  Located in the Perseus cluster, NGC 1271 is an early-type galaxy with a small
effective radius of 2.2 kpc and a large stellar velocity dispersion of 276 km/s
for its K-band luminosity of 8.9x10^{10} L_sun. We present a mass measurement
for the black hole in this compact, high-dispersion galaxy using observations
from the integral field spectrograph NIFS on the Gemini North telescope
assisted by laser guide star adaptive optics, large-scale integral field unit
observations with PPAK at the Calar Alto Observatory, and Hubble Space
Telescope WFC3 imaging observations. We are able to map out the stellar
kinematics on small spatial scales, within the black hole sphere of influence,
and on large scales that extend out to four times the galaxy's effective
radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise
in the velocity dispersion. Through the use of orbit-based stellar dynamical
models, we determine that the black hole has a mass of (3.0^{+1.0}_{-1.1}) x
10^9 M_sun and the H-band stellar mass-to-light ratio is 1.40^{+0.13}_{-0.11}
M_sun/L_sun (1-sigma uncertainties). NGC 1271 occupies the sparsely-populated
upper end of the black hole mass distribution, but is very different from the
Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are
expected to host the most massive black holes. Interestingly, the black hole
mass is an order of magnitude larger than expectations based on the galaxy's
bulge luminosity, but is consistent with the mass predicted using the galaxy's
bulge stellar velocity dispersion. More compact, high-dispersion galaxies need
to be studied using high spatial resolution observations to securely determine
black hole masses, as there could be systematic differences in the black hole
scaling relations between these types of galaxies and the BCGs/giant
ellipticals, thereby implying different pathways for black hole and galaxy
growth.
