11.1 Non-Newtonian Gravity

By now it will have become apparent that most of the evidence for DM around galaxies is based on the assumption that the dominant force in these systems is Newtonian gravity. If the virial theorem is inapplicable on galactic scales, much of the evidence for DM would therefore be eliminated. One possibility is that Newtonian gravity breaks down at the low accelerations characteristic of galaxies.

Milgrom (1983) investigated such an idea and introduced his theory of MOdified Newtonian Dynamics (MOND). In this picture, the usual Newtonian gravitational acceleration g_N is replaced by µ(x)g, where g is the observed gravitational acceleration and x g/a₀. For x >> 1, µ 1 and the usual Newtonian law applies. However, when x << 1, g g_N a₀ = (GMa₀ r^-2)^1/2. Thus the constant a₀ sets the acceleration at which MOND differs significantly from the Newtonian limit.

The asymptotic rotation velocity predicted by MOND in the non-Newtonian limit is

(11.1)

Here M is the total mass of the system, so that at low accelerations, MOND always predicts flat rotation curves. Thus the dynamics of spiral galaxies are understood in this theory as a natural consequence of the low-acceleration limit and there is no need for DM. Detailed comparison of MOND predictions with observed rotation curves of spirals have produced good agreement (e.g. Begeman, Broeils and Sanders 1991).

Lake and Skillman (1989) and Lake (1989) compared the predictions of MOND with observations of dwarf galaxies. They found that such galaxies put an upper limit on the parameter a₀ that was significantly smaller than the value advanced by Milgrom (1988) to explain the rotation curves of ordinary spirals. The inability of MOND to explain the rotation curves of dwarf and ordinary disk galaxies with the same value of a₀ would rule out the theory. However, Milgrom (1991) has suggested that observational errors in the distance and inclination of the dwarf galaxies are sufficiently large that MOND is still viable. The magnitude of the errors required by Milgrom (1991) seems a little extreme. Moreover, recent observations of dwarfs have produced at least one rotation curve that appears to be completely irreconcilable with the value a₀ required for normal galaxies (Smith and Lake 1992).

It is worth noting that the decline in some rotation curves at large radii (see Section 6.4 above), which has been interpreted as indicating the edge of the dark halo, are incompatible with MOND which always produces flat rotation curves at large radii. As pointed out by van der Kruit (1992), the spirals NGC 891 and NGC 7418 have very different light profiles, but similar rotation curves. This is difficult to understand in the context of MOND, since in the absence of dark halos rotation curves reflect the visible mass distribution. It is conceivable, but unlikely, that a large gas masses in these galaxies could rescue MOND.