We fit a flexible double power-law (`αβγ') model to the stellar density fields observed for the Milky Way's known dwarf spheroidal satellite galaxies. We show that where standard criteria for model selection are decisive, the αβγ model is favored over the special case of the Plummer model, and also over the model and its special case, the exponential. The Milky Way's dSph population exhibits a diverse range of stellar density profile shapes, as quantified by the values we infer for outer and inner power-law indices β and γ. Several of the most massive dSphs (e.g., Eridanus II, Fornax, Leo I, Leo II) have steeply-declining outer profiles, with β≳ 8; others (e.g., Sextans, Boötes I) fade slowly, with β≲ 4. The inner profiles of dSphs with stellar mass ≳ 10^5 M_⊙ are consistent with `cores' of uniform stellar density (γ≈ 0). At lower masses the slopes of inner density profiles are poorly constrained, except in a few ultrafaint dSphs (e.g., Hercules, Ursa Major II) where we infer steep stellar cusps, with γ≳ 1.5. Owing to the αβγ model's flexibility, the inferred halflight radii and total stellar masses are significantly more uncertain than previous estimates, with halflight radii larger by up to an order of magnitude in some cases. Finally, we demonstrate that allowing for flexibility in the shape of the stellar density profile is crucial for dSph mass modeling, where systematic errors associated with choice of stellar density profile can outweigh random errors in the observed velocity dispersions.

Aims. We investigate the constraints placed on the inner stellar density profile from the photometric data of dwarf spheroidal and ultra-faint dwarf galaxies. Our aim is to clarify the conditions in which cored stellar profiles require dark matter halos that are also cored, deviating from the cuspy profiles expected for cold dark matter halos. Methods. We considered a variety of spherically symmetric stellar profiles, which we classified as ‘strong’ or ‘weak’ cores and cusps according to the behaviour of the slope ( b 0 ) and logarithmic slope ( γ 0 ) at their centres. We explored which profiles lead to unphysical negative distribution functions when embedded in a cuspy halo, while treating the isotropic and anisotropic kinematics separately. Results. We find that weakly cored stellar profiles in 3D (i.e. b 0 ≠ 0, γ 0 = 0) can be consistent with cuspy dark matter profiles, but strong 3D cores ( b 0 = γ 0 = 0) are not. However, both weak and strong 3D cores yield nearly indistinguishable inner profiles in projection, which implies that ruling out a dark matter cusp from photometric data alone is highly challenging. As an example, we studied the profiles of ultra-faint dwarf galaxies and found that they are consistent with both weak and strong 3D cores. This result is not solely applicable to the limited numbers of stars in these systems, since we reached the same conclusion even for Fornax, one of the most luminous and best-studied dwarf spheroidal companions of the Milky Way. Conclusions. We conclude that based on current data and analysis techniques, cored surface density profiles in nearby dwarf galaxies cannot be taken as strong evidence against the presence of cuspy dark matter halos.

Most dwarf spheroidal (dSph) satellites of the Milky Way follow exponential surface density profiles that decline sharply in the outer regions. The Sculptor (Scl) and Ursa Minor (UMi) dSphs deviate from this trend and show a clear excess of stars in the outskirts. Individual members have recently been identified as far as ∼10 effective radii from the center in both systems. We study whether far-outlying stars in Scl and UMi may result from Galactic tidal forces using idealized N-body simulations. Our results indicate that, on their current orbits, neither galaxy has experienced tidal forces sufficient to affect its stellar density profile. The observed velocity dispersion and size of Scl and UMi imply the dwarfs are simply too dense to have been affected by Galactic tides. We also find weak tidal evolution when including the effects of the Large Magellanic Cloud, which our simulations suggest substantially perturbed Scl's orbit during a close encounter. Our results are insensitive to assumptions about the detailed dark matter density profile of either galaxy, including the presence of an inner core. We conclude that the outlying stars in Scl or UMi are not of tidal origin, but rather innate features that possibly reflect past merger events or the presence of multiple dynamical components.

Cosmological simulations of galaxy clusters are unable to resolve dwarf galaxies due to limited numerical resolution, which drives the artificial disruption of dark matter substructures. We address these limitations by combining the results of the cosmological hydrodynamical simulation TNG50 in ΛCDM with an empirical model of tidal evolution of cluster galaxies calibrated using high-resolution idealized N-body simulations. Applied to the three most massive clusters in TNG50, our model allows us to study the stellar mass and radial distribution of dwarfs well below the formal resolution limit of the parent simulation. We find that, at z=0, clusters with virial mass [Formula: see text]  [Formula: see text] host a vast population of dwarf galaxies within the virial radius, amounting to 2000-7000 systems with [Formula: see text]  [Formula: see text]. Taken together, these satellites follow a radial distribution that matches the underlying dark matter profile of the host. However, applying a minimum mass or luminosity threshold for detection, as expected in observational studies, tends to exclude the most heavily stripped objects, which tend to populate the inner regions. Future surveys targeting ultra-faint galaxies in group and cluster environments, such as those made possible by the Euclid, Rubin, or Roman telescope, will be fundamental to refute or confirm this prediction.

Assuming spherical symmetry and dynamical equilibrium within a given gravitational potential, a dwarf spheroidal (dSph) galaxy's globally averaged stellar velocity dispersion depends entirely on the shape of its stellar density profile. Thus, the dynamical inference of a dSph's gravitational potential is necessarily sensitive to assumptions about that shape. Relaxing standard assumptions, we fit flexible stellar density models to observations of the Milky Way's known dSph satellites. Considering various choices for the density profile shape and spatial extent of a host dark matter halo, we use the virial theorem to propagate observational uncertainties about the shapes of the inferred dSph stellar density profiles to uncertainties in the inferred dynamical masses. We find that the observed structural diversity of the Milky Way dSph population implies a large range of potential systematic errors (up to factors of 10) associated with standard dynamical mass estimators. We show that accounting for these observational and systematic uncertainties can significantly alter the appearance and behavior of dSph dynamical scaling relations, including enclosed dynamical mass vs. stellar mass and the Radial Acceleration Relation.

The Böotes III (Boo3) dwarf galaxy has long been suspected of being the progenitor of Styx, a 50°-long stellar stream that was simultaneously discovered in the same region of sky. Boo3's diffuse morphology, large velocity dispersion, small pericenter, and excess of candidate stars at large radii suggest it is undergoing active tidal disruption. A link to Styx is therefore logical; however, a clear connection between these structures has not yet been clearly demonstrated. Here, we re-examine the Boo3-Styx association by searching for Boo3's tidal debris using a combination of Gaia-selected members, new CaHK narrow-band imaging with CFHT/MegaCam, and stellar tracer catalogues of blue horizontal branch and red giant branch stars. We also conduct a broad search for a putative stream using matched filter techniques applied to SDSS DR17 and DELVE DR2. Despite our extensive search, we find no observational evidence directly linking Boo3 to Styx. Furthermore, our results suggest that either Boo3's extended substructure is too diffuse to be detected with current data, or that its particular orbit may have erased a coherent tidal signature. Boo3 thus remains an enigmatic system, and exemplifies the need for spectroscopic follow-up to properly disentangle the nature between this faint Milky Way satellite and nearby stream.

We use controlled N-body simulations to study the collisional exchange of energy between stars and dark matter in ultra-faint galaxies. We find that dynamical friction between stars and subsolar-mass dark matter particles results in the depletion of dark matter from the galaxies' centers, thereby transforming dark matter cusps into constant-density cores. The process is particularly effective in tidally limited galaxies with low stellar velocity dispersion. As high-mass stars sink toward the center of the dark matter halo, the dynamical-to-stellar mass ratio within the stellar half-light radius decreases monotonically. The stellar population of a dark matter-dominated galaxy is thereby compacted into a dense, baryon-dominated cluster, surrounded by a dark matter halo. Such a cluster would share the chemical composition of an ultra-faint galaxy, yet would be virtually dark matter-free within its half-light radius. We moreover find that the collisional cooling with dark matter particles provides an efficient pathway for the formation of stellar binaries in the contracting cluster. The contraction is eventually slowed down due to the decreasing central dark matter densities and the formation of stellar binaries. Our models highlight that the dynamical processes governing the faintest galaxies give rise to a rich phenomenology, blurring the line between the dynamics of globular clusters and galaxies.

We present results of a spectroscopic campaign around the diffuse dwarf galaxy Crater 2 (Cra2) and its tidal tails as part of the Southern Stellar Stream Spectroscopic Survey (S^5). Cra2 is a Milky Way dwarf spheroidal satellite with extremely cold kinematics, but a huge size similar to the Small Magellanic Cloud, which may be difficult to explain within collisionless cold dark matter. We identify 143 Cra2 members, of which 114 belong to the galaxy's main body and 29 are deemed part of its stellar stream. We confirm that Cra2 is dynamically cold (central velocity dispersion 2.51^+0.33_-0.30 km s^-1) and also discover a ≈7σ velocity gradient consistent with its tidal debris track. We separately estimate the stream velocity dispersion to be 5.74^+0.98_-0.83 km s^-1. We develop a suite of N-body simulations with both cuspy and cored density profiles on a realistic Cra2 orbit to compare with S^5 observations. We find that the velocity dispersion ratio between Cra2 stream and galaxy (2.30^+0.41_-0.35) is difficult to reconcile with a cuspy halo with fiducial concentration and an initial mass predicted by standard stellar mass-halo mass relationships. Instead, either a cored halo with relatively small core radius or a low-concentration cuspy model can reproduce this ratio. Despite tidal mass loss, Cra2 is metal-poor (⟨[Fe/H]⟩=-2.16±0.04) compared to the stellar mass-metallicity relation for its luminosity. Other diffuse dwarf galaxies similar to Cra2 in the Local Group (Antlia 2 and Andromeda 19) also challenge galaxy formation models. Finally, we discuss possible formation scenarios for Cra2, including ram-pressure stripping of a gas-rich progenitor combined with tides.

We study the response of mono-energetic stellar populations with initially isotropic kinematics to impulsive and adiabatic changes to an underlying dark matter potential. Half-light radii expand and velocity dispersions decrease as enclosed dark matter is removed. The details of this expansion and cooling depend on the timescale on which the underlying potential changes. In the adiabatic regime, the product of half-light radius and average velocity dispersion is conserved. We show that the stellar populations maintain centrally isotropic kinematics throughout their adiabatic evolution, and their densities can be approximated by a family of analytical radial profiles. Metallicity gradients within the galaxy flatten as dark matter is slowly removed. In the case of strong impulsive perturbations, stellar populations develop power-law-like density tails with radially biased kinematics. We show that the distribution of stellar binding energies within the dark matter halo substantially widens after an impulsive perturbation, no matter the sign of the perturbation. This allows initially energetically separated stellar populations to mix, to the extent that previously chemo-dynamically distinct populations may masquerade as a single population with large metallicity and energy spread. Finally, we show that in response to an impulsive perturbation, stellar populations that are deeply embedded in cored dark matter halos undergo a series of damped oscillations before reaching a virialized equilibrium state, driven by inefficient phase mixing in the harmonic potentials of cored halos. This slow return to equilibrium adds substantial systematic uncertainty to dynamical masses estimated from Jeans modeling or the virial theorem.

We use analytical and N-body methods to study the evolution of dwarf spheroidal galaxies (dSphs) embedded in dark matter (DM) haloes that host a sizeable subhalo population. Dark subhaloes generate a fluctuating gravitational field that injects energy into stellar orbits, driving a gradual expansion of dSphs. Despite the overall expansion, the stellar density profile preserves its initial shape, suggesting that the evolution proceeds in a self-similar manner. Meanwhile, the velocity dispersion profile, initially flat, evolves as the galaxy expands: the inner regions heat up, while the outer regions cool down. Kinematically, this resembles gravothermal collapse but with an inverted evolution, instead of collapsing the stellar system expands within a fluctuating halo potential. As the half-light radius r(half) approaches the halo peak velocity radius r(max), the expansion slows, and the velocity dispersion peaks at sigma(max) similar or equal to 0.54v(max). The stellar heat capacity remains positive for deeply embedded stars but diverges near r(max), turning negative beyond this threshold, which indicates a phase transition in the dynamical response to energy injection. The relaxation time-scales as t(rel) similar to r(half)(3/2), showing that orbital diffusion slows as the galaxy expands. Ultrafaint dSphs, having the smallest sizes and shortest relaxation times, are particularly sensitive to the presence of dark subhaloes. Some of our dSph models expand beyond the detection of current photometric surveys, becoming 'stealth' galaxies with luminosities and metallicities akin to known ultra-faints but with larger sizes and higher velocity dispersions. These objects would display half-light radii and dispersions similar to ultra-diffuse galaxies, but remain orders of magnitude fainter, representing a distinct, yet currently undetected, population of DM-dominated satellites.

We study the effect of stellar mass segregation driven by collisional relaxation within the potential well of a smooth dark matter halo. This effect is of particular relevance for old stellar systems with short crossing times, where small collisional perturbations accumulate over many dynamical timescales. We run collisional N -body simulations tailored to the ambiguous stellar systems Ursa Major 3/Unions 1, Delve 1, and Eridanus 3, modeling their stellar populations as two-component systems of high- and low-mass stars, respectively. For Ursa Major 3/Unions 1 (Delve 1), assuming a dynamical-to-stellar mass ratio of 10, we find that after 10 Gyr of evolution, the radial extent of its low-mass stars will be twice as large as (40% larger than) that of its high-mass stars. We show that weak tides do not alter this relative separation of half-light radii, whereas for the case of strong tidal fields, mass segregation facilitates the tidal stripping of low-mass stars. We further find that as the population of high-mass stars contracts and cools, the number of dynamically formed binaries within that population increases. Our results call for caution when using stellar mass segregation as a criterion to separate star clusters from dwarf galaxies, and suggest that mass segregation increases the abundance of massive binaries in the central regions of dark matter-dominated dwarf galaxies.

We present Gemini/GHOST high-resolution spectra of five stars observed in two low surface brightness Milky Way satellites, Sagittarius II (Sgr2) and Aquarius II (Aqu2). For Aqu2, the velocities and metallicities of the two stars are consistent with membership in a dark-matter-dominated ultra-faint dwarf galaxy (UFD). The chemical abundance ratios suggest inefficient star formation from only one or a few supernovae (e.g., low Na, Sr, Ba), and enriched potassium (K) from super-AGB stars. For Sgr2, the velocity and metallicity dispersions of its members are not clearly resolved, and our detailed chemical abundances show typical ratios for metal-poor stars, with low dispersions. There is only one exception—we report the discovery of an r -process enhanced star (Sgr 2584, [Eu/Fe] = +0.7 ± 0.2; thus, an r-I star). As r-I stars are found in both UFDs (Tuc III, Tuc IV, and Grus II) and globular clusters (M15 and M92), then this does not help to further classify the nature of Sgr2. Our exploration of Sgr2 demonstrates the difficulty in classifying some of the faintest (ambiguous) satellites. We advocate for additional diagnostics in analyzing the ambiguous systems, such as exploring radial segregation (by mass and/or chemistry), N -body simulations, and the need for dark matter to survive Galactic tidal effects. The spectra analyzed in this paper were taken as part of the GHOST commissioning observations, testing faint observation limits ( G < 18.8) and the single and double integrated field unit observing modes.

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.

We present the discovery of Ursa Major III/UNIONS 1, the least luminous known satellite of the Milky Way, which is estimated to have an absolute V-band magnitude of $+2.2^{+0.4}_{-0.3}$ mag, equivalent to a total stellar mass of 16$^{+6}_{-5}$ M$_{\odot}$. Ursa Major III/UNIONS 1 was uncovered in the deep, wide-field Ultraviolet Near Infrared Optical Northern Survey (UNIONS) and is consistent with an old ($\tau > 11$ Gyr), metal-poor ([Fe/H] $\sim -2.2$) stellar population at a heliocentric distance of $\sim$ 10 kpc. Despite being compact ($r_{\text{h}} = 3\pm1$ pc) and composed of so few stars, we confirm the reality of Ursa Major III/UNIONS 1 with Keck II/DEIMOS follow-up spectroscopy and identify 11 radial velocity members, 8 of which have full astrometric data from $Gaia$ and are co-moving based on their proper motions. Based on these 11 radial velocity members, we derive an intrinsic velocity dispersion of $3.7^{+1.4}_{-1.0}$ km s$^{-1}$ but some caveats preclude this value from being interpreted as a direct indicator of the underlying gravitational potential at this time. Primarily, the exclusion of the largest velocity outlier from the member list drops the velocity dispersion to $1.9^{+1.4}_{-1.1}$ km s$^{-1}$, and the subsequent removal of an additional outlier star produces an unresolved velocity dispersion. While the presence of binary stars may be inflating the measurement, the possibility of a significant velocity dispersion makes Ursa Major III/UNIONS 1 a high priority candidate for multi-epoch spectroscopic follow-ups to deduce to true nature of this incredibly faint satellite.

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 $16^{+6}_{-5}\,\rm M_\odot$ and a half-light radius of $3\pm1$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 use $N$-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 0.4Gyr), 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 ~$10^9\rm M_\odot$ cuspy LCDM halo, its velocity dispersion would be predicted to be of order ~1km/s. This is roughly consistent with the current estimate, which, neglecting binaries, places $\sigma_{\rm los}$ in the range 1 to 4km/s. 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.

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, isolated N -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 an N -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.

We present an atlas and follow-up spectroscopic observations of 87 thin stream-like structures detected with the STREAMFINDER algorithm in Gaia DR3, of which 29 are new discoveries. Here we focus on using these streams to refine mass models of the Galaxy. Fits with a double power law halo with the outer power law slope set to $-\beta_h=3$ yield an inner power law slope $-\gamma_h=0.97^{+0.17}_{-0.21}$, a scale radius of $r_{0, h}=14.7^{+4.7}_{-1.0}$ kpc, a halo density flattening $q_{m, h}=0.75\pm0.03$, and a local dark matter density of $\rho_{h, \odot}=0.0114\pm0.0007 {\rm M_\odot pc^{-3}}$. Freeing $\beta$ yields $\beta=2.53^{+0.42}_{-0.16}$, but this value is heavily influenced by our chosen virial mass limit. The stellar disks are found to have a combined mass of $4.20^{+0.44}_{-0.53}\times10^{10} {\rm M_\odot}$, with the thick disk contributing $12.4\pm0.7$\% to the local stellar surface density. The scale length of the thin and thick disks are $2.17^{+0.18}_{-0.08}$ kpc and $1.62^{+0.72}_{-0.13}$ kpc, respectively, while their scale heights are $0.347^{+0.007}_{-0.010}$ kpc and $0.86^{+0.03}_{-0.02}$ kpc, respectively. The virial mass of the favored model is $M_{200}=1.09^{+0.19}_{-0.14}\times 10^{12} {\rm M_\odot}$, while the mass inside of 50 kpc is $M_{R<50}=0.46\pm0.03\times 10^{12} {\rm M_\odot}$. We introduce the Large Magellanic Cloud (LMC) into the derived potential models, and fit the "Orphan" stream therein, finding a mass for the LMC that is consistent with recent estimates. Some highlights of the atlas include the nearby trailing arm of $\omega$-Cen, and a nearby very metal-poor stream that was once a satellite of the Sagittarius dwarf galaxy. Finally, we unambiguously detect a hot component around the GD-1 stream, consistent with it having been tidally pre-processed within its own DM subhalo.

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.

The cuspy central density profiles of cold dark matter (CDM) haloes make them highly resilient to disruption by tides. Self-interactions between dark matter particles, or the cycling of baryons, may result in the formation of a constant-density core which would make haloes more susceptible to tidal disruption. We use N-body simulations to study the evolution of NFW-like "cored" subhaloes in the tidal field of a massive host, and identify the criteria and timescales for full tidal disruption. Our results imply that the survival of Milky Way satellites places constraints on the sizes of dark matter cores. Indeed, we find that no subhaloes with cores larger than 1 per cent of their initial NFW scale radius can survive for a Hubble time on orbits with pericentres <10 kpc. A satellite like Tucana 3, with pericentre 3.5 kpc, must have a core size smaller than 2 pc to survive just three orbital periods on its current orbit. The core sizes expected in self-interacting dark matter (SIDM) models with a velocity-independent cross section of 1 cm^2/g seem incompatible with ultra-faint satellites with small pericentric radii, such as Tuc 3, Seg 1, Seg 2, Ret 2, Tri 2, and Wil 1, as these should have fully disrupted if accreted on to the Milky Way >10 Gyr ago. These results suggest that many satellites have vanishingly small core sizes, consistent with CDM cusps. The discovery of further Milky Way satellites on orbits with small pericentric radii would strengthen these conclusions and allow for stricter upper limits on the core sizes.

We use N-body simulations to model the tidal evolution of dark matter-dominated dwarf spheroidal galaxies embedded in cuspy Navarro-Frenk-White subhalos. Tides gradually peel off stars and dark matter from a subhalo, trimming it down according to their initial binding energy. This process strips preferentially particles with long orbital times, and comes to an end when the remaining bound particles have crossing times shorter than a fraction of the orbital time at pericentre. The properties of the final stellar remnant thus depend on the energy distribution of stars in the progenitor subhalo, which in turn depends on the initial density profile and radial segregation of the initial stellar component. The stellar component may actually be completely dispersed if its energy distribution does not extend all the way to the subhalo potential minimum, although a bound dark remnant may remain. These results imply that 'tidally-limited' galaxies, defined as systems whose stellar components have undergone substantial tidal mass loss, neither converge to a unique structure nor follow a single tidal track, as claimed in earlier work. On the other hand, tidally limited dwarfs do have characteristic sizes and velocity dispersions that trace directly the characteristic radius ($r_{max}$) and circular velocity ($V_{max}$) of the subhalo remnant. This result places strong upper limits on the size of satellites whose unusually low velocity dispersions are often ascribed to tidal effects. In particular, the large size of kinematically-cold 'feeble giant' satellites like Crater 2 or Antlia 2 cannot be explained as due to tidal effects alone in the Lambda Cold Dark Matter scenario.