galaxy mass modelling which indicates that spirals with small halo core radii rarely have warps (Bosma 1991; Bosma, van der Hulst and Athanassoula 1988).
Steiman-Cameron, Durisen and Kormendy (DMW) have taken a different approach. They use galactic accretion disks to probe the potential of the dark halo. The idea is to model the accretion of a satellite in order to understand how the final state of the gas disk reflects various parameters, including the shape of the halo (see Steiman-Cameron and Durisen 1990). Under certain conditions, analytic solutions to the problem may be obtained (Steiman-Cameron and Durisen 1988). So far, the results indicate fairly spherical halos. For instance, for the S0 galaxy NGC 4753, Steiman-Cameron et al. (DMW) find a ratio for the minor to major axes of the halo of between 0.84 and 0.99.
Steiman-Cameron (1991) has also emphasized that if twists in disks are caused by differential precession, then the sense of the twist (whether it leads or trails the rotation) reveals whether the mass distribution is oblate or prolate. In the S0 galaxy NGC 4753, the halo proves to be oblate. On the other hand, NGC 5033 and 5055 have prolate halos.
Teuben (1991) notes that warped disks are more easily understood if the surrounding dark halos are triaxial. The ubiquity of warps (Bosma 1991) then supports the notion that many dark halos are triaxial. Teuben (1991) shows that fitting tilted ring models (Begeman 1987; 1989) to gas disks provides a method of inferring the presence of triaxial potentials. Such models reveal deviations from circular motion which are indicative of non-axisymmetric potentials. However, there are other mechanisms that can excite and preserve warps that do not necessarily require triaxial halos (e.g. Bertin and Casertano 1982).
Blitz and Spergel (1991) suggest that a rotating triaxial halo can explain observed asymmetries in the HI distribution of the Milky Way. They also find that the dark halo is nearly axisymmetric at large radii, with an axis ratio of b/a > 0.87.
Observations of edge-on spirals indicate that the scale height of most gas disks increases with radius. This flaring is not surprising since the velocity dispersion of the gas remains constant with radius, whereas the gravitational potential of the stellar disk declines. However, the HI disk is also responding to the potential of the halo, so in principle mass modelling of the stellar disk and the gas disk can provide information about the shape of the halo.
Maloney (DMW) is investigating this technique. Unfortunately, his results indicate that the thickness of the HI layer is rather insensitive to the shape of the halo. Thus, while halos as flat as the disk can be ruled out, more detailed information can not be obtained. Prospects are better for the Milky Way where one can incorporate estimates of the gas density of the disk to constrain halo models.