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Revisiting the influence of unidentified binaries on velocity dispersion measurements in ultra-faint stellar systems

Velocity dispersion measurements of recently discovered Milky Way satellites with $M_V\gtrsim-7$ imply they posses high mass-to-light ratios. The expected velocity dispersions due to their baryonic mass are $\sim0.2$\,km\,s$^{-1}$, but values $\gtrsim3$\,km\,s$^{-1}$ are measured. We perform Monte Carlo simulations of mock radial velocity measurements of these systems assuming they have mass-to-light ratios similar to globular clusters and posses an unidentified binary star population, to determine if these stars could boost the velocity dispersion to the observed values. We find that this hypothesis is unlikely to produce dispersions much in excess of $\sim 4.5$\,km\,s$^{-1}$, in agreement with previous work. However, for the systems with potentially the smallest velocity dispersions, values consistent with observations are produced in 5-40% of our simulations for binary fractions in excess of $f_{bin}(P\le10$\,yrs$)\sim5%$. This sample includes the dwarf galaxy candidates that lie closest to classical globular clusters in $M_V-r_h$ space. Considered as a population, it is unlikely that all of these dwarf galaxy candidates have mass-to-light ratios typical of globular clusters, but boosting of the observed dispersion by binaries from near-zero values cannot be ruled out at high confidence for several individual dwarf galaxy candidates. Given the importance of obtaining accurate velocity dispersions and dynamical masses for the faintest satellites, it is clearly desirable to exclude directly the possible effect of binaries on these systems. This requires multi-epoch radial velocity measurements with individual uncertainties of $\lesssim$1\,km\,s$^{-1}$ to identify spectroscopic binaries with orbital velocities of order the observed velocity dispersion.