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Abstract Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolatedN-body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against anN-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system. 

ABSTRACT We present results from simultaneous modelling of 2D (projected along the line of sight) position, proper motion, and line-of-sight velocity for Gaia- and Apache Point Observatory Galactic Evolution Experiment (APOGEE)-observed stars near the centre of the Sagittarius (Sgr) dwarf spheroidal galaxy. We use a mixture model that allows for independent sub-populations contributed by the Sgr galaxy, its nuclear star cluster Messier 54 (M54), and the Milky Way foreground. We find an offset of $$0.295\pm 0.029$$ deg between the inferred centroids of Sgr and M54, corresponding to a (projected) physical separation of $$0.135\pm 0.013$$ kpc. The detected offset might plausibly be driven by unmodelled asymmetry in Sgr’s stellar configuration; however, standard criteria for model selection favour our symmetric model over an alternative that allows for bilateral asymmetry. We infer an offset between the proper motion centres of Sgr and M54 of $$[\Delta \mu _{\alpha }\cos \delta ,\Delta \mu _{\delta }]=[4.9, -19.7] \pm [6.8, 6.2] \ \mu \mathrm{ as}\,\mathrm{ yr}^{-1}$$ ($$[0.61, -2.46] \pm [0.85, 0.77] \ \mathrm{ km}\,\mathrm{ s}^{-1}$$), with magnitude similar to the covariance expected due to spatially correlated systematic error. We infer an offset of $$4.1\pm 1.2 \ \mathrm{ km}\,\mathrm{ s}^{-1}$$ in line-of-sight velocity. Using inferred values for the systemic positions and motions of Sgr and M54 as initial conditions, we calculate the recent orbital history of a simplified Sgr/M54 system, which we demonstrate to be sensitive to any line-of-sight distance offset between M54 and Sgr, and to the distribution of dark matter within Sgr. 

ABSTRACT We use analytical and N-body methods to study the capture of field stars by gravitating substructures moving across a galactic environment. The majority of stars captured by a substructure move on temporarily bound orbits that are lost to galactic tides after a few orbital revolutions. In numerical experiments where a substructure model is immersed into a sea of field particles on a circular orbit, we find a population of particles that remain bound to the substructure potential for indefinitely long times. This population is absent from substructure models, initially placed outside the galaxy on an eccentric orbit. We show that gravitational capture is most efficient in dwarf spheroidal galaxies (dSphs) on account of their low velocity dispersions and high stellar phase-space densities. In these galaxies, ‘dark’ sub-subhaloes, which do not experience in situ star formation, may capture field stars and become visible as stellar overdensities with unusual properties: (i) they would have a large size for their luminosity, (ii) contain stellar populations indistinguishable from the host galaxy, and (iii) exhibit dark matter (DM)-dominated mass-to-light ratios. We discuss the nature of several ‘anomalous’ stellar systems reported as star clusters in the Fornax and Eridanus II dSphs that exhibit some of these characteristics. DM sub-subhaloes with a mass function $${\rm d}N/{\rm d}M_\bullet \sim M_\bullet ^{-\alpha }$$ are expected to generate stellar systems with a luminosity function, $${\rm d}N/{\rm d}M_\star \sim M_\star ^{-\beta }$$, where $$\beta =(2\alpha +1)/3=1.6$$ for $$\alpha =1.9$$. Detecting and characterizing these objects in dSphs would provide unprecedented constraints on the particle mass and cross-section of a large range of DM particle candidates. 

Abstract A fundamental prediction of the Lambda cold dark matter cosmology is the centrally divergent cuspy density profile of dark matter haloes. Density cusps render cold dark matter haloes resilient to tides, and protect dwarf galaxies embedded in them from full tidal disruption. The hierarchical assembly history of the Milky Way may therefore give rise to a population of “microgalaxies”; i.e., heavily stripped remnants of early accreted satellites, which can reach arbitrarily low luminosity. Assuming that the progenitor systems are dark matter dominated, we use an empirical formalism for tidal stripping to predict the evolution of the luminosity, size, and velocity dispersion of such remnants, tracing their tidal evolution across multiple orders of magnitude in mass and size. The evolutionary tracks depend sensitively on the progenitor distribution of stellar binding energies. We explore three cases that likely bracket most realistic models of dwarf galaxies: one where the energy distribution of the most tightly bound stars follows that of the dark matter, and two where stars are defined by either an exponential density or surface brightness profile. The tidal evolution in the size–velocity dispersion plane is quite similar for these three models, although their remnants may differ widely in luminosity. Microgalaxies are therefore best distinguished from globular clusters by the presence of dark matter; either directly, by measuring their velocity dispersion, or indirectly, by examining their tidal resilience. Our work highlights the need for further theoretical and observational constraints on the stellar energy distribution in dwarf galaxies. 

Abstract The recently discovered stellar system Ursa Major III/UNIONS 1 (UMa3/U1) is the faintest known Milky Way satellite to date. With a stellar mass of ${16}_{-5}^{+6}{M}_{\odot }$and a half-light radius of 3 ± 1 pc, it is either the darkest galaxy ever discovered or the faintest self-gravitating star cluster known to orbit the Galaxy. Its line-of-sight velocity dispersion suggests the presence of dark matter, although current measurements are inconclusive because of the unknown contribution to the dispersion of potential binary stars. We useN-body simulations to show that, if self-gravitating, the system could not survive in the Milky Way tidal field for much longer than a single orbit (roughly 0.4 Gyr), which strongly suggests that the system is stabilized by the presence of large amounts of dark matter. If UMa3/U1 formed at the center of a ∼10⁹M_⊙cuspy LCDM halo, its velocity dispersion would be predicted to be of order ∼1 km s⁻¹. This is roughly consistent with the current estimate, which, neglecting binaries, placesσ_losin the range 1–4 km s⁻¹. Because of its dense cusp, such a halo should be able to survive the Milky Way tidal field, keeping UMa3/U1 relatively unscathed until the present time. This implies that UMa3/U1 is plausibly the faintest and densest dwarf galaxy satellite of the Milky Way, with important implications for alternative dark matter models and for the minimum halo mass threshold for luminous galaxy formation in the LCDM cosmology. Our results call for multi-epoch high-resolution spectroscopic follow-up to confirm the dark matter content of this extraordinary system. 

Abstract We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass–anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally averaged value $\overline{{\beta }_{\mathrm{B}}}=-{0.20}_{-0.53}^{+0.28}$, (where 1 – ${\beta }_{\mathrm{B}}\equiv 〈v_{\tan }^2〉/〈v_{\mathrm{rad}}^2〉$in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γ_dark, is $-{0.83}_{-0.37}^{+0.32}$, consistent with the inner cusp predicted in ΛCDM cosmology. As expected given Draco’s low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, and 942 pc at 1σ, 2σ, and 3σconfidence, respectively, thus imposing important constraints on the self-interacting DM cross section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is ${24.19}_{-2.97}^{+6.31}\mathrm{km}{\mathrm{s}}^{-1}$. We infer a dynamical distance of ${75.37}_{-4.00}^{+4.73}$kpc and show that Draco has a modest LOS rotation, with $\left(v/\sigma \right)=0.22\pm 0.09$. Our results provide a new stringent test of the so-called “cusp–core” problem that can be readily extended to other dwarfs. 

Abstract We present spectroscopic data for 16,369 stellar targets within and/or toward 38 dwarf spheroidal galaxies and faint star clusters within the Milky Way halo environment. All spectra come from observations with the multiobject, fiber-fed echelle spectrographs M2FS at the Magellan/Clay telescope or Hectochelle at the MMT, reaching a typical limiting magnitudeG≲ 21. Data products include processed spectra from all observations and catalogs listing estimates—derived from template model fitting—of line-of-sight velocity (median uncertainty 1.4 km s⁻¹) effective temperature (255 K), (base-10 logarithm of) surface gravity (0.59 dex in cgs units), [Fe/H] (0.4 dex) and [Mg/Fe] (0.27 dex) abundance ratios. The sample contains multiepoch measurements for 3720 sources, with up to 15 epochs per source, enabling studies of intrinsic spectroscopic variability. The sample contains 6087 likely red giant stars (based on surface gravity), and 4492 likely members (based on line-of-sight velocity and Gaia-measured proper motion) of the target systems. The number of member stars per individual target system ranges from a few, for the faintest systems, to ∼850 for the most luminous. For most systems, our new samples extend over wider fields than have previously been observed; of the likely members in our samples, 820 lie beyond 2 times the projected half-light radius of their host system, and 42 lie beyond 5R_half. 

Context.The C-19 stellar stream is the most metal-poor stream known to date. While its wth and velocity dispersion indicate a dwarf galaxy origin, its metallicity spread and abundance patterns are more similar to those of globular clusters (GCs). If it is indeed of GC origin, its extremely low metallicity ([Fe/H]=−3.4, estimated from giant stars) implies that these stellar systems can form out of gas that is as extremely poor in metals as this. Previously, only giant stream stars were observed spectroscopically, although the majority of stream stars are unevolved stars. Aims.We pushed the spectroscopic observations to the subgiant branch stars (G≈ 20) in order to consolate the chemical and dynamical properties of C-19. Methods.We used the high-efficiency spectrograph X-shooter fed by the ESO 8.2m VLT telescope to observe 15 candate subgiant C-19 members. The spectra were used to measure radial velocities and to determine chemical abundances using the MyGIsFOS code. Results.We developed a likelihood model that takes metallicity and radial velocities into account. We conclude that 12 stars are likely members of C-19, while 3 stars (S05, S12, and S13) are likely contaminants. When these 3 stars are excluded, our model implies a mean metallicity 〈[Fe/H]〉 = −3.1 ± 0.1, the mean radial velocity is 〈v_r〉 = −192 ± 3km s⁻¹, and the velocity dispersion is σ_vr= 5.9_−5.9^+3.6km s⁻¹. This all agrees within errors with previous studies. The A(Mg) of a sample of 15 C-19 members, including 6 giant stars, shows a standard deviation of 0.44 dex, and the mean uncertainty on Mg is 0.25 dex. Conclusions.Our preferred interpretation of the current data is that C-19 is a disrupted GC. We cannot completely rule out the possibility that the GC could have belonged to a dwarf galaxy that contained more metal-rich stars, however. This scenario would explain the radial velocity members at higher metallicity, as well as the wth and velocity dispersion of the stream. In either case, a GC formed out of gas as poor in metals as these stars seems necessary to explain the existence of C-19. The possibility that no GC was associated with C-19 cannot be ruled out either. 

m2fs_HiRes_catalog_public.fits: public catalog of measurements derived from spectroscopic observations of individual targets with the Magellan/M2FS spectrograph in HiRes configuration</p> m2fs_MedRes_catalog_public.fits: public catalog of measurements derived from spectroscopic observations of individual targets with the Magellen/M2FS spectrograph in MedRes configuration</p> hecto_catalog_public.fits: public catalog of measurements derived from spectroscopic observations of individual targets with the MMT/Hectochelle spectrograph</p> fits_files.tar.gz: Supplementary data products, including all sky-subtracted spectra from individual targets and best-fitting model spectra.</p> template_spectra.tar.gz: synthetic template spectra (columns are wavelength in air (Angstroms), normalized flux)</p>