How well can we Measure the Intrinsic Velocity Dispersion of Distant
  Disk Galaxies?
  The kinematics of distant galaxies, from z=0.1 to z>2, play a key role in our
understanding of galaxy evolution from early times to the present. One of the
important parameters is the intrinsic, or local, velocity dispersion of a
galaxy, which allows one to quantify the degree of non-circular motions such as
pressure support. However, this is difficult to measure because the observed
dispersion includes the effects of (often severe) beam smearing on the velocity
gradient. Here we investigate four methods of measuring the dispersion that
have been used in the literature, to assess their effectiveness at recovering
the intrinsic dispersion. We discuss the biasses inherent in each method, and
apply them to model disk galaxies in order to determine which methods yield
meaningful quantities, and under what conditions. All the mean weighted
dispersion estimators are affected by (residual) beam smearing. In contrast,
the dispersion recovered by fitting a spatially and spectrally convolved disk
model to the data is unbiassed by the beam smearing it is trying to compensate.
Because of this, and because the bias it does exhibit depends only on the
signal-to-noise, it can be considered reliable. However, at very low
signal-to-noise, all methods should be used with caution.
