Annu. Rev. Astron. Astrophys. 1978. 16: 103-39 Copyright © 1978 by Annual Reviews. All rights reserved

3.2. Rotation Curves in the Outer Parts of Spiral Galaxies

Radio measurements of the HI 21-cm line velocities in galaxies have considerably increased the radial distance to which rotation curves can be obtained; optically derived rotation curves rarely extend beyond ~ 1/3R_Ho, while in HI they often reach beyond R_Ho. Before such observations were available it was usually assumed that at large radii the rotation curves eventually became Keplerian, V_rot R^-1/2. In fact actual rotation curves are now found to decline much more slowly or even not at all (Roberts 1975b, Huchtmeier 1975, Combes et al. 1977). Bosma (1978a, b) has recently analyzed HI velocity fields in a sample of about 20 galaxies, based on data from new observations with the WSRT and on results available in the literature. His results can be summarized as follows: The rotation curves are almost always either flat or slowly declining in the outer parts. ⁽³⁾ Construction of mass models shows indeed that out to the last observed point the total mass M_out still does not converge to an asymptote. The ratio M_out/L_tot is about 5-15 independent of type (H₀ = 75 km/sec/Mpc) indication in a number of galaxies that M_out/L_tot has a tendency to increase with radius. However, Bosma cautions that, given the uncertainties arising from noncircular motions, beam smoothing, thin disk approximation, etc, these results should be considered as very tentative.

Krumm & Salpeter (1977; see also Salpeter 1978) have extended the HI rotation curves of six mainly edge-on spiral galaxies to even larger distances (84 kpc for NGC 4565 if H = 50 km/sec/Mpc) using the Arecibo radio telescope. They find further evidence that V_rot refuses to decrease in the outer parts of these galaxies; however, the very existence of HI there disagrees in two notable cases with observations made with the WSRT (NGC 4565 and 4631, Sancisi 1978) so that these results require further verification.

Rotation curves that remain high at large distances imply increasing M/L ratios in the outer parts of galaxies. Indeed, if the surface brightness continues the exponential decrease found in the brighter parts of the disk (e.g. Freeman 1970a) and the rotation curve remains constant with R, then M_out/L_tot is proportional to R. Roberts & Whitehurst (1975) derived local M/L values of 200 or more at 30 kpc radius in M31, assuming that the HI velocities that they measured were due to pure rotation and taking a particular model for the mass distribution [see also Roberts (1976)]. Observations of M31 at Cambridge (Emerson & Baldwin 1973) seemed at first to indicate that the rotation curve differed from that derived by Roberts and Whitehurst; however, a more recent analysis (Emerson 1976, Newton & Emerson 1977) has removed the discrepancy. Furthermore, Newton and Emerson conclude that the high degree of (anti-) symmetry of the velocity field on either side of the minor axis of M31 strongly suggests that the observed velocities indeed result from rotation, to better than 10 km/sec.

Finally, we discuss briefly the question of whether the forms of the rotation curves provide any evidence for massive halos around galaxies. It is certainly true that more mass is waiting to be found beyond the last measured HI points on many rotation curves; the values of a few × 10¹¹ M currently quoted for Luminosity Class I and II galaxies refer to radii of 20-50 kpc. However, the great increase (factors of 10 to 100) in masses advocated by Einasto et al. (1974) and by Ostriker et al. (1974) involve estimates at much greater radial distances, from 200-500 kpc. As has been stated by Turner & Ostriker (1977), there is no evidence in favour of such massive halos within the visible disks of galaxies; the standard rotation curve analyses give values of M_out at some R that differ by only ~ 20% if one assumes a spherical rather than a flattened mass distribution. Nevertheless, it is a fact that not a single galaxy has been found with a Keplerian rotation curve at large R. We must conclude that the results from rotation curves are not inconsistent with the existence of extensive, massive halos around galaxies, although the prime evidence for them comes from studies of binary galaxies and outlying globular clusters (e.g. Turner & Ostriker 1977, Sargent 1977).

³ A notable exception to this general statement is M81 (Rots 1975), where the observed rotation curve on the northwest side begins to increase again beyond about 10 kpc. A convenient excuse for this may be found in a postulated interaction of M81 with M82 and NGC 3077 (see Section 4.6 below). The observed rotation curve on the southeast side continues to decline. Back.