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.

We apply a statistical deconvolution of the parallax errors based on Lucy’s inversion method (LIM) to the Gaia DR3 sources to measure their 3D velocity components in the range of Galactocentric distances R between 8 and 30 kpc with their corresponding errors and rms values. We find results that are consistent with those obtained by applying LIM to the Gaia DR2 sources, and we conclude that the method gives convergent and more accurate results by improving the statistics of the data set and lowering observational errors. The kinematic maps reconstructed with LIM up to R ≈ 30 kpc show that the Milky Way is characterized by asymmetrical motions with significant gradients in all velocity components. Furthermore, we determine the Galaxy rotation curve V C (R) up to ≈27.5 kpc with the cylindrical Jeans equation assuming an axisymmetric gravitational potential. We find that V C (R) is significantly declining up to the largest radius investigated. Finally, we also measure V C (R) at different vertical heights, showing that, for R < 15 kpc, there is a marked dependence on Z, whereas at larger R the dependence on Z is negligible.

By combining LAMOST DR4 and Gaia DR2 common red clump stars with age and proper motion, we analyze the amplitude evolution of the stellar warp independently of any assumption with a simple model. The greatest height of the warp disk increases with galactocentric distance in different populations and is dependent on age: the younger stellar populations exhibit stronger warp features than the old ones, accompanied by the warp amplitude γ (age) decreasing with age, and its first derivative is different from zero. The azimuth of the line of nodes ϕ w is stable at −5° without clear time evolution, which perfectly confirms some previous works. All of this self-consistent evidence supports that our Galactic warp should most likely be a long-lived but nonsteady structure and not a transient one, which is supporting that the warp originated from gas infall onto the disk or other hypotheses that suppose that the warp mainly affects the gas, and consequently, younger populations tracing the gas are stronger than older ones. In other words, the Galactic warp is induced by the nongravitational interaction over the disk models.