Characterizing a cluster's dynamic state using a single epoch of radial
  velocities
  Radial velocity measurements can be used to constrain the dynamical state of
a stellar cluster. However, for clusters with velocity dispersions smaller than
a few km/s the observed radial velocity distribution tends to be dominated by
the orbital motions of binaries rather than the stellar motions through the
potential well of the cluster. Our goal is to characterize the intrinsic
velocity distribution of a cluster from a single epoch of radial velocity data,
even for a cluster with a velocity dispersion of a fraction of a km/s, using a
maximum likelihood procedure. Assuming a period, mass ratio, and eccentricity
distribution for the binaries in the observed cluster this procedure fits a
dynamical model describing the velocity distribution for the single stars and
center of masses of the binaries, simultaneously with the radial velocities
caused by binary orbital motions, using all the information available in the
observed velocity distribution. We find that the fits to the intrinsic velocity
distribution depend only weakly on the binary properties assumed, so the
uncertainty in the fitted parameters tends to be dominated by statistical
uncertainties. Based on Monte Carlo simulations we provide an estimate of how
these statistical uncertainties vary with the velocity dispersion, binary
fraction, and the number of observed stars, which can be used to estimate the
sample size needed to reach a specific accuracy. Finally we test the method on
the well-studied open cluster NGC 188, showing that it can reproduce a velocity
dispersion of only 0.5 km/s using a single epoch of the multi-epoch radial
velocity data. If the binary period, mass ratio, and eccentricity distribution
of the observed stars are roughly known, this procedure can be used to correct
for the effect of binary orbital motions on an observed velocity distribution.
[Abridged]
