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We introduce a comprehensive analysis of multi-epoch stellar line-of-sight velocities to determine the intrinsic velocity dispersion of the ultrafaint satellites of the Milky Way. Our method includes a simultaneous Bayesian analysis of both membership probabilities and the contribution of binary orbital motion to the observed velocity dispersion within a 14-parameter likelihood. We apply our method to the Segue 1 dwarf galaxy and conclude that Segue 1 is a dark-matter-dominated galaxy at high probability with an intrinsic velocity dispersion of 3. 7^+1. 4-₁. ₁ km/sec. The dark matter halo required to produce this dispersion must have an average density of 2. 5^+4. 1-₁. ₉ solar mass/pc³ within a sphere that encloses half the galaxy's stellar luminosity. This is the highest measured density of dark matter in the Local Group. Our results show that a significant fraction of the stars in Segue 1 may be binaries with the most probable mean period close to 10 years, but also consistent with the 180 year mean period seen in the solar vicinity at about 1 sigma. Despite this binary population, the possibility that Segue 1 is a bound star cluster with the observed velocity dispersion arising from the orbital motion of binary stars is disfavored by the multi-epoch stellar velocity data at greater than 99% C. L. Finally, our treatment yields a projected (two-dimensional) half-light radius for the stellar profile of Segue 1 of 28^+5-₄ pc, in excellent agreement with photometric measurements.
Martinez et al. (Thu,) studied this question.