  We present the first direct measurement of the central black hole mass, M_BH,
in NGC 6086, the Brightest Cluster Galaxy (BCG) in Abell 2162. Our
investigation demonstrates for the first time that stellar dynamical
measurements of M_BH in BCGs are possible beyond the nearest few galaxy
clusters. We observed NGC 6086 with laser guide star adaptive optics and the
integral-field spectrograph (IFS) OSIRIS at the W.M. Keck Observatory, and with
the seeing-limited IFS GMOS-N at Gemini Observatory North. We combined the two
IFS data sets with existing major-axis kinematics, and used axisymmetric
stellar orbit models to determine M_BH and the R-band stellar mass-to-light
ratio, M*/L_R. We find M_BH = 3.6(+1.7)(-1.1) x 10^9 M_Sun and M*/L_R =
4.6(+0.3)(-0.7) M_Sun/L_Sun (68% confidence), from models using the most
massive dark matter halo allowed within the gravitational potential of the host
cluster. Models fitting only IFS data confirm M_BH ~ 3 x 10^9 M_Sun and M*/L_R
~ 4 M_Sun/L_Sun, with weak dependence on the dark matter halo structure. When
data out to 19 kpc are included, the unrealistic omission of dark matter causes
the best-fit black hole mass to decrease dramatically, to 0.6 x 10^9 M_Sun, and
the best-fit stellar mass-to-light ratio to increase to 6.7 M_Sun/L_Sun. The
latter value is at further odds with stellar population studies favoring M*/L ~
2 M_Sun/L_Sun,R. Biases from dark matter omission could extend to dynamical
models of other galaxies with central stellar cores, and new measurements of
M_BH from models with dark matter could steepen the empirical scaling
relationships between black holes and their host galaxies.
