Constraining the Impact of Circumnuclear Disk Warping on Black Hole Mass Measurements With ALMA CO Imaging

Circumnuclear disks (CNDs) are found at the centers of ~10% of all nearby, massive early-type galaxies (ETGs), with radii spanning a few ×100 pc to a few kpc. Recently, high angular resolution CO imaging with the Atacama Large Millimeter/submillimeter Array (ALMA) have revealed these molecular gas disks to be in dynamically cold rotation. Despite the apparent morphological roundness of these dusty disks, CO kinematics show a near ubiquity of either small (5-10° inclination warp) or moderate (10-30°) kinematic warping across the disk extent. Ongoing gas-dynamical modeling of these ALMA emission-line cubes now produce reliable black hole (BH) mass measurements, including a few highly precise BH masses. However, these current modeling efforts have primarily targeted mildly warped disks where the CNDs are treated as geometrically flat. In the one such modeling case to date, inclusion of a more general disk structure did not greatly impact the BH mass measurement. To explore the impact of moderately warped CNDs on BH mass measurement, we present detailed gas-dynamical modeling of the CNDs in NGC 3268, NGC 3557, and NGC 4697 using ALMA CO(2-1) imaging. To account for disk warping, we employ a fully-free tilted-ring model during the modeling process. Using this tilted-ring formalism, we determine best-fitting BH masses ranging from about 0.7 and 1.6x10⁹ solar masses for these three ETGs, with modeling error budgets of about 15-20%. While warped-disk modeling requires significantly greater computation time, the addition of a tilted-ring model greatly improves the fit of the model kinematics to the data. In the worst case, we find that using a flat-disk model systematically biases the BH mass upward by about ~16%, which is larger than any other systematic effect identified in the modeling process.