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The connection between the Stellar Velocity Ellipsoid (SVE) and the dynamicalevolution of galaxies has been a matter of debate in the last years and thereis no clear consensus whether different heating agents (e.g. spiral arms, giantmolecular clouds, bars and mergers) leave clear detectable signatures in thepresent day kinematics. Most of these results are based on a single and globalSVE and have not taken into account that these agents do not necessarilyequally affect all regions of the stellar disc.We study the 2D spatialdistribution of the SVE across the stellar discs of Auriga galaxies, a set ofhigh resolution magneto-hydrodynamical cosmological zoom-in simulations, tounveil the connection between local and global kinematic properties in the discregion. We find very similar, global, $\sigma_{z}/\sigma_{r}$= 0.80$\pm$ 0.08values for galaxies of different Hubble types. This shows that the globalproperties of the SVE at z=0 are not a good indicator of the heating andcooling events experienced by galaxies. We also find that similar$\sigma_{z}/\sigma_{r}$radial profiles are obtained through differentcombinations of $\sigma_{z}$ and $\sigma_{r}$ trends: at a local level, thevertical and radial components can evolve differently, leading to similar$\sigma_{z}/\sigma_{r}$ profiles at z=0. By contrast, the 2D spatialdistribution of the SVE varies a lot more from galaxy to galaxy. Present dayfeatures in the SVE spatial distribution may be associated with specificinteractions such as fly-by encounters or the accretion of low mass satelliteseven in the cases when the global SVE is not affected. The stellar populationsdecomposition reveals that young stellar populations present colder and lessisotropic SVEs and more complex 2D distributions than their older and hottercounterparts.

Local variations of the Stellar Velocity Ellipsoid-I: the disc of galaxies in the Auriga simulations