VLT Diffraction Limited Imaging and Spectroscopy in the NIR: Weighing the black hole in Centaurus A with NACO

We present high spatial resolution near-infrared spectra and images of the nucleus of Centaurus A (NGC 5128) obtained with NAOS-CONICA at the VLT. The adaptive optics corrected data have a spatial resolution of 0.06" (FWHM) in K- and 0.11" in H-band. The mean velocities and velocity dispersions of the ionized gas ([FeII]) are mapped along four slit positions. The observed gas motions suggest a kinematically hot disk which is orbiting a central object and is oriented nearly perpendicular to the nuclear jet. We model the central rotation and velocity dispersion curves of the [FeII] gas orbiting in the combined potential of the stellar mass and the (dominant) black hole. Our physically most plausible model, a dynamically hot and geometrically thin gas disk, yields a black hole mass of M_bh = (8.6 +/- 0.3) x 10^7 M_sun. As the physical state of the gas is not well understood, we also consider two limiting cases: first a cold disk model, which completely neglects the velocity dispersion, but is in line with many earlier gas disk models; it yields an M_bh estimate that is almost three times lower. The other extreme case is to model a spherical gas distribution in hydrostatic equilibrium through Jeans equation. Compared to the hot disk model the best-fit black hole mass increases by a factor of 1.5. This wide mass range spanned by the limiting cases shows how important the gas physics is even for high resolution data. Our overall best-fitting black hole mass is a factor of 2.5 lower than previous measurements. With our revised M_bh estimate, CenA's offset from the M_bh-sigma relation is significantly reduced, but it still falls above this relation by a factor of ~3. (Abridged