Description
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 star 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 order one. However, if the stellar initial mass function is bottom light, as it may be for UFD galaxies, then this value increase by half a dex. Our results apply to systems of populations of zero-age main-sequence stars rather than the populations of present-day red-giant branch (RGB) stars that have been studied previously in the context of dwarf-spheroidal galaxies.
