Dark Matter in Spiral Galaxies

Mass models of spiral galaxies based on the observed light distribution, assuming constant M/L for bulge and disc, are able to reproduce the observed rotation curves in the inner regions, but fail to do so increasingly towards and beyond the edge of the visible material. The discrepancy in the outer region can be accounted for by invoking dark matter; some galaxies require at least four times as much dark matter as luminous matter. There is no evidence for a dependence on galaxy luminosity or morphological type. Various arguments support the idea that a distribution of visible matter with constant M/L is responsible for the circular velocity in the inner region, i.e. inside approximately 2.5 disc scalelengths. Luminous matter and dark matter seem to 'conspire' to produce the flat observed rotation curves in the outer region. It seems unlikely that this coupling between disc and halo results from the large-scale gravitational interaction between the two components. Attempts to determine the shape of dark halos have not yet produced convincing results. We have studied the discrepancy between dynamical and luminous mass in spiral galaxies (in the context of Newtonian gravity). The amount and distribution of dark matter are derived on the assumption that the mass:light ratio of luminous matter is constant (separately for bulge and disc) and equal to the maximum value allowed by the rotation curve. This 'maximum-disc' hypothesis is supported by several observational and theoretical arguments. The main conclusions are: (1) There is clear evidence for dark matter in the outer regions of galaxies. The most convincing cases are those of six spiral galaxies with exponential light profiles and flat rotation curves measured out to about 10 disc scalelengths (ca. three times the optical radius R₂₅). (2) The amount of dark matter inside 10 disc scalelengths (20-40 kpc) is three to five times the amount of luminous matter. (3) In the inner region, i.e. inside ca. 2.5 disc scalelengths, luminous matter dominates. (4) The distributions of luminous and dark matter are closely coupled: bulge, disc and halo 'conspire' to produce flat rotation curves. (5) The ratio M_dark/M_lum inside the optical radius, derived with the maximum-disc hypothesis, appears to be independent of galaxy luminosity. (6) Self-consistent halo models show that the large-scale gravitational interaction of disc and dark halo does not alleviate the problem of disc-halo coupling: for a given (maximum) disc there is a unique halo. (7) No convincing information is available yet on the shape of the distribution of dark matter. It is not possible to discriminate between a spherical or flattened halo, or a flaring disc, but a flat disc seems unlikely. Many colleagues contributed to this paper through fruitful discussions and comments, in particular: J. N. Bahcall, S. Casertano, S. M. Kent, R. H. Sanders and J. A. Sellwood. We are grateful to S. M. Kent for letting us use his photometry of UGC 2885, and for sending us inspiring information on his work on dark matter in spiral galaxies. We also thank K. Begeman for the use of his rotation curve data before publication and assistance with the preparation of figures, S. Casertano for the use of his software, and J. Sellwood for providing us with the results of the stability analysis for disc-halo models for NGC 3198. Note added in proof (1 September 1986). In Sellwood's calculations described in section 3d it has been assumed that the Q-value for the disc is equal to 1.5. Different Q-values of this order do not affect the result. In galactic discs with an effective Q-value close to one, two-armed spiral structure could be present for much lower disc densities, and the conclusion reached would not be valid. The possible existence of such cold discs is a matter of dispute however. We thank G. Bertin, C. C. Lin and A. Toomre for correspondence and discussions on this point.