Galactic rotation curves in brane world models

In the brane world scenario the four-dimensional effective Einstein equation has extra source terms, which arise from the embedding of the three-brane in the bulk. These non-local effects, generated by the free gravitational field of the bulk, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic centre, which is usually explained by postulating the existence of the dark matter. In the present paper we consider the asymptotic behaviour of the galactic rotation curves in the brane world models, and compare the theoretical results with observations of both high surface brightness and low surface brightness galaxies. For the chosen sample of galaxies we determine first the baryonic parameters by fitting the photometric data to the adopted galaxy model; then we test the hypothesis of the Weyl fluid acting as dark matter on the chosen sample of spiral galaxies by fitting the tangential velocity equation of the combined baryonic-Weyl model to the rotation curves. We give an analytical expression for the rotational velocity of a test particle on a stable circular orbit in the exterior region to a galaxy, with Weyl fluid contributions included. The model parameter ranges for which the χ2 test provides agreement (within 1σ confidence level) with observations on the velocity fields of the chosen galaxy sample are then determined. There is a good agreement between the theoretical predictions and observations, showing that extra-dimensional models can be effectively used as a viable alternative to the standard dark matter paradigm.