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Galaxies and their dark-matter haloes have posed several challenges to the dark energy plus cold dark matter ( Λ CDM) cosmological model. These discrepancies between observations and theory intensify for the lowest-mass (‘dwarf’) galaxies. Λ CDM predictions for the number, spatial distribution and internal structure of low-mass dark-matter haloes have historically been at odds with observed dwarf galaxies, but this is partially expected, because many predictions modelled only the dark-matter component. Any robust Λ CDM prediction must include, hand in hand, a model for galaxy formation to understand how baryonic matter populates and affects dark-matter haloes. In this Review, we consider the most notable challenges to Λ CDM regarding dwarf galaxies, and we discuss how recent cosmological numerical simulations have pinpointed baryonic solutions to these challenges. We identify remaining tensions, including the diversity of the inner dark-matter content, planes of satellites, stellar morphologies and star-formation quenching. Their resolution, or validation as actual problems with Λ CDM, will probably require both refining of galaxy-formation models and improving numerical accuracy in simulations. Galaxies and their dark-matter haloes have posed several challenges to the dark energy plus cold dark matter ( Λ CDM) cosmological model. This Review discusses the most notable challenges to Λ CDM regarding dwarf galaxies and the insights provided by recent cosmological numerical simulations.

We use N-body cosmological simulations and empirical galaxy models to study the merger history of dwarf-mass galaxies (with M_halo~10^10 M_Sun). Our input galaxy models describe the stellar mass-halo mass relation, and the galaxy occupation fraction. The number of major and minor mergers depends on the type of dark matter; in particular, minor mergers are greatly suppressed in warm dark matter models. In addition, the number of mergers that bring in stars is strongly dependent on the galaxy occupation model. For example, minor mergers are negligible for stellar halo growth in models with a high mass threshold for galaxy formation (i.e. 10^9.3 M_Sun at z=0). Moreover, this threshold for galaxy formation can also determine the relative difference (if any) between the stellar haloes of satellite and field dwarfs. Using isolated simulations of dwarf-dwarf mergers, we show that the relative frequency of major and minor mergers predict very different stellar haloes: Typically, \"intermediate\" dark matter merger ratios (~1:5) maximise the growth of distant stellar haloes. We discuss the observability of dwarf stellar haloes and find that the surface brightness of these features are incredibly faint. However, when several dwarfs are stacked together models that form particularly rich stellar haloes could be detectable. Finally, we show that stellar streams in the Galactic halo overlapping in phase-space with known dwarf satellites are likely remnants of their stripped stellar haloes. The mere existence of dwarf stellar haloes can already put constraints on some small-scale models, and thus observational probes should be a high priority.

We use the APOSTLE suite of cosmological hydrodynamical simulations of the Local Group to examine the high speed tail of the local dark matter velocity distribution in simulated Milky Way analogues. The velocity distribution in the Solar neighborhood is well approximated by a generalized Maxwellian distribution sharply truncated at a well-defined maximum ``escape\" speed. The truncated generalized Maxwellian distribution accurately models the local dark matter velocity distribution of all our Milky Way analogues, with no evidence for any separate extragalactic high-speed components. The local maximum speed is well approximated by the terminal velocity expected for particles able to reach the Solar neighborhood in a Hubble time from the farthest confines of the Local Group. This timing constraint means that the local dark matter velocity distribution is unlikely to contain any high-speed particles contributed by the Virgo Supercluster ``envelope\", as argued in recent works. Particles in the Solar neighborhood with speeds close to the local maximum speed can reach well outside the virial radius of the Galaxy, and, in that sense, belong to the Local Group envelope posited in earlier work. The local manifestation of such envelope is thus not a distinct high-speed component, but rather simply the high-speed tail of the truncated Maxwellian distribution.

We present predictions for proper motions, infall times and times of first pericentric passage for 39 of M31's satellite galaxies. We estimate these by sampling satellite orbits from cosmological N-body simulations matched on mass, distance and velocity along the line of sight, in addition to properties of the host system. Our predictions are probabilistic based on repeated sampling from the uncertainty distributions of all quantities involved. We use these constraints on the satellites' orbital histories in conjunction with their published star formation histories to investigate the dominant environmental mechanisms for quenching satellites of M31-like hosts. Around half of the satellites appear to have quenched before their first pericentric passage around M31. Only the most massive satellites (with stellar masses > 10^8 M_sun) are able to maintain star formation for up to billions of years after infall. The majority of faint satellites, with stellar masses < 10^8 M_sun , were likely quenched before entering the M31 system. We compare our results for M31 against predictions for the Milky Way's satellites from the literature; M31's has a more active recent accretion history with more recently quenched satellites than the Milky Way.

The powerful combination of Gaia with other Milky Way large survey data has ushered in a deeper understanding of the assembly history of our Galaxy, which is marked by the accretion of Gaia-Enceladus/Sausage (GES). As a step towards reconstructing this significant merger, we examine the existence and destruction of its stellar metallicity gradient. We investigate 8 GES-like progenitors from the Auriga simulations and find that all have negative metallicity gradients at infall with a range of -0.09 to -0.03 dex/kpc against radius and -1.99 to -0.41 dex/\\( 10^-5 km^2s^-2\\) against the stellar orbital energy. These gradients get blurred and become shallower when measured at \\(z=0\\) in the Milky Way-like host. The percentage change in the radial metallicity gradient is consistently high (78-98\\%), while the percentage change in the energy space varies much more (9-91\\%). We also find that the most massive progenitors show the smallest changes in their energy metallicity gradients. At the same present-day galactocentric radius, lower metallicity stars originate from the outskirts of the GES progenitor. Similarly, at fixed metallicity, stars at higher galactocentric radii tend to originate from the GES outskirts. We find that the GES stellar mass, total mass, infall time, and the present-day Milky Way total mass are correlated with the percentage change in metallicity gradient, both in radius and in energy space. It is therefore vital to constrain these properties further to pin down the infall metallicity gradient of the GES progenitor and understand the onset of such ordered chemistry at cosmic noon.

The unusually low velocity dispersion and large size of Crater II pose a challenge to our understanding of dwarf galaxies in the Lambda Cold Dark Matter (LCDM) cosmogony. The low velocity dispersion suggests either a dark halo mass much lower than the minimum expected from hydrogen cooling limit arguments, or one that is in the late stages of extreme tidal stripping. The tidal interpretation has been favoured in recent work and is supported by the small pericentric distances consistent with available kinematic estimates. We use N-body simulations to examine this interpretation in detail, assuming a Navarro-Frenk-White (NFW) profile for Crater II's progenitor halo. Our main finding is that, although the low velocity dispersion can indeed result from the effect of tides, the large size of Crater II is inconsistent with this hypothesis. This is because galaxies stripped to match the observed velocity dispersion are also reduced to sizes much smaller than the observed half-light radius of Crater II. Unless its size has been substantially overestimated, reconciling this system with LCDM requires that either (i) it is not bound and near equilibrium (unlikely, given its crossing time is shorter than the time elapsed since pericentre), or that (ii) its progenitor halo deviates from the assumed NFW profile. The latter alternative may signal that baryons can affect the inner halo cusp even in extremely faint dwarfs or, more intriguingly, may signal effects associated with the intimate nature of the dark matter, such as finite self-interactions, or other such deviations from the canonical LCDM paradigm.

We use 12 cosmological \\(N\\)-body simulations of Local Group systems (the Apostle models) to inspect the relation between the virial mass of the main haloes (\\(M_ vir,1\\) and \\(M_ vir,2\\)), the mass derived from the relative motion of the halo pair (\\(M_ tim\\)), and that inferred from the local Hubble flow (\\(M_ lhf\\)). We show that within the Spherical Collapse Model (SCM), the correspondence between the three mass estimates is exact, i.e. \\(M_ lhf=M_ tim=M_ vir,1+M_ vir,2\\). However, comparison with Apostle simulations reveals that, contrary to what the SCM states, a relatively large fraction of the mass that perturbs the local Hubble flow and drives the relative trajectory of the main galaxies is not contained within \\(R_ vir\\), and that the amount of \"extra-virial\" mass tends to increase in galaxies with a slow accretion rate. In contrast, modelling the peculiar velocities around the Local Group returns an unbiased constraint on the virial mass ratio of the main galaxy pair. Adopting the outer halo profile found in \\(N\\)-body simulations, which scales as \\( R^-4\\) at \\(R R_ vir\\), indicates that the galaxy masses perturbing the local Hubble flow roughly correspond to the asymptotically-convergent (total) masses of the individual haloes. We show that estimates of \\(M_ vir\\) based on the dynamics of tracers at \\(R R_ vir\\) require a priori information on the internal matter distribution and the growth rate of the main galaxies, both of which are typically difficult to quantify.

We present the new ARTEMIS Emulator suite of high resolution (baryon mass of \\(2.23 10^4\\) \\(h^-1\\)M\\(_\\)) zoom-in simulations of Milky Way mass systems. Here, three haloes from the original ARTEMIS sample have been rerun multiple times, systematically varying parameters for the stellar feedback model, the density threshold for star formation, the reionisation redshift and the assumed warm dark matter (WDM) particle mass (assuming a thermal relic). From these simulations emulators are trained for a wide range of statistics that allow for fast predictions at combinations of parameters not originally sampled, running in \\( 1\\)ms (a factor of \\( 10^11\\) faster than the simulations). In this paper we explore the dependence of the central haloes' stellar mass on the varied parameters, finding the stellar feedback parameters to be the most important. When constraining the parameters to match the present-day stellar mass halo mass relation inferred from abundance matching we find that there is a strong degeneracy in the stellar feedback parameters, corresponding to a freedom in formation time of the stellar component for a fixed halo assembly history. We additionally explore the dependence of the satellite stellar mass function, where it is found that variations in stellar feedback, the reionisation redshift and the WDM mass all have a significant effect. The presented emulators are a powerful tool which allows for fundamentally new ways of analysing and interpreting cosmological hydrodynamic simulations. Crucially, allowing their free (subgrid) parameters to be varied and marginalised, leading to more robust constraints and predictions.

Our Local Group, dominated in mass by the Milky Way (MW) and M31, provides a unique laboratory for testing \\(\\)CDM cosmology on small scales owing to its proximity. However, its connection to the surrounding large-scale environment, which is essential for interpreting its properties, is inadequately understood. In this work, we explore the connection between Local Group analogues (LGAs) and their surrounding large-scale environments using the ABACUSSUMMIT simulation suite, highlighting the key role of the coupling energy of the MW-M31 orbit, \\(E_ coupling\\). We find that LGAs with high \\(E_ coupling\\) preferentially reside in denser regions, whereas those with low \\(E_ coupling\\) tend to occupy low-density environments. Furthermore, LGAs with low \\(E_ coupling\\) exhibit strong alignment with cosmic filaments, manifested as a pronounced polar anisotropy in the distribution of tracer haloes. By contrast, LGAs with high \\(E_ coupling\\) show a weaker polar anisotropy but an enhanced azimuthal anisotropy, with large-scale tracer haloes preferentially lying in the plane spanned by the halo pair and the orbital spin vector. Within this framework, our Local Group is characterised by typical \\(E_ coupling\\) residing in a relatively under-dense environment, yet it remains consistent with the 95\\% range of analogue systems identified in the simulation.

The low dark matter density in the Fornax dwarf galaxy is often interpreted as being due to the presence of a constant density `core', but it could also be explained by the effects of Galactic tides. The latter interpretation has been disfavoured because it is apparently inconsistent with the orbital parameters and star formation history of Fornax. We revisit these arguments with the help of the APOSTLE cosmological hydrodynamics simulations. We show that simulated dwarfs with similar properties to Fornax are able to form stars after infall, so that star formation is not necessarily a good tracer of infall time. We also examine the constraints on the pericentre of Fornax and point out that small pericentres (<50 kpc) are not currently ruled out by the data, allowing for Fornax to be tidally influenced on its current orbit. Furthermore, we find that some dwarfs with large orbital pericentres can be stripped prior to infall due to interactions with more massive galaxies. Tidal effects lead to a reduction in the dark matter density, while the profile remains cuspy. Navarro-Frenk-White profiles are consistent with the kinematic data within 3\\(\\) in the innermost regions, while profiles with shallow cusps or cores provide a better fit. We predict that if the reduction of the dark matter density in Fornax occurs, at least in part, because of the action of Galactic tides, then tidal tails should be visible with a surface brightness limit of \\(35-36\\) mag arcsec\\(^-2\\) over a survey area of \\(\\)100 deg\\(^2\\).