The Mass-to-Light Ratios of the Draco and Ursa Minor Dwarf Spheroidal Galaxies. II. The Binary Population and Its Effect in the Measured Velocity Dispersions of Dwarf Spheroidal Galaxies

Abstract

We use a large set of radial velocities in the Ursa Minor and Draco dwarf spheroidal galaxies to search for binary stars and to infer the binary frequency. Of the 118 stars in our sample with multiple observations, six are velocity variables with $χ^2$ probabilities below 0.001. We use Monte Carlo simulations that mimic our observations to determine the efficiency with which our observations find binary stars. Our best, though significantly uncertain, estimate of the binary frequency for stars near the turnoff in Draco and UMi is 0.2--0.3 per decade of period in the vicinity of periods of one year, which is 3--5$\times$ that found for the solar neighborhood. This frequency is high enough that binary stars might significantly affect the measured velocity dispersions of some dwarf spheroidal galaxies according to some previous numerical experiments. However, in the course of performing our own experiments, we discovered that this previous work had inadvertently overestimated binary orbital velocities. Our first set of simulations of the effects of binaries is based on the observed scatter in the individual velocity measurements for the multiply-observed Draco and Ursa Minor stars. This scatter is small compared to measured velocity dispersions and, so, the effect of binaries on the dispersions is slight. This result is supported by our second set of experiments, which are based on a model binary population normalized by the observed binary frequency in Draco and Ursa Minor. We conclude that binary stars have had no significant effect on the measured velocity dispersion and inferred mass-to-light ratio of any dwarf spheroidal galaxy.