Testing dark matter halos using rotation curves and lensing: A warning on the determination of the halo mass

There are two observations of galaxies that can offer some insight into the nature of dark matter (DM), namely, the rotation curves and the gravitational lensing. While the first one can be studied using the Newtonian limit, the second one is completely relativistic. Each one separately cannot determine the nature of DM, but both together give us key information about this open problem. In this work we use a static and spherically symmetric metric to model the DM halo in a galaxy or in a galaxy cluster. The metric contains two free functions, one associated with the distribution of mass and the other one with the gravitational potential. We use galactic, typical rotation curves to uniquely determine the kinematics of the halos. We compute separately the mass functions for a perfect fluid and a scalar field, and demonstrate that both models can be fitted to the observations, though with different masses. We then employ lensing to discriminate between these models. This procedure represents a test of models using two measurements: rotation curves and lensing.

Figure 1

Comparison of the masses using the rotation velocity profile from the NFW model with a perfect fluid (upper curve) and scalar field (lower curve).

Figure 2

Deflection angle generated by the gravitational lensing of a NFW rotation profile with a perfect fluid (upper curve) and scalar field (lower curve).