We present Sauron 2D spectrography of the central 1.5 kpc of the nearby Sey2 galaxy NGC1068, encompassing the well-known NIR inner bar. We have successively disentangled the respective contributions of the ionized gas and stars, thus deriving their 2D distribution and kinematics. The [OIII] and Hbeta emission lines exhibit very different spatial distribution and kinematics, the latter following inner spiral arms with clumps associated with star formation. Strong inwards streaming motions are observed in both the Hbeta and [OIII] kinematics. The stellar kinematics also exhibit clear signatures of a non-axisymmetric tumbling potential, with a twist in both the velocity and h3 fields. We re-examined the long-slit data of Shapiro et al (2003) using pPXF: a strong decoupling of h3 is revealed, and the central decrease in h4 hinted in the Sauron data is confirmed. These data also suggest that NGC1068 is a good candidate for a so-called sigma-drop. We confirm the possible presence of two pattern speeds. We also examine the stellar kinematics of bars formed in N-body+SPH simulations built from axisymmetric initial conditions. These successfully reproduce a number of properties observed in the 2D kinematics of NGC1068, and the long-slit data, showing that the kinematic signature of the NIR bar is imprinted in the stellar kinematics. The remaining differences between the models and the observed properties are mostly due to the exclusion of star formation and the lack of the primary large-scale oval/bar in the simulations. These models suggest that the inner bar could drive a significant amount of gas down to a scale of ~300 pc. This is consistent with the interpretation of the sigma-drop in NGC1068 being the result of central gas accretion followed by an episode of star formation.
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