2025MNRAS.542.2542D

We present the results of determining the parameters characterizing the shape and orientation of residual velocity ellipsoids from the Gaia DR3 red giants and sub-giants. We show the distribution of velocity dispersions $\sigma ^2_\xi , \sigma ^2_\eta , \sigma ^2_\zeta$ in the Galactic plane obtained from three components of the spatial velocity, as well as the coordinate distribution of the intersection points of the velocity ellipsoid axes with the celestial sphere, in particular the deviations of the longitudes and latitudes of the vertices of stellar regions located within spheres with a radius of 1 kpc centred in the Galactic mid-plane. Based on modelling, we also conduct a study of the influence of random errors that can lead to systematic distortions of the real ellipsoid parameters. The area of the Galactic disc under study is in the range of Galactocentric coordinates $0< R< 15$ kpc and $120^\circ <\theta < 240^\circ$. We show that the vertex deviations in some regions of the Galactic mid-plane can reach $30^\circ$ in longitude, and $15^\circ$ in latitude. This indicates the presence of kinematic distortions of the stellar velocity field, especially noticeable in the angular range of $150^\circ <\theta < 210^\circ$ at a distance of approximately 13 kpc. We propose to consider the deviation angles of the longitudes and latitudes of the ellipsoid axes of residual stellar velocities as kinematic signatures of various Galactic deformations, determined by the real spatial velocity fields. We present the distribution of parameters characterizing the shapes of velocity ellipsoids, as well as the distribution of their semi-axes length ratios. We indicate a local feature in this distribution and in the distribution of the ellipsoid oblongnesses. We perform a comparison of the results obtained from the tensor of deformation velocities and from the observed spatial velocities.