We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy. We find M_1/2 = 3 \sigma_los^2 r_1/2 / G ~ 4 \sigma_los^2 R_eff / G, where \sigma_los^2 is the luminosity-weighted square of the line-of-sight velocity dispersion and R_eff is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 M_sun in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The M/L vs. M_1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 3,200 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.Comment: 20 pages, 13 figures. Accepted to MNRAS on March 27th, 201

We present the results of a comprehensive Keck/DEIMOS spectroscopic survey of the ultra-faint Milky Way satellite galaxy Segue 1. We have obtained velocity measurements for 98.2% of the stars within 67 pc (10 ′ , or 2.3 half-light radii) of the center of Segue 1 that have colors and magnitudes consistent with membership, down to a magnitude limit of r = 21.7. Based on photometric, kinematic, and metallicity information, we identify 71 stars as probable Segue 1 members, including some as far out as 87 pc. After correcting for the influence of binary stars using repeated velocity measurements, we determine a velocity dispersion of 3.7 +1.4 −1.1 km s −1 . The mass within the half-light radius is 5.8 +8.2 −3.1 × 10 5 M ⊙ . The stellar kinematics of Segue 1 require very high mass-to-light ratios unless the system is far from dynamical equilibrium, even if the period distribution of unresolved binary stars is skewed toward implausibly short periods. With a total luminosity less than that of a single bright red giant and a V-band mass-to-light ratio of 3400 M ⊙ /L ⊙ , Segue 1 is the darkest galaxy currently known. We critically re-examine recent claims that Segue 1 is a tidally disrupting star cluster and that kinematic samples are contaminated by the Sagittarius stream. The extremely low metallicities ([Fe/H] < −3) of two Segue 1 stars and the large metallicity spread among the members demonstrate conclusively that Segue 1 is a dwarf galaxy, and we find no evidence in favor of tidal effects. We also show that contamination by the Sagittarius stream has been overestimated. Segue 1 has the highest estimated dark matter density of any known galaxy and will therefore be a prime testing ground for dark matter physics and galaxy formation on small scales.

Local Group dwarf spheroidal satellite galaxies are the faintest extragalactic stellar systems known. We examine recent data for these objects in the plane of the Baryonic Tully-Fisher Relation (BTFR). While some dwarf spheroidals adhere to the BTFR, others deviate substantially. We examine the residuals from the BTFR and find that they are not random. The residuals correlate with luminosity, size, metallicity, ellipticity, and susceptibility of the dwarfs to tidal disruption in the sense that fainter, more elliptical, and tidally more susceptible dwarfs deviate farther from the BTFR. These correlations disfavor stochastic processes and suggest a role for tidal effects. We identify a test to distinguish between ΛCDM and MOND based on the orbits of the dwarf satellites of the Milky Way and how stars are lost from them.

We present new Keck/DEIMOS spectroscopic observations of hundreds of individual stars along the sightline to the first three of the Andromeda (M31) dwarf spheroidal (dSph) galaxies to be discovered, And I, II, and III, and combine them with recent spectroscopic studies by our team of three additional M31 dSphs, And VII, X, and XIV, as a part of the SPLASH Survey (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo). Member stars of each dSph are isolated from foreground Milky Way dwarf stars and M31 field contamination using a variety of photometric and spectroscopic diagnostics. Our final spectroscopic sample of member stars in each dSph, for which we measure accurate radial velocities with a median uncertainty (random plus systematic errors) of 4-5 km s −1 , includes 80 red giants in And I, 95 in And II, 43 in And III, 18 in And VII, 22 in And X, and 38 in And XIV. The sample of confirmed members in the six dSphs is used to derive each system's mean radial velocity, intrinsic central velocity dispersion, mean abundance, abundance spread, and dynamical mass. This combined data set presents us with a unique opportunity to perform the first systematic comparison of the global properties (e.g., metallicities, sizes, and dark matter masses) of one-third of Andromeda's total known dSph population with Milky Way counterparts of the same luminosity. Our overall comparisons indicate that the family of dSphs in these two hosts have both similarities and differences. For example, we find that the luminosity-metallicity relation is very similar between L ∼ 10 5 and 10 7 L , suggesting that the chemical evolution histories of each group of dSphs are similar. The lowest luminosity M31 dSphs appear to deviate from the relation, possibly suggesting tidal stripping. Previous observations have noted that the sizes of M31's brightest dSphs are systematically larger than Milky Way satellites of similar luminosity. At lower luminosities between L = 10 4 and 10 6 L , we find that the sizes of dSphs in the two hosts significantly overlap and that four of the faintest M31 dSphs are smaller than Milky Way counterparts. The first dynamical mass measurements of six M31 dSphs over a large range in luminosity indicate similar mass-to-light ratios compared to Milky Way dSphs among the brighter satellites, and smaller mass-to-light ratios among the fainter satellites. Combined with their similar or larger sizes at these luminosities, these results hint that the M31 dSphs are systematically less dense than Milky Way dSphs. The implications of these similarities and differences for general understanding of galaxy formation and evolution are summarized.

We predict that there is a population of low-luminosity dwarf galaxies orbiting within the halo of the Milky Way that have surface brightnesses low enough to have escaped detection in star-count surveys. The overall count of stealth galaxies is sensitive to the presence (or lack) of a low-mass threshold in galaxy formation. These systems have luminosities and stellar velocity dispersions that are similar to those of known ultrafaint dwarf galaxies but they have more extended stellar distributions (half light radii greater than about 100 pc) because they inhabit dark subhalos that are slightly less massive than their higher surface brightness counterparts. As a result, the typical peak surface brightness is fainter than 30 mag per square arcsec. One implication is that the inferred common mass scale for Milky Way dwarfs may be an artifact of selection bias. If there is no sharp threshold in galaxy formation at low halo mass, then ultrafaint galaxies like Segue 1 represent the high-mass, early forming tail of a much larger population of objects that could number in the hundreds and have typical peak circular velocities of about 8 km s −1 and masses within 300 pc of about 5 million solar masses. Alternatively, if we impose a low-mass threshold in galaxy formation in order to explain the unexpectedly high densities of the ultrafaint dwarfs, then we expect only a handful of stealth galaxies in the halo of the Milky Way. A complete census of these objects will require deeper sky surveys, 30m-class follow-up telescopes, and more refined methods to identify extended, self-bound groupings of stars in the halo.

We examine scaling relations of dispersion-supported galaxies over more than eight orders of magnitude in luminosity by transforming standard fundamental plane parameters into a space of mass, radius, and luminosity. The radius variable r 1/2 is the de-projected (3-D) half-light radius, the mass variable M 1/2 is the total gravitating mass within this radius, and L 1/2 is half the luminosity. We find that from ultra-faint dwarf spheroidals to giant cluster spheroids, dispersion-supported galaxies scatter about a one-dimensional "fundamental curve" through this MRL space. The mass-radius-luminosity relation transitions from M 1/2 ∼ r 1.44 1/2 ∼ L 0.30 1/2 for the faintest dwarf spheroidal galaxies to M 1/2 ∼ r 1.42 1/2 ∼ L 3.2 1/2 for the most luminous galaxy cluster spheroids. The weakness of the M 1/2 − L 1/2 slope on the faint end may imply that potential well depth limits galaxy formation in small galaxies, while the stronger dependence on L 1/2 on the bright end suggests that baryonic physics limits galaxy formation in massive galaxies. The mass-radius projection of this curve can be compared to median dark matter halo mass profiles of ΛCDM halos in order to construct a virial mass-luminosity relationship (M vir − L) for galaxies that spans seven orders of magnitude in M vir . Independent of any global abundance or clustering information, we find that (spheroidal) galaxy formation needs to be most efficient in halos of M vir ∼ 10 12 M ⊙ and to become inefficient above and below this scale. Moreover, this profile matching technique for deriving the M vir − L is most accurate at the high and low luminosity extremes (where dark matter fractions are highest) and is therefore quite complementary to statistical approaches that rely on having a well-sampled luminosity function. We also consider the significance and utility of the scatter about this relation, and find that in the dSph regime observational errors are almost at the point where we can explore the intrinsic scatter in the luminosity-virial mass relation. Finally, we note that purely stellar systems like Globular Clusters and Ultra Compact Dwarfs do not follow the fundamental curve relation. This allows them to easily be distinguished from dark-matter dominated dSph galaxies in MRL space.

We investigate the mass distributions within eight classical Milky Way dwarf spheroidal galaxies (MW dSphs) using an equilibrium Jeans analysis and we compare our results to the mass distributions predicted for subhalos in dissipationless ΛCDM simulations. In order to match the dark matter density concentrations predicted, the stars in these galaxies must have a fairly significant tangential velocity dispersion anisotropy (β ≃ −1.5). For the limiting case of an isotropic velocity dispersion (β = 0), the classical MW dSphs predominantly prefer to live in halos that are less concentrated than ΛCDM predictions. We also investigate whether the dSphs prefer to live in halos with constant density cores in the limit of isotropic velocity dispersion. Interestingly, even in this limit, not all of the dSphs prefer large constant-density cores: the Sculptor dSph prefers a cusp while Carina, Draco and Leo I prefer cores. The other four dSphs do not show a statistically significant preference for either cuspy or cored profiles. Finally, we re-examine the hypothesis that the density profiles of these eight MW dSphs can be quantified by a common dark matter halo.

Mass profile determinations for dispersion supported galaxies from line-of-sight velocities are subject to large uncertainties associated with the unknown stellar velocity anisotropy. We demonstrate both analytically and with available kinematic data (for systems spanning eight decades in luminosity) that the mass-anisotropy degeneracy is effectively eliminated at a characteristic radius that is close to the 3D deprojected half-light radius of the stars. This allows a simple, yet accurate formula to describe the half-light dark matter masses of all hot systems, including dwarf spheroidal galaxies (dSphs), based on directly observable parameters: M 1/2 = 4 σ 2 LOS R half / G, where R half is the 2D projected half-light radius and σ LOS is the luminosity-weighted square of the line-of-sight velocity dispersion. The fact that masses are well-constrained within a characteristic stellar radius has allowed our group to perform systematic, accurate mass determinations for Milky Way dSphs and to conclude that they all have a common mass scale of approximately 10 7 M within 300 pc of their centers. We extend this work to the satellite population of Andromeda using Keck/DEIMOS spectroscopy of individual stars. We find that the Andromeda dSphs are also consistent with sharing a common mass, but that it is offset from the scale of the Milky Way dSphs by a factor of ∼ 2. 79at https://www.cambridge.org/core/terms. https://doi