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 \bar { \rho } _ { 1 / 2 } = 2.5 ^ { +4.1 } _ { -1.9 } M _ { \odot } { 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 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 R _ { 1 / 2 } = 28 ^ { +5 } _ { -4 } pc , in excellent agreement with photometric measurements .