A wide-field H I mosaic of Messier 31 - II. The disk warp, rotation, and the dark matter halo

Aims. We test cosmological models of structure formation using the rotation curve of the nearest spiral galaxy, M 31, determined using a recent deep, full-disk 21-cm imaging survey smoothed to 466 pc resolution. Methods. We fit a tilted ring model to the HI data from 8 to 37 kpc and establish conclusively the presence of a dark halo and its density distribution via dynamical analysis of the rotation curve. Results. The disk of M 31 warps from 25 kpc outwards and becomes more inclined with respect to our line of sight. Newtonian dynamics without a dark matter halo provide a very poor fit to the rotation curve. In the framework of modified Newtonian dynamic (MOND) however the 21-cm rotation curve is well fitted by the gravitational potential traced by the baryonic matter density alone. The inclusion of a dark matter halo with a density profile as predicted by hierarchical clustering and structure formation in a ACDM cosmology makes the mass model in newtonian dynamic compatible with the rotation curve data. The dark halo concentration parameter for the best fit is C = 12 and its total mass is 1.2 x 10 12 M ⊙ . If a dark halo model with a constant-density core is considered, the core radius has to be larger than 20 kpc in order for the model to provide a good fit to the data. We extrapolate the best-fit ACDM and constant-density core mass models to very large galactocentric radii, comparable to the size of the dark matter halo. A comparison of the predicted mass with the M 31 mass determined at such large radii using other dynamical tracers, confirms the validity of our results. In particular the ACDM dark halo model which best fits the 21-cm data well reproduces the mass of M 31 traced out to 560 kpc. Our best estimate for the total mass of M 31 is 1.3 x 10 12 M ⊙ , with 12% baryonic fraction and only 6% of the baryons in the neutral gas phase.