Constraining the distribution of dark matter in dwarf spheroidal galaxies with stellar tidal streams

We use high-resolution N-body simulations to follow the formation and evolution of tidal streams associated to dwarf spheroidal galaxies (dSphs). The dSph models are embedded in dark matter (DM) haloes with either a centrally-divergent 'cusp', or an homogeneous-density 'core'. In agreement with previous studies, we find that as tides strip the galaxy the evolution of the half-light radius and the averaged velocity dispersion follows well-defined tracks that are mainly controlled by the amount of mass lost. Crucially, the evolutionary tracks behave differently depending on the shape of the DM profile: at a fixed remnant mass, dSphs embedded in cored haloes have larger sizes and higher velocity dispersions than their cuspy counterparts. The divergent evolution is particularly pronounced in galaxies whose stellar component is strongly segregated within their DM halo and becomes more disparate as the remnant mass decreases. Our analysis indicates that the DM profile plays an important role in defining the internal dynamics of tidal streams. We find that stellar streams associated to cored DM models have velocity dispersions that lie systematically above their cuspy counterparts. Our results suggest that the dynamics of streams with known dSph progenitors may provide strong constraints on the distribution of DM on the smallest galactic scales.Comment: 5 pages, 4 figure

Can tides disrupt cold dark matter subhaloes?

The clumpiness of dark matter on sub-kpc scales is highly sensitive to the tidal evolution and survival of subhaloes. In agreement with previous studies, we show that N-body realisations of cold dark matter subhaloes with centrally-divergent density cusps form artificial constant-density cores on the scale of the resolution limit of the simulation. These density cores drive the artificial tidal disruption of subhaloes. We run controlled simulations of the tidal evolution of a single subhalo where we repeatedly reconstruct the density cusp, preventing artificial disruption. This allows us to follow the evolution of the subhalo for arbitrarily large fractions of tidally stripped mass. Based on this numerical evidence in combination with simple dynamical arguments, we argue that cuspy dark matter subhaloes cannot be completely disrupted by smooth tidal fields. Modelling stars as collisionless tracers of the underlying potential, we furthermore study the tidal evolution of Milky Way dwarf spheroidal galaxies. Using a model of the Tucana III dwarf as an example, we show that tides can strip dwarf galaxies down to sub-solar luminosities. The remnant 'micro-galaxies' would appear as co-moving groups of metal-poor, low-mass stars of similar age, embedded in sub-kpc dark matter subhaloes.Comment: accepted for publication in MNRAS, 11 pages, 9 figure

Tidal evolution of dwarf spheroidal galaxies and dark matter subhalos

Understanding the distribution of dark matter (DM) on galactic scales is at the root of constraining the nature of DM and processes of galaxy formation like baryonic feedback. Dwarf spheroidal galaxies (dSphs), lying at the faintest end of the galaxy luminosity function, are the most DM dominated systems known to date. They are a promising candidates to probe the DM distribution on kpc scales. In this work, we study the tidal evolution, abundance and observable properties of dSphs embedded in DM subhaloes. Tidal evolution of subhaloes and dwarf galaxies We run controlled simulations of the tidal evolution of a single cold dark matter subhalo with a centrally-divergent density cusp, tailored to follow the evolution of the subhalo for arbitrarily large fractions of tidally stripped mass. Based on simple dynamical arguments and numerical experiments, we argue that cuspy DM subhaloes cannot be completely disrupted by smooth tidal fields. Using a model of the Tucana III dSph galaxy as an example, we show that tides can strip dSph galaxies down to sub-solar luminosities. The remnant micro-galaxies would appear as co-moving groups of metal-poor, low-mass stars of similar age, embedded in sub-kpc DM subhaloes. Subhalo depletion driven by the galactic disc To further quantify the abundance of subhaloes in Milky Way-like galaxies containing a galactic disc, we use high-resolution re-simulations of all subhaloes of the Aquarius A2 merger tree with masses M > 10^8 Msol at accretion. We model the tidal evolution of subhaloes with both cuspy and cored DM profiles, finding that cuspy models have twice as many surviving subhaloes within the virial radius of the host at redshift z=0 as their cored counterparts. The presence of a galactic disc reduces the number of surviving subhaloes further by a factor of < 2 for subhaloes on orbits that pass through the disc. Mass estimates for Milky Way dwarf galaxies With the aim of comparing observed properties of Milky Way dSph galaxies to simulations, we construct an estimator for enclosed masses based on the virial theorem, insensitive to anisotropy in the velocity dispersion and tailored to yield masses with minimum uncertainty introduced by our ignorance on (i) the shape of the inner DM profile, and (ii) how deeply the stellar component is embedded within the subhalo. Tests against controlled simulations show that the estimator provides unbiased masses with an accuracy of ~10 per cent. Application to published kinematic data of Milky Way dSph galaxies reveals a tight correlation between enclosed mass and luminosity. Comparison against cuspy and cored DM haloes extracted from controlled cosmological simulations shows that the high mass densities of ultrafaint galaxies are not compatible with large DM cores, and that the (total) halo masses of the classical Milky Way dSph galaxies span a remarkably narrow range (8 < log10 M/Msol < 10) at present, showing no clear trend with either galaxy size or luminosity

The Formation of Ultra Diffuse Galaxies in Cored Dark Matter Halos Through Tidal Stripping and Heating

We propose that the Ultra-Diffuse Galaxy (UDG) population represents a set of satellite galaxies born in $\sim10^{10}-10^{11}$ M$_\odot$ halos, similar to field dwarfs, which suffer a dramatic reduction in surface brightness due to tidal stripping and heating. This scenario is observationally motivated by the radial alignment of UDGs in Coma as well as the significant dependence of UDG abundance on cluster mass. As a test of this formation scenario, we apply a semi-analytic model describing the change in stellar mass and half-light radius of dwarf satellites, occupying either cored or cuspy halos, to cluster subhalos in the Illustris-dark simulation. Key to this model are results from simulations which indicate that galaxies in cored dark-matter halos expand significantly in response to tidal stripping and heating, whereas galaxies in cuspy halos experience limited size evolution. Our analysis indicates that a population of tidally-stripped dwarf galaxies, residing in cored halos (like those hosting low-surface brightness field dwarfs), is able to reproduce the observed sizes and stellar masses of UDGs in clusters remarkably well.Comment: Resubmitted to MNRAS; comments welcome

Systematics in virial mass estimators for pressure-supported systems

Mass estimators are a key tool to infer the dark matter content in pressure-supported systems like dwarf spheroidal galaxies (dSphs). We construct an estimator for enclosed masses based on the virial theorem which is insensitive to anisotropy in the velocity dispersion and tailored to yield masses with minimum uncertainty introduced by our ignorance on (i) the shape of the inner halo profile, and (ii) how deeply the stellar component is embedded within the halo: $M(<1.8\,R_\mathrm{h}) \approx 3.5 \times 1.8\,R_\mathrm{h} \langle \sigma_\mathrm{los}^2 \rangle G^{-1}$, where by $R_\mathrm{h}$ we denote the projected half-light radius and by $\langle \sigma_\mathrm{los}^2 \rangle$ the luminosity-averaged squared line-of-sight velocity dispersion. Tests against controlled simulations show that this estimator provides unbiased enclosed masses with an accuracy of $\sim 10$ per cent. This confirms the robustness of similar previously proposed mass estimators. Application to published kinematic data of Milky Way dSphs reveals a tight correlation between enclosed mass and luminosity. Using $N$-body models we show that tidal stripping has little effect on this relation. Comparison against cuspy and cored dark matter haloes extracted from controlled re-simulations of the Aquarius A2 merger tree shows that the high mass densities of ultrafaint galaxies are not compatible with large dark matter cores, and that the (total) halo masses of the classical Milky Way dSphs span a remarkably narrow range ($8 \lesssim \mathrm{log_{10}}\,(M/\mathrm{M_\odot}) \lesssim 10$) at present, showing no clear trend with either galaxy size or luminosity.Comment: 18 pages, 12 figures. Accepted for publication in MNRAS. Edited to match accepted versio

Dark matter halo cores and the tidal survival of Milky Way satellites

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 during galaxy formation, 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. Applied to the Milky Way (MW), our results imply that the survival of MW satellites places interesting constraints on core formation. 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, Wil 1, as these would fully disrupt in less than 10 Gyr after infall. 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 implied by the survival of Milky Way satellites.Comment: 13 pages, 13 figures, submitted to MNRAS, comments welcom

Micro galaxies as a falsifiable prediction of LCDM cosmology

A fundamental prediction of the Lambda Cold Dark Matter (LCDM) cosmology are the centrally-divergent cuspy density profiles of dark matter haloes. These density cusps render CDM 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 "micro galaxies"; i.e., heavily-stripped remnants of early accreted satellites which may 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 two 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 another where stars are less tightly bound and have a well-defined finite density core. The tidal evolution in the size-velocity dispersion plane is quite similar for these two models, although their remnants may differ widely in luminosity. Micro galaxies 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.Comment: submitted to ApJ, comments welcom

The discovery of the faintest known Milky Way satellite using UNIONS

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.Comment: 21 pages, 9 figures, 3 tables; Accepted for publication in Ap

Collisionless relaxation from near equilibrium configurations: Linear theory and application to tidal stripping

International audiencePlaced slightly out of dynamical equilibrium, an isolated stellar system quickly returns towards 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 per cent 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. We further confirm that relaxation is responsible for depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against $N$-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