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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.