Local variations of the Stellar Velocity Ellipsoid-II: the effect of the
  bar in the inner regions of Auriga galaxies
  Theoretical works have shown that off-plane motions of bars can heat stars in
the vertical direction during buckling but is not clear how do they affect the
rest of components of the Stellar Velocity Ellipsoid (SVE). We study the 2D
spatial distribution of the vertical, $\sigma_{z}$, azimuthal, $\sigma_{\phi}$
and radial, $\sigma_{r}$ velocity dispersions in the inner regions of Auriga
galaxies, a set of high-resolution magneto-hydrodynamical cosmological zoom-in
simulations, to unveil the influence of the bar on the stellar kinematics.
$\sigma_{z}$ and $\sigma_{\phi}$ maps exhibit non-axisymmetric features that
closely match the bar light distribution with low $\sigma$ regions along the
bar major axis and high values in the perpendicular direction. On the other
hand, $\sigma_{r}$ velocity dispersion maps present more axisymmetric
distributions. We show that isophotal profile differences best capture the
impact of the bar on the three SVE components providing strong correlations
with bar morphology proxies although there is no relation with individual
$\sigma$. Time evolution analysis shows that these differences are a
consequence of the bar formation and that they tightly coevolve with the
strength of the bar. We discuss the presence of different behaviours of
$\sigma_{z}$ and its connection with observations. This work helps us
understand the intrinsic $\sigma$ distribution and motivates the use of
isophotal profiles as a mean to quantify the effect of bars.
