Mass discrepancies in galaxies: dark matter and alternatives

Abstract

Neutral hydrogen line observations of the extended rotation curves of spiral galaxies imply that there exist significant discrepancies between the luminous and dynamical mass beyond the bright optical discs. This means either that galaxies contain significant quantities of non-luminous matter (matter with a mass-to-light ratio very much higher than that of ordinary stars), or that the law of gravity on the scale of galaxies is not the usual Newtonian inverse square law. Attempts to account for the observed discrepancy in the context of these two explanations are reviewed here with emphasis given to the second and less conventional alternative. It is argued that the standard picture of spiral galaxy halo and disc formation in the context of cold dark matter cannot account for the observed systematics of the discrepancy — notably rotation curves which are seen to be flat and featureless from the bright inner regions where the visible matter dominates the dynamics (in some cases overwhelmingly) to the outer regions where the dark halo dominates. It is demonstrated that in those galaxies with well-observed rotation curves, the discrepancy apparently appears below a critical acceleration. Any dark matter explanation of the discrepancy must account for this fact. Moreover, this would also eliminate empirically motivated modifications of Newton's law in which the deviation from 1/r occurs beyond a fundamental length scale. The suggestion by Milgrom in which the force law becomes essentially 1/r below a critical acceleration (MOND) can account for most of the observed systematics of galaxy rotation curves and, significantly, leads to the observed luminosity-velocity relationship in spiral galaxies (the Tully-Fisher law). Generally covariant theories of gravity which predict this phenomenology in the weak-field limit are described. Although there is not yet a theory which obviously meets all of the requirements for a physically viable alternative to dark matter, a generalized scalar-tensor theory of the form suggested by Bekenstein (phase coupling gravitation) is the currently leading candidate and has the advantage of being testable locally.