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4.1. Gas Velocity Fields

Detailed reviews of gas velocity fields have been published by van der Kruit and Allen (1978), Faber and Gallagher (1979), Rubin (1979a, b, 1982), Bosma (1981b, 1982), and others. To save space, I will confine my discussion to the kinematic evidence for large amounts of dark matter in galaxies.

Figure 30

Figure 30. Combined optical and H I rotation curves for galaxies of various Hubble types, from Bosma (1978, 1981b). The measurements reach an average radius of 2.1 (dispersion = 1.2) times the radius of the 25 B mag arcsec-2 contour. Near the center, the resolution of many observations is inadequate, and the curves are schematic. At large radii, many curves are affected by oval distortions, warps, asymmetries and interactions with other galaxies (see the above references). Distances are calculated using H0 = 75 km s-1 Mpc-1. A similar figure showing flat rotation curves from optical measurements is given in Rubin, Ford and Thonnard (1980).

It is now well known that galaxy rotation curves are flat out to remarkably large radii (e.g., Fig. 30). I am not aware of any unambiguous measurements of falling rotation curves, i.e., ones which clearly indicate that most of the mass is interior to the outermost point measured (see Rubin 1979a, b). If V(r) appeq constant, very simple and general arguments indicate that there are large amounts of unseen mass in galaxies, especially at large radii. The following discussion assumes a spherical galaxy; if the mass distribution is flattened, the amount of material required is changed by less than a factor of two (Krumm and Salpeter 1977, see also Bahcall, Schmidt and Soneira 1982). For test particles in circular orbits in a spherical potential, V2 / r = GM(r) / r2, where M(r) is the mass contained within radius r, and G is the gravitational constant. The consequences of a V = constant rotation curve are,

Equation 15 (15)

where rhovol and rhoproj are the unprojected and projected mass densities. The linear rise of M(r) with r is illustrated in Figure 6 of Rubin, Ford and Thonnard (1978b), in Figure 5 of Bosma (1981b), and in Figure 3 of Burstein et al. (1982). There is no sign that M(r) is beginning to converge on a total mass. While rhoproj propto r-1, the projected surface brightness is decreasing much more rapidly, like 1.7 ltapprox n ltapprox 2 in ellipticals and like e-r/r0 (or even faster) in spirals. Necessarily, then, the local mass-to-light ratio M/L increases with increasing radius. This important result is illustrated in Figure 31 (Bosma 1978, 1981b). Similar results are derived by Krumm and Salpeter (1977), Schweizer (1978a), Rubin et al. (1978a), Peterson et al. (1978b), Bosma and van der Kruit (1979), Petrou (1981) and Burstein et al. (1982). Flat rotation curves and hence M/L ratios which increase outward are also seen in absorption-line measurements of S0 galaxies (e.g., NGC 4762, Illingworth 1981; NGC 3115, Illingworth and Schechter 1982, and references therein; NGC 1553, Figure 47). The same is true for barred galaxies (section 5.1.3), an interesting result in view of the fact that massive envelopes were proposed on theoretical grounds in order to get rid of bars (Ostriker and Peebles 1973). Kinematic data on ellipticals are consistent with the presence of massive envelopes (see Gunn 1980 for a review, also section 4.2.5), but do not make a strong statement, because there is little gas to give a direct measure of the mass distribution (e.g., Raimond et al. 1981). However, other techniques, especially X-ray observations, indicate that there are massive halos in at least some (possibly special?) galaxies (e.g., M87: Bahcall and Sarazin 1977; Mathews 1978; Fabricant, Lecar and Gorenstein 1980, but contrast Binney and Cowie 1981). Further discussion of the importance of halos as a function of Hubble type is given in section 2.3.

Figure 31

Figure 31. Radial variations of the local mass-to-light ratio, from Bosma (1978, 1981b) and Bosma and van der Kruit (1979). The luminosity data have not been corrected for internal or Galactic absorption except in IC 342 (AB = 2.2 mag). Distances are based on H0 = 75 km s-1 Mpc-1.

Thus there is a great deal of direct evidence for unseen, massive envelopes in galaxies. Further indirect evidence is discussed in Faber and Gallagher (1979). The need now is for data and models which are accurate enough so that we can determine the properties of these halos. It is clear that they are larger than visible galaxies, but what are their core radii? How does the halo mass depend on galaxy mass and type? Are halos triaxial, and if so, what effect does this have? Can the answers to these questions put useful constraints on the composition of halos?

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