Abstract
Ultrafaint dwarf (UFD) galaxies are dominated by dark matter, the distribution of which may be inferred from the kinematics of that galaxy's stellar population. Star-by-star observations are available for the satellite UFD galaxies of the Milky Way, making them uniquely good laboratories in which to test cosmological predictions at the smallest scales. However, the kinematics of these galaxies are complicated by the presence of binary stars, which alter the stellar velocity distribution. In particular, these binary stars increase the galaxy's stellar velocity dispersion, which is related to the total galactic mass by the virial theorem. Without correctly eliminating or accounting for binary stars, we may therefore overestimate the masses of UFD galaxies or even confuse globular clusters for UFD galaxies. Here, we write down the probability density function for the observed line-of-sight (LOS) velocity of a stellar population containing both visual and spectroscopic binary stars, which we then use to determine the effect of those binary stars on the observed LOS velocity dispersion. For the coldest UFD galaxies, the fractional increase in LOS velocity dispersion is of the order of 1 and for the coldest globular clusters is of the order of 100. However, if the stellar initial mass function is bottom light, as it may be for UFD galaxies and globular clusters, then both of these values increase by half a dex.