Correcting Velocity Dispersions of Dwarf Spheroidal Galaxies for Binary Orbital Motion

We show that the measured velocity dispersions of dwarf spheroidal galaxies from about 4 to 10 km s^(–1) are unlikely to be inflated by more than 30% 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 yr 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

A Complete Spectroscopic Survey of the Milky Way Satellite Segue 1: The Darkest Galaxy

Spectroscopic study of the Segue 1 dwarf galaxy. --author-supplied descriptio

Robust velocity dispersion and binary population modeling of the ultra-faint dwarf galaxy Reticulum II

We apply a Bayesian method to model multi-epoch radial velocity measurements in the ultra-faint dwarf galaxy Reticulum II, fully accounting for the effects of binary orbital motion and systematic offsets between different spectroscopic datasets. We find that the binary fraction of Ret II is higher than 0.5 at the 90% confidence level, if the mean orbital period is assumed to be 30 years or longer. Despite this high binary fraction, we infer a best-fit intrinsic dispersion of 2.8$_{-1.2}^{+0.7}$ km/s, which is smaller than previous estimates, but still indicates Ret II is a dark-matter dominated galaxy. We likewise infer a $\lesssim$ 1% probability that Ret II's dispersion is due to binaries rather than dark matter, corresponding to the regime $M_{\odot}/L_{\odot} \lesssim$ 2. Our inference of a high close binary fraction in Ret II echoes previous results for the Segue 1 ultra-faint dwarf and is consistent with studies of Milky Way halo stars that indicate a high close binary fraction tends to exist in metal-poor environments.Comment: 9 pages, 5 figures, to be submitted to MNRA

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/sec. The dark matter halo required to produce this dispersion must have an average density of 2.5^{+4.1}_{-1.9} solar mass/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 28^{+5}_{-4} pc, in excellent agreement with photometric measurements.Comment: 15 pages, 19 figure

Effects of galaxy-halo alignment and adiabatic contraction on gravitational lens statistics

We study the strong gravitational lens statistics of triaxial cold dark matter (CDM) halos occupied by central early-type galaxies. We calculate the image separation distribution for double, cusp and quad configurations. The ratios of image multiplicities at large separations are consistent with the triaxial NFW model, and at small separations are consistent with the singular isothermal ellipsoid (SIE) model. At all separations, the total lensing probability is enhanced by adiabatic contraction. If no adiabatic contraction is assumed, naked cusp configurations become dominant at approximately 2.5'', which is inconsistent with the data. We also show that at small-to-moderate separations, the image multiplicities depend sensitively on the alignment of the shapes of the luminous and dark matter projected density profiles. In constrast to other properties that affect these ratios, the degree of alignment does not have a significant effect on the total lensing probability. These correlations may therefore be constrained by comparing the theoretical image separation distribution to a sufficiently large lens sample from future wide and deep sky surveys such as Pan-Starrs, LSST and JDEM. Understanding the correlations in the shapes of galaxies and their dark matter halo is important for future weak lensing surveys.Comment: 10 pages, 7 figure