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

TL;DR

This paper investigates how combining galaxy rotation curves and gravitational lensing can test dark matter halo models, highlighting potential ambiguities in mass determination and the importance of using both observations together.

Contribution

It introduces a method to model dark matter halos with a metric containing two free functions and demonstrates how rotation curves and lensing can jointly discriminate between different dark matter models.

Findings

Both perfect fluid and scalar field models fit rotation curves with different masses.

Lensing can help distinguish between these models despite similar rotation curve fits.

Using both observations together provides a more robust test of dark matter models.

Abstract

There are two observations of galaxies that can offer some insight into the nature of the 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 can not 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 univocally 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.