We present two-dimensional gas-kinematic maps of the central region in Centaurus A. The adaptive optics (AO) assisted SINFONI data from the VLT have a resolution of 0.12 in K-band. The ionized gas species (Br_gamma, [FeII], [SiVI]) show a rotational pattern that is increasingly overlaid by non-rotational motion for higher excitation lines in direction of Cen As radio jet. The emission lines of molecular hydrogen (H_2) show regular rotation and no distortion due to the jet. The molecular gas seems to be well settled in the gravitational potential of the stars and the central supermassive black hole and we thus use it as a tracer to model the mass in the central +/-1.5. These are the first AO integral-field observations on the nucleus of Cen A, enabling us to study the regularity of the rotation around the black hole, well inside the radius of influence, and to determine the inclination angle of the gas disk in a robust way. The gas kinematics are best modeled through a tilted-ring model that describes the warped gas disk; its mean inclination angle is ~34deg and the mean position angle of the major axis is ~155deg. The best-fit black hole mass is M_BH~4.5x10^7 Msolar, based on a kinematically hot disk model where the velocity dispersion is included through the Jeans equation. This black hole mass estimate is somewhat lower than, but consistent with the mass values previously derived from ionized gas kinematics. It is also consistent with the stellar dynamical measurement from the same AO observations, which we present in a separate paper. It brings Cen A in agreement with the M_BH-sigma relation.
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