Black hole mass measurement using molecular gas kinematics: what ALMA
  can do
  We study the limits of the spatial and velocity resolution of radio
interferometry to infer the mass of supermassive black holes (SMBHs) in
galactic centres using the kinematics of circum-nuclear molecular gas, by
considering the shapes of the galaxy surface brightness profile,
signal-to-noise ratios (S/Ns) of the position-velocity diagram (PVD) and
systematic errors due to the spatial and velocity structure of the molecular
gas. We argue that for fixed galaxy stellar mass and SMBH mass, the spatial and
velocity scale that need to be resolved increase and decrease, respectively,
with decreasing \sersic\ index of the galaxy surface brightness profile. We
validate our arguments using simulated PVDs for varying beam size and velocity
channel width. Furthermore, we consider the systematic effects on the inference
of the SMBH mass by simulating PVDs including the spatial and velocity
structure of the molecular gas, which demonstrates that their impacts are not
significant for a PVD with good S/N unless the spatial and velocity scale
associated with the systematic effects are comparable to or larger than the
angular resolution and velocity channel width of the PVD from pure circular
motion. Also, we caution that a bias in a galaxy surface brightness profile
owing to the poor resolution of a galaxy photometric image can largely bias the
SMBH mass by an order of magnitude. This study shows the promise and the limit
of ALMA observations for measuring SMBH mass using molecular gas kinematics and
provides a useful technical justification for an ALMA proposal with the science
goal of measuring SMBH mass.
