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.