A self-consistent dynamical model of the Milky Way disc adjusted to Gaia data

International audienceContext. Accurate astrometry achieved by Gaia for many stars in the Milky Way provides an opportunity to reanalyse the Galactic stellar populations from a large and homogeneous sample and to revisit the Galaxy gravitational potential. Aims. This paper shows how a self-consistent dynamical model can be obtained by fitting the gravitational potential of the Milky Way to the stellar kinematics and densities from Gaia data. Methods. We derived a gravitational potential using the Besancon Galaxy Model, and computed the disc stellar distribution functions based on three integrals of motion ( E , L z , I 3 ) to model stationary stellar discs. The gravitational potential and the stellar distribution functions are built self-consistently, and are then adjusted to be in agreement with the kinematics and the density distributions obtained from Gaia observations. A Markov chain Monte Carlo (MCMC) is used to fit the free parameters of the dynamical model to Gaia parallax and proper motion distributions. The fit is done on several sets of Gaia data, mainly a subsample of the GCNS ( Gaia catalogue of nearby stars to 100 pc) with G < 17, together with 26 deep fields selected from eDR3, widely spread in longitudes and latitudes. Results. We are able to determine the velocity dispersion ellipsoid and its tilt for subcomponents of different ages, both varying with R and z . The density laws and their radial scale lengths for the thin and thick disc populations are also obtained self-consistently. This new model has some interesting characteristics that come naturally from the process, such as a flaring thin disc. The thick disc is found to present very distinctive characteristics from the old thin disc, both in density and kinematics. This lends significant support to the idea that thin and thick discs were formed in distinct scenarios, as the density and kinematics transition between them is found to be abrupt. The dark matter halo is shown to be nearly spherical. We also derive the solar motion with regards to the Local Standard of Rest (LSR), finding U ⊙ = 10.79 ± 0.56 km s −1 , V ⊙ = 11.06 ± 0.94 km s −1 , and W ⊙ = 7.66 ± 0.43 km s −1 , in close agreement with recent studies. Conclusions. The resulting fully self-consistent gravitational potential, still axisymmetric, is a good approximation of a smooth mass distribution in the Milky Way and can be used for further studies, including finding streams, substructures, and to compute orbits for real stars in our Galaxy