Spectroastrometry of rotating gas disks for the detection of
  supermassive black holes in galactic nuclei. I. Method and simulations
  This is the first in a series of papers in which we study the application of
spectroastrometry in the context of gas kinematical studies aimed at measuring
the mass of supermassive black holes. The spectroastrometrical method consists
in measuring the photocenter of light emission in different wavelength or
velocity channels. In particular we explore the potential of spectroastrometry
of gas emission lines in galaxy nuclei to constrain the kinematics of rotating
gas disks and to measure the mass of putative supermassive black holes. By
means of detailed simulations and test cases, we show that the fundamental
advantage of spectroastrometry is that it can provide information on the
gravitational potential of a galaxy on scales significantly smaller (~ 1/10)
than the limit imposed by the spatial resolution of the observations. We then
describe a simple method to infer detailed kinematical informations from
spectroastrometry in longslit spectra and to measure the mass of nuclear mass
concentrations. Such method can be applied straightforwardly to integral field
spectra, which do not have the complexities due to a partial spatial covering
of the source in the case of longslit spectra.
