6.4 The Edge of the Halo
The difficulties in constructing reliable mass models of spirals discussed in Section 6.1 above illustrate the importance of detecting the edge of the halo in spirals. This is of obvious interest anyway, since it represents the most direct way of establishing the extent of dark halos and the mass contained within them, but it would also help improve constraints on halo mass models.
If a rotation curve can be traced to the edge of the halo, the expected signature is a drop in rotational velocity. It is important to stress the difference between this situation and the drop in the inner rotation curves of many bright spirals discussed in Section 6.2 above. In the latter case, the drop is due to the increase in the rotation velocity caused by the presence of the disk. In fact, it might be better to describe such rotation curves as having a ``disk bump'' rather than a drop. This contrasts with a rotation curve that approaches the edge of the halo. In this case, the rotation curve is expected to remain relatively flat at large radii, and then exhibit a decline.
There are a handful of examples of this kind of behaviour. I mentioned in Section 5 that the extremely extended rotation curve of the dwarf irregular DDO 154 shows a decline at large radii (see Figure 1). Amongst the galaxies studied by Casertano and van Gorkom (1991), NGC 3521 has a relatively flat rotation curve from about 5 to 20 kpc, but the last three points of the rotation curve show a steady decline from about 210 to 160 km s-1. Similar behaviour is shown by NGC 7793 (Carignan and Puche 1990a), although here the rotation curve does not appear to have a flat portion at all. However, there is a marked decline from 116 to 88 km s-1 that appears to occur at large enough radii that the disk bump can not be responsible. (In any case, this galaxy is fainter than objects usually exhibiting a disk bump.)
It is conceivable that, in most galaxies, the HI does not extend to the edge of the halo. In this case, it is clearly impossible to detect the edge of spiral halos using HI measurements! However, there is some evidence that the extent and surface density of the HI and DM may be correlated (Bosma 1978; Sancisi 1983). Carignan and Puche (1990a) found that if the halo of NGC 7793 was modelled by an isothermal sphere then the ratio of HI and DM surface densities is constant with radius. A similar result was found for NGC 3109 by Jobin and Carignan (1990) and for NGC 6469 by Carignan et al. (1990). Carignan (DMW) suggests this may be a general property of spirals. Whether this is physically important is not yet clear. For instance, Lake (DMW) suggests that this may be a selection effect, arising from the detectability of HI. An increase in the HI density leads to the formation of H2, whereas a significant decrease makes the HI undetectable.
Finally, it is worth noting that the edge of dark halos may not be a well-defined quantity. For instance, if there is a background of unclustered DM, as is the case if the Universe has the critical density required for closure, then the halos presumably merge into this background. This is one of the motivations for indirect methods to explore the extent of halos which I discuss in Section 8.