Abstract
In the braneworld scenario the four dimensional effective Einstein equation has extra source terms, which arise from the embedding of the 3-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 center, which is usually explained by postulating the existence of the dark matter. In the present paper we consider the asymptotic behavior of the galactic rotation curves in the brane world models, and we 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 $\chi^2$ test provides agreement (within 1$\sigma$ 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.
Highlights
Gravitational effects which require more matter than what is visible can be explained in terms of a mysterious dark matter, the nature of which remains a long-standing problem in modern astrophysics
We model the distribution of baryonic mass in High Surface Brightness galaxies as a sum of disk and bulge components with constant, but distinct mass-to-light ratios
At the end of this subsection we prove that the ”truncation” of the Weyl fluid at rb does not induce any distributional source layer at rb, it is consistent with the junction conditions across the sphere with radius rb
Summary
Gravitational effects which require more matter than what is visible can be explained in terms of a mysterious dark matter, the nature of which remains a long-standing problem in modern astrophysics. A second method consists in closing the field equations on the brane by imposing the condition of the constancy of the rotational velocity curves for particles in stable orbits It is the purpose of the present paper to consider the general behavior of the vacuum gravitational field equations in the brane world model in the region of constant tangential rotational velocity of test particles in stable circular orbits, and to compare the predictions of our model with the existing observational data. This situation is characteristic for particles gravitating in circular orbits around the galactic center (Binney & Tremaine 1987).
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