The effect of unresolved binaries on globular cluster proper-motion
  dispersion profiles
  High-precision kinematic studies of globular clusters require an accurate
knowledge of all possible sources of contamination. Amongst other sources,
binary stars can introduce systematic biases in the kinematics. Using a set of
Monte Carlo cluster simulations with different concentrations and binary
fractions, we investigate the effect of unresolved binaries on proper-motion
dispersion profiles, treating the simulations like HST proper-motion samples.
Since globular clusters evolve towards a state of partial energy equipartition,
more massive stars lose energy and decrease their velocity dispersion. As a
consequence, on average, binaries have a lower velocity dispersion, since they
are more massive kinematic tracers. We show that, in the case of clusters with
high binary fraction (initial binary fraction of 50%) and high concentration
(i.e., closer to energy equipartition), unresolved binaries introduce a
color-dependent bias in the velocity dispersion of main-sequence stars of the
order of 0.1-0.3 km s$^{-1}$ (corresponding to $1-6$% of the velocity
dispersion), with the reddest stars having a lower velocity dispersion, due to
the higher fraction of contaminating binaries. This bias depends on the ability
to distinguish binaries from single stars, on the details of the
color-magnitude diagram and the photometric errors. We apply our analysis to
the HSTPROMO data set of NGC 7078 (M15) and show that no effect ascribable to
binaries is observed, consistent with the low binary fraction of the cluster.
Our work indicates that binaries do not significantly bias proper-motion
velocity-dispersion profiles, but should be taken into account in the error
budget of kinematic analyses.
