  NGC 6240 is a pair of colliding disk galaxies, each with a black hole in its
core. We have used laser guide star adaptive optics on the Keck II telescope to
obtain high-resolution ($\sim 0.06$") near-infrared integral-field spectra of
the region surrounding the supermassive black hole in the south nucleus of this
galaxy merger. We use the K-band CO absorption bandheads to trace stellar
kinematics. We obtain a spatial resolution of about 20 pc and thus directly
resolve the sphere of gravitational influence of the massive black hole. We
explore two different methods to measure the black hole mass. Using a Jeans
Axisymmetric Multi-Gaussian mass model, we investigate the limit that a relaxed
mass distribution produces all of the measured velocity dispersion, and find an
upper limit on the black hole mass at $2.0 \pm 0.2 \times 10^9 M_{\sun}$. When
assuming the young stars whose spectra we observe remain in a thin disk, we
compare Keplerian velocity fields to the measured two-dimensional velocity
field measured and fit for a mass profile containing a black hole point mass
plus a radially-varying spherical component, which suggests a lower limit for
the black hole mass of $8.7 \pm 0.3 \times 10^8 M_{\sun}$. Our measurements of
the stellar velocity dispersion place this AGN within the scatter of the
$M_{BH}$-$\sigma_{*}$ relation. As NGC 6240 is a merging system, this may
indicate that the relation is preserved during a merger at least until the
final coalescence of the two nuclei.
