A Universal Coupling Relation between Luminous and Dark Matter Surface Densities in Disk Rotating Galaxies

Abstract

The mutual dynamical evolution of visible and dark matter in spiral galaxies may have resulted in some kind of coupling between the distributions of visible and dark matter today. This conjecture is empirically explored in the present paper, where rotation curves of 60 spiral galaxies and universal rota- tion curves are —tted using dark halo models with a distribution that depends on the luminous mass distribution. It is shown that the dark matter pro—les of any universal rotation curve can be decomposed into two components: (1) a main component, called ii coupled halo,ˇˇ and (2) a component having a gaslike distribution, negligible in bright galaxies, but of increasing signi—cance toward faint galaxies. Once the disk component (stars, gas, and gaslike component) is subtracted, the dark halo integrated surface densities, are in a plane (in log scale) where the fundamental parameters are p c , only and characterizes the relative importance of the dark halo to the disk mass. This is the coupled halo. In the case of an exponential disk, the coupled halo has a central pro—le of the form o P r~1 and a —at curve at The fact that the gaslike component decreases with luminosity suggests that it may r r opt . be transformed into stars, and therefore could be dark baryons, possibly cold gas in the disk. In these models, the baryonic fraction (stars, gas, and gaslike component) is almost a constant over a range of 5 mag, that is, D30% at 1.5 optical radii. The stellar fraction of baryonic matter increases with luminosity. The model predicts a large fraction of gaslike baryonic dark matter in faint spiral galaxies, i.e., in H I gasrich systems. The mass fraction of this gaslike component is negligible in a galaxy like the Milky Way, and reaches half the halo mass in the faint, low surface brightness galaxy DDO 154. Some —ne- tuning relations, which look mysterious in the context of isothermal halos, are deduced from the coupled halos. The Tully-Fisher relation results from the coupling relation between visible and dark matter surface densities and from the virial theorem. The empirical coupling relation can be used in simulations of the dynamical evolution of gas and stars plus dark matter subsystems to constrain the nature of the halo dark matter. If a form of halo dark matter complies with the coupling relation, it will —t rotation curves without —ne-tuning conspiracies. Subject headings: dark mattergalaxies: fundamental parameters ¨ galaxies: kinematics and dynamicsgravitation