Modelling the Milky Way through adiabatic compression of cold dark matter halo

We use the adiabatic compression theory to build a physically well - motivated Milky Way mass model in agreement with the observational data. The visible mass of the Galaxy is distributed in a spheroidal bulge and a multi - components disc parametrized by three galactic parameters, the Sun distance to the galactic centre, R_0, the total bulge mass, M_{bulge}, and the local disc surface density, \Sigma_{\odot}. To model the dark matter component, we adiabatically compress a Navarro, Frenk and White (NFW) halo (with concentration $c$ and total mass M_{vir}) for fixed values of the spin parameter, \lambda, the fraction of the mass in baryons, $m_b$, and the thin disc contribution to total angular momentum, j_d. An iterative selection procedure is used to explore in very detail the wide space of parameters only selecting those combinations of {R_0, M_{bulge}, \Sigma_{\odot}, \lambda, m_b, j_b, c, M_{vir}} that give rise to a Milky Way model in agreement with the observational constraints. This analysis leads us to conclude that only models with R_0 = 8.5 kpc, $0.8 x 10^{10} M_{\odot} < M_{bulge} < 1.6 x 10^{10} M_{\odot}$ and $49 M_{\odot} pc^{-2} \le \Sigma_{\odot} \le 56 M_{\odot} pc^{-2}$ can be reconciled with the set of observational constraints. As regard the parameters entering the adiabatic compression, we find $0.03 \le \lambda \le 0.10$ and $0.04 \le m_b \le 0.10$, while the final estimates of the parameters describing the initial halo profile turn out to be $5 \stackrel{<}{\sim} c \stackrel{<}{\sim} 12$ and $7 x 10^{11} M_{\odot} \stackrel{<}{\sim} M_\mathrm{vir} \stackrel{<}{\sim} 17 x 10^{11} M_{\odot}$ (all at 95.7% CL).