8.2 Galaxies in Groups

Erickson, Gottesman and Hunter (1987; 1990) adapted van Moorsel's (1987) method described above in order to study galaxies in small groups. Specifically, they obtained HI observations of spiral galaxies that were surrounded by one or more gas-rich satellites. Dynamical masses for the primary galaxies were obtained from HI rotation curves, and a statistical measure of the mass beyond the rotation curves was obtained from the projected distances and velocity separations of the galaxies. On average, the satellites probed distances about 3 times greater than the rotation curves.

Erickson et al. (1987; 1990) concluded that the halos of the primary spiral galaxies contained about 3 times as much mass as the dynamical mass of the spiral disks. They argued that this result favored small halo masses. However, it is important to notice that these authors compared the halo masses probed with the satellites to dynamical disk masses. In other words, their disk masses are a combination of the mass of the stellar disk and the halo mass within the last measured point of the rotation curve. Since the mean distance between primaries and satellites is about 3 times the average extent of their rotation curves, these results actually support extended, roughly isothermal halos.

Erickson et al. (1990) further argued that the primary halos were unlikely to be very extended on the grounds that the satellites showed little evidence for major tidal damage. Their preferred halos consequently had radii of about 60 kpc for the primary spiral galaxies in their sample. However, observations of the satellites of the Milky Way challenge this assertion. There is good evidence that the Galactic halo extends to at least 100 kpc. The Magellanic Clouds, which are similar to the satellites of other galaxies considered by Erickson et al. (1990), are currently well within this radius. While the Magellanic Clouds are a little ruffled, and may even be fragments of a disrupted galaxy (e.g. Mathewson, Ford and Visvanathan 1986), they are still identified as individual objects.

A similar study has been carried out by Zaritsky et al. (1993). They have a larger sample of satellite galaxies relative to the Erickson et al. (1990) work and, more importantly, a greater mean separation of primaries and satellites which allows the halos of spirals to be probed to greater distances. Zaritsky et al. (1993) conclude that the spirals in their sample are typically surrounded by about 10¹² M of DM within about 200 kpc. This is comparable to the estimated mass of the Milky Way halo discussed in Section 3.

In the M96 group of galaxies in Leo, there is an enormous ring of intergalactic gas surrounding the central pair of galaxies, M105 and NGC 3384Schneider et al. 1989). In order for the ring to survive, Schneider (1991) has argued that it must lie outside the dark halos of M105 and NGC 3384. This limits their halo radii to about 60 kpc which is consistent with the combined dynamical mass of the pair of 6 x 10¹¹ M inferred from the ring kinematics. This is only twice the mass inferred for the two galaxies from their rotation curves, corresponding to a total mass-to-light ratio of 25. Such a low value is a little unusual, although it is possible that the location of these galaxies in the center of a group may have led to the truncation of their halos (see also Section 8.3 below).

Puche and Carignan (1988) carried out a study of the Sculptor group of galaxies. They adopted a novel method of ascertaining group membership by applying the virial theorem to a region of the sky centered on Sculptor. Puche and Carignan (1988) calculated the virial mass of the group from all galaxies in this region and then rejected galaxies that were driving the derived mass to exceptionally high values. They found that the virial mass converged to a value around 2 x 10¹² M when 5 group members remained. Puche and Carignan (1988) concluded that only these galaxies constituted a physically bound group, and that the remaining three galaxies previously suspected of group membership were interlopers.

Individual rotation curves were obtained for the 5 galaxies identified as members of Sculptor (Carignan and Puche 1990a, b; Puche, Carignan and Bosma 1990; Puche, Carignan and Wainscoat 1991; Puche, Carignan and van Gorkom 1991). Puche and Carignan (1991) used these measurements to obtain the sum of the masses of the individual galaxies. They found a total mass in the galaxies of 2 x 10¹¹ M, and concluded that if the halos extended 10 times further than the measured curves, then all the DM in this group could be associated with individual galaxies. This requires that the halos have an average radius of 42 kpc. This low value reflects the relatively low M/L_B of 83 ± 10 that Puche and Carignan (1988) derive for this group. Dynamical estimates in other groups and clusters typically give values of M/L_B 200-500h.

One concern with this analysis is that the overdensity for the group derived by Puche and Carignan (1988) is very low. This can be quantified by recalling that the density of fluctuations at turnaround is 9²/16 times the critical background density at that epoch (e.g. Gott and Turner 1977). The virialization of such an overdense region increases its density by another factor of 8, during which time the density of the Universe has decreased by a factor of 4 (higher if the density of the Universe is less than critical). For an object such as a galaxy halo to have virialized by the present epoch, it must therefore have a density of at least 18² times the critical background density (cf. Ashman and Carr 1988; Lake 1990b; Ashman 1991).

Translating this argument into something more manageable, I obtain

(8.2)

Only halos with densities satisfying equation (8.2) have virialized by the present epoch. It is risky at best to apply the virial theorem to lower density systems. The results of Puche and Carignan (1988) imply that the mean density of the Sculptor group is no more than about 5 x 10^-29 gcm^-3, so that Sculptor does not appear to be virialized. Under certain circumstances, application of the virial theorem to an unvirialized system can underestimate its mass. Further, the procedure for determining group membership relies on throwing out galaxies that give a large value for the group mass. It is therefore conceivable that the mass-to-light ratio of Sculptor is somewhat higher than Puche and Carignan (1988) claim.

Equation (8.2) also indicates that merely requiring that the crossing time of a system is less than the age of the Universe is not a sufficient condition to apply the virial theorem. In fact, since the crossing time scales as ^-1/2, the above considerations imply that the crossing time of a system must be less than about a tenth the age of the Universe in order for the virial theorem to be applied.