Correcting velocity dispersions of dwarf spheroidal galaxies for binary orbital motion

We show that measured velocity dispersions of dwarf spheroidal galaxies from about 4 to 10 km/s are unlikely to be inflated by more than 20% due to the orbital motion of binary stars, and demonstrate that the intrinsic velocity dispersions can be determined to within a few percent accuracy using two-epoch observations with 1-2 years as the optimal time interval. The crucial observable is the threshold fraction--the fraction of stars that show velocity changes larger than a given threshold between measurements. The threshold fraction is tightly correlated with the dispersion introduced by binaries, independent of the underlying binary fraction and distribution of orbital parameters. We outline a simple procedure to correct the velocity dispersion to within a few percent accuracy by using the threshold fraction and provide fitting functions for this method. We also develop a methodology for constraining properties of binary populations from both single- and two-epoch velocity measurements by including the binary velocity distribution in a Bayesian analysis.