4.3 Dispensing with Dark Matter
Throughout this Section it has been assumed that stellar velocity dispersions reflect the gravitational potential of a system in virial equilibrium, so that velocities exceeding those that can be explained by the visible mass in dwarf spheroidals are interpreted as evidence for DM. There are two possible ways of avoiding this conclusion that have been discussed in the literature. The first is the suggestion by Milgrom (1983) and others that at low accelerations Newtonian gravity breaks down. Since this suggestion has implications for all types of galaxies I defer a discussion until Section 11.
The second possibility applies specifically to dwarf spheroidals and is based on the idea that the local systems with large velocity dispersions are not in virial equilibrium. Kuhn and Miller (1989) noted that as dwarf spheroidals orbit the Milky Way the gravitational field that they experience changes. This tidal effect could drive pulsations in the dwarf spheroidals and boost the stellar velocity dispersion above the equilibrium value. In this case, interpreting velocity dispersions as being due to the gravitational potential of a virialized galaxy would lead to the erroneous conclusion that the galaxy contained DM.
If Kuhn and Miller (1989) are correct, the dwarf speroidals which show high velocity dispersions are unbound. This is potentially the most serious problem for the model. Pryor (1992) suggests that Draco, Ursa Minor, and Carina will have dissolved within 108 years if their velocity dispersions are due to tidal effects. It seems plausible that unbound dwarf spheroidals could remain as identifiable single structures for longer than this. The stars in such a system will certainly drift apart, but they will still tend to follow similar orbits around the Milky Way. Numerical studies may be the only way of resolving this issue.
Some support for the Kuhn and Miller (1989) scenario comes from the observations of the dwarf spheroidal companions of M31. Caldwell et al. (1992) find that the flattest galaxies have the lowest central surface brightnesses. This is expected in the Kuhn-Miller picture since the galaxies that are experiencing the strongest tidal effects, and thus losing stars the most rapidly, tend to be the most flattened. Another intriguing result that is consistent with the Kuhn-Miller picture is the detection of stars beyond the tidal radius of Sextans (Gould et al. 1992). These ideas are somewhat reminiscent of Lynden-Bell's (1982) suggestion that the dwarf spheroidals around the Milky Way represent tidal debris from disrupted satellite galaxies.
It is not yet clear whether the survival of dwarf spheroidals is a fatal flaw in the Kuhn and Miller (1989) scheme. It is clear, however, that unbound galaxies will lose stars, so a test of the model is to look for stars strung along the orbits of the dwarf spheroidals. The axes of these galaxies are expected to point in the direction of the orbit, thereby providing another observational test.