2017MNRAS.470.2034D

Dwarf galaxies, among the most dark matter dominated structures of our Universe, are excellent test-beds for dark matter theories. Unfortunately, mass modelling of these systems suffers from the well-documented mass-velocity anisotropy degeneracy. For the case of spherically symmetric systems, we describe a method for non-parametric modelling of the radial and tangential velocity moments. The method is a numerical velocity anisotropy 'inversion', with parametric mass models, where the radial velocity dispersion profile, σ_rr², is modelled as a B-spline, and the optimization is a three-step process that consists of (i) an evolutionary modelling to determine the mass model form and the best B-spline basis to represent σ_rr²; (ii) an optimization of the smoothing parameters and (iii) a Markov chain Monte Carlo analysis to determine the physical parameters. The mass-anisotropy degeneracy is reduced into mass model inference, irrespective of kinematics. We test our method using synthetic data. Our algorithm constructs the best kinematic profile and discriminates between competing dark matter models. We apply our method to the Fornax dwarf spheroidal galaxy. Using a King brightness profile and testing various dark matter mass models, our model inference favours a simple mass-follows-light system. We find that the anisotropy profile of Fornax is tangential (β(r) < 0) and we estimate a total mass of M_ tot_ = 1.613^+0.050_–0.075 ×10⁸ ^ M^_☉, and a mass-to-light ratio of Υ_V=_8.93^+0.32_–0.47   ( M_☉/ L_☉). The algorithm we present is a robust and computationally inexpensive method for non-parametric modelling of spherical clusters independent of the mass-anisotropy degeneracy.