Toward Precision Black Hole Masses with ALMA: NGC 1332 as a Case Study
  in Molecular Disk Dynamics
  We present first results from a program of Atacama Large
Millimeter/submillimeter Array (ALMA) CO(2-1) observations of circumnuclear gas
disks in early-type galaxies. The program was designed with the goal of
detecting gas within the gravitational sphere of influence of the central black
holes. In NGC 1332, the 0.3"-resolution ALMA data reveal CO emission from the
highly inclined (i~ 83 degrees) circumnuclear disk, spatially coincident with
the dust disk seen in Hubble Space Telescope images. The disk exhibits a
central upturn in maximum line-of-sight velocity reaching +-500 km/s relative
to the systemic velocity, consistent with the expected signature of rapid
rotation around a supermassive black hole. Rotational broadening and beam
smearing produce complex and asymmetric line profiles near the disk center. We
constructed dynamical models for the rotating disk and fitted the modeled CO
line profiles directly to the ALMA data cube. Degeneracy between rotation and
turbulent velocity dispersion in the inner disk precludes the derivation of
strong constraints on the black hole mass, but model fits allowing for a
plausible range in the magnitude of the turbulent dispersion imply a central
mass in the range ~(4-8)x10^8 Msun. We argue that gas-kinematic observations
resolving the black hole's projected radius of influence along the disk's minor
axis will have the capability to yield black hole mass measurements that are
largely insensitive to systematic uncertainties in turbulence or in the stellar
mass profile. For highly inclined disks, this is a much more stringent
requirement than the usual sphere-of-influence criterion.
