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.