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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 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.