  We measure the black hole mass in the nearby active galaxy Centaurus A (NGC
5128) using a new method based on spectroastrometry of a rotating gas disk. The
spectroastrometric approach consists in measuring the photocenter position of
emission lines for different velocity channels. In a previous paper we focused
on the basic methodology and the advantages of the spectroastrometric approach
with a detailed set of simulations demonstrating the possibilities for black
hole mass measurements going below the conventional spatial resolution. In this
paper we apply the spectroastrometric method to multiple longslit and integral
field near infrared spectroscopic observations of Centaurus A. We find that the
application of the spectroastrometric method provides results perfectly
consistent with the more complex classical method based on rotation curves: the
measured BH mass is nearly independent of the observational setup and spatial
resolution and the spectroastrometric method allows the gas dynamics to be
probed down to spatial scales of ~0.02", i.e. 1/10 of the spatial resolution
and ~1/50 of BH sphere of influence radius. The best estimate for the BH mass
based on kinematics of the ionized gas is then log(MBH (sin i)^2/M\odot)=7.5
\pm 0.1 which corresponds to MBH = 9.6(+2.5-1.8) \times 10^7 M\odot for an
assumed disk inclination of i = 35deg. The complementarity of this method with
the classic rotation curve method will allow us to put constraints on the disk
inclination which cannot be otherwise derived from spectroastrometry. With the
application to Centaurus A, we have shown that spectroastrometry opens up the
possibility of probing spatial scales smaller than the spatial resolution,
extending the measured MBH range to new domains which are currently not
accessible: smaller BHs in the local universe and similar BHs in more distant
galaxies.
