Context. The structure of outer disc of our Galaxy is still not well described, and many features need to be better understood. The second Gaia data release (DR2) provides data in unprecedented quality that can be analysed to shed some light on the outermost parts of the Milky Way. Aims. We calculate the stellar density using star counts obtained from Gaia DR2 up to a Galactocentric distance R=20 kpc with a deconvolution technique for the parallax errors. Then we analyse the density in order to study the structure of the outer Galactic disc, mainly the warp. Methods. In order to carry out the deconvolution, we used the Lucy inversion technique for recovering the corrected star counts. We also used the Gaia luminosity function of stars with MG < 10 to extract the stellar density from the star counts. Results. The stellar density maps can be fitted by an exponential disc in the radial direction hr = 2.07 ± 0.07 kpc, with a weak dependence on the azimuth, extended up to 20 kpc without any cut-off. The flare and warp are clearly visible. The best fit of a symmetrical S-shaped warp gives zw ≈ z + (37 ± 4.2(stat.) − 0.91(syst.))pc · (R/R ) 2.42±0.76(stat.)+0.129(syst.) sin(φ + 9.3 • ± 7.37 • (stat.) + 4.48 • (syst.)) for the whole population. When we analyse the northern and southern warps separately, we obtain an asymmetry of an ∼ 25% larger amplitude in the north. This result may be influenced by extinction because the Gaia G band is quite prone to extinction biases. However, we tested the accuracy of the extinction map we used, which shows that the extinction is determined very well in the outer disc. Nevertheless, we recall that we do not know the full extinction error, and neither do we know the systematic error of the map, which may influence the final result. The analysis was also carried out for very luminous stars alone (MG < −2), which on average represents a younger population. We obtain similar scale-length values, while the maximum amplitude of the warp is 20 − 30% larger than with the whole population. The north-south asymmetry is maintained.

Context. Recent statistical deconvolution methods have produced extended kinematical maps in a range of heliocentric distances that are a factor of two to three larger than those analysed in Gaia Collaboration (2018, A&A, 616, A11) based on the same data. Aims. In this paper, we use such maps to derive the rotation curve both in the Galactic plane and in off-plane regions and to analyse the density distribution. Methods. By assuming stationary equilibrium and axisymmetry, we used the Jeans equation to derive the rotation curve. Then we fit it with density models that include both dark matter and predictions of the MOND (Modified Newtonian dynamics) theory. Since the Milky Way exhibits deviations from axisymmetry and equilibrium, we also considered corrections to the Jeans equation. To compute such corrections, we ran N-body experiments of mock disk galaxies where the departure from equilibrium becomes larger as a function of the distance from the centre. Results. The rotation curve in the outer disk of the Milky Way that is constructed with the Jeans equation exhibits very low dependence on R and z and it is well-fitted both by dark matter halo and MOND models. The application of the Jeans equation for deriving the rotation curve, in the case of the systems that deviate from equilibrium and axisymmetry, introduces systematic errors that grow as a function of the amplitude of the average radial velocity. In the case of the Milky Way, we can observe that the amplitude of the radial velocity reaches ∼10% that of the azimuthal one at R ≈ 20 kpc. Based on this condition, using the rotation curve obtained from the Jeans equation to calculate the mass may overestimate its measurement.

Context. In our Paper I, by using statistical deconvolution methods, extended kinematics maps of Gaia-DR2 data have been produced in a range of heliocentric distances that are a factor of two to three larger than those analyzed previously by the Gaia Collaboration with the same data. It added the range of Galactocentric distances between 13 kpc and 20 kpc to the previous maps. Aims. Here, we investigate the dynamical effects produced by different mechanisms that can explain the radial and vertical components of these extended kinematic maps, including a decomposition of bending and breathing of the vertical components. This paper as a whole tries to be a compendium of different dynamical mechanisms whose predictions can be compared to the kinematic maps. Methods. Using analytical methods or simulations, we are able to predict the main dynamical factors and compare them to the predictions of the extended kinematic maps of Gaia-DR2. Results. The gravitational influence of Galactic components that are different from the disk, such as the long bar or bulge, the spiral arms, or a tidal interaction with Sagittarius dwarf galaxy, may explain some features of the velocity maps, especially in the inner parts of the disk. However, they are not sufficient in explaining the most conspicuous gradients in the outer disk. Vertical motions might be dominated by external perturbations or mergers, although a minor component may be due to a warp whose amplitude evolves with time. Here, we show with two different methods, which analyze the dispersion of velocities, that the mass distribution of the disk is flared. Despite these partial explanations, the main observed features can only be explained in terms of out-of-equilibrium models, which are either due to external perturbers or to the fact that the disk has not had time to reach equilibrium since its formation.

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Context. The outer Galactic disc contains some features such as the warp and flare, whose origin is still debated. The Gaia data provide an excellent opportunity to probe the Galactic disc at large distances and study these features. Aims. We derive the density distributions of the average (old) whole population and the supergiants (representative of a young population), and we use them to constrain their warp and flare. By comparing the results, we study how the properties of these phenomena depend on the studied population. Methods. We used Lucy's deconvolution method to recover corrected star counts as a function of distance, from which we derive the density distribution. Results. We find that supergiants have an asymmetric warp, reaching a maximum amplitude of z w = 0.658 kpc and minimum amplitude of z w = −0.717 kpc at a distance of R = [19.5, 20] kpc, which is almost twice as high as the amplitude of the whole population of the disc. We find a significant flare of the whole population, especially in the thick disc. The scale height increases from h z,thick ≈ 0.8 kpc and h z,thin ≈ 0.3 kpc in the solar neighbourhood, to h z,thick ≈ 3 kpc and h z,thin ≈ 0.7 kpc in the remote regions of the Milky Way (R ≈ 18 kpc). The supergiants' population has only a small flare.