A COMPLETE SPECTROSCOPIC SURVEY OF THE MILKY WAY SATELLITE SEGUE 1: DARK MATTER CONTENT, STELLAR MEMBERSHIP, AND BINARY PROPERTIES FROM A BAYESIAN ANALYSIS

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 s-1. The dark matter halo required to produce this dispersion must have an average density of ρ-bar1/2 = 2.5-1.9+4.1, Msun, pc-3 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 1σ. 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 R1/2 = 28+5-4 pc, in excellent agreement with photometric measurements.