Milky Way-sized Halo Research Articles

Observed versus simulated halo c–Mvir relations

ABSTRACT The concentration – virial mass relation is a well-defined trend that reflects the formation of structure in an expanding universe. Numerical simulations reveal a marked correlation that depends on the collapse time of dark matter haloes and their subsequent assembly history. However, observational constraints are mostly limited to the massive end via X-ray emission of the hot diffuse gas in clusters. An alternative approach, based on gravitational lensing over galaxy scales, revealed an intriguingly high concentration at Milky Way-sized haloes. This letter focuses on the robustness of these results by adopting a bootstrapping approach that combines stellar and lensing mass profiles. We also apply the identical methodology to simulated haloes from eagle to assess any systematic. We bypass several shortcomings of ensemble type lens reconstruction and conclude that the mismatch between observed and simulated concentration–to–virial–mass relations are robust, and need to be explained either invoking a lensing-related sample selection bias, or a careful investigation of the evolution of concentration with assembly history. For reference, at a halo mass of 1012M⊙, the concentration of observed lenses is c$_{12}\, \sim 40\ \pm$ 5, whereas simulations give c$_{12}\, \sim 15\ \pm$ 1.

Orbital pericentres and the inferred dark matter halo structure of satellite galaxies

ABSTRACT Using the phat-ELVIS suite of Milky Way-sized halo simulations, we show that subhalo orbital pericentres, rperi, correlate with their dark matter halo structural properties. Specifically, at fixed maximum circular velocity, Vmax, subhaloes with smaller rperi are more concentrated (have smaller rmax values) and have lost more mass, with larger peak circular velocities, Vpeak, prior to infall. These trends provide information that can tighten constraints on the inferred Vmax and Vpeak values for known Milky Way satellites. We illustrate this using published pericentre estimates enabled by Gaia for the nine classical Milky Way dwarf spheroidal satellites. The two densest dSph satellites (Draco and Ursa Minor) have relatively small pericentres, and this pushes their inferred rmax and Vmax values lower than they would have been without pericentre information. For Draco, we infer $V_{\rm max} = 23.5 \, \pm 3.3$ km s−1 (compared to $27.3 \, \pm 7.1$ km s−1 without pericentre information). Such a shift exacerbates the traditional Too Big to Fail problem. Draco’s peak circular velocity range prior to infall narrows from Vpeak = 21–51 km s−1 without pericentre information to Vpeak = 25–37 km s−1 with the constraint. Over the full population of classical dwarf spheroidals, we find no correlation between Vpeak and stellar mass today, indicative of a high level of stochasticity in galaxy formation at stellar masses below ∼107 M⊙. As proper motion measurements for dwarf satellites become more precise, they should enable useful priors on the expected structure and evolution of their host dark matter subhaloes.

New empirical constraints on the cosmological evolution of gas and stars in galaxies

ABSTRACT We combine the latest observationally motivated constraints on stellar properties in dark matter haloes, along with data-driven predictions for the atomic (H I) and molecular (H2) gas evolution in galaxies, to derive empirical relationships between the build-up of galactic components and their evolution over cosmic time. At high redshift (z ≳ 4), the frameworks imply that galaxies acquire their cold gas (both atomic and molecular) mostly by accretion, with the fraction of cold gas reaching about 20 per cent of the cosmic baryon fraction. We infer a strong dependence of the star formation rate on the H2 mass, suggesting a near-universal depletion time-scale of 0.1–1 Gyr in Milky Way-sized haloes (of masses 1012 M⊙ at z = 0). There is also evidence for a near-universality of the Kennicutt–Schmidt relation across redshifts, with very little dependence on stellar mass, if a constant conversion factor (αCO) of CO luminosity to molecular gas mass is assumed. Combining the atomic and molecular gas observations with the stellar build-up illustrates that galactic mass assembly in Milky Way-sized haloes proceeds from smooth accretion at high redshifts towards becoming merger-dominated at late times (z ≲ 0.6). Our results can be used to constrain numerical simulations of the dominant growth and accretion processes of galaxies over cosmic history.

Statistical properties of substructures around Milky Way-sized haloes and their implications for the formation of stellar streams

Stellar streams originating in disrupted dwarf galaxies and star clusters are observed around the Milky Way and nearby galaxies. Such substructures are the important tracers that record how the host haloes have accreted progenitor galaxies. Based on the cosmological context, we investigate the relationship between structural properties of substructures such as length and thinness at $z=0$, and orbits of their progenitors. We model stellar components of a large sample of substructures around Milky Way-sized haloes by combining semi-analytic models with a high-resolution cosmological $N$-body simulation. Using the Particle Tagging method, we embed stellar components in progenitor haloes and trace phase-space distributions of the substructures down to $z=0$. We find that the length and thinness of substructures vary smoothly as the redshift when the host haloes accrete their progenitors. For substructures observed like streams at $z=0$, a large part of the progenitors is accreted by their host haloes at redshift $0.5\lesssim z\lesssim 2.5$. Substructures with progenitors out of this accretion redshift range are entirely or less disrupted by $z=0$ and cannot be observed as streams. We also find that the distributions of length and thinness of substructures vary smoothly as pericenter and apocenter of the progenitors. Substructures observed like streams tend to have the specific range of $10\ {\rm kpc} \lesssim r_{\rm peri}\lesssim100\ {\rm kpc}$ and $50\ {\rm kpc} \lesssim r_{\rm apo}\lesssim300\ {\rm kpc}$.

Gravitational lensing and the power spectrum of dark matter substructure: Insights from the ETHOS N -body simulations

Strong gravitational lensing has been identified as a promising astrophysical probe to study the particle nature of dark matter. In this paper we present a detailed study of the power spectrum of the projected mass density (convergence) field of substructure in a Milky Way-sized halo. This power spectrum has been suggested as a key observable that can be extracted from strongly-lensed images and yield important clues about the matter distribution within the lens galaxy. We use two different $N$-body simulations from the ETHOS framework: one with cold dark matter and another with self-interacting dark matter and a cutoff in the initial power spectrum. Despite earlier works that identified $k\ensuremath{\gtrsim}100\text{ }\text{ }{\mathrm{kpc}}^{\ensuremath{-}1}$ as the most promising scales to learn about the particle nature of dark matter we find that even at lower wave numbers---which are actually within reach of observations in the near future---we can gain important information about dark matter. Comparing the amplitude and slope of the power spectrum on scales $0.1\ensuremath{\lesssim}k/{\mathrm{kpc}}^{\ensuremath{-}1}\ensuremath{\lesssim}10$ from lenses at different redshifts can help us distinguish between cold dark matter and other exotic dark matter scenarios that alter the abundance and central densities of subhalos. Furthermore, by considering the contribution of different mass bins to the power spectrum we find that subhalos in the mass range $1{0}^{7}\ensuremath{-}{10}^{8}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ are on average the largest contributors to the power spectrum signal on scales $2\ensuremath{\lesssim}k/{\mathrm{kpc}}^{\ensuremath{-}1}\ensuremath{\lesssim}15$, despite the numerous subhalos with masses $>{10}^{8}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ in a typical lens galaxy. Finally, by comparing the power spectra obtained from the subhalo catalogs to those from the particle data in the simulation snapshots we find that the seemingly-too-simple halo model is in fact a fairly good approximation to the much more complex array of substructure in the lens.

Simulating a metallicity-dependent initial mass function: consequences for feedback and chemical abundances

Observational and theoretical arguments increasingly suggest that the initial mass function (IMF) of stars may depend systematically on environment, yet most galaxy formation models to date assume a universal IMF. Here we investigate simulations of the formation of Milky Way analogues run with an empirically derived metallicity-dependent IMF and the moving-mesh code AREPO in order to characterize the associated uncertainties. In particular, we compare a constant Chabrier and a varying metallicity-dependent IMF in cosmological, magneto-hydrodynamical zoom-in simulations of Milky Way-sized halos. We find that the non-linear effects due to IMF variations typically have a limited impact on the morphology and the star formation histories of the formed galaxies. Our results support the view that constraints on stellar-to-halo mass ratios, feedback strength, metallicity evolution and metallicity distributions are in part degenerate with the effects of a non-universal, metallicity-dependent IMF. Interestingly, the empirical relation we use between metallicity and the high mass slope of the IMF does not aid in the quenching process. It actually produces up to a factor of 2-3 more stellar mass if feedback is kept constant. Additionally, the enrichment history and the z = 0 metallicity distribution are significantly affected. In particular, the alpha enhancement pattern shows a steeper dependence on iron abundance in the metallicity-dependent model, in better agreement with observational constraints.

On the relevance of chaos for halo stars in the solar neighbourhood II

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

Origin of chemically distinct discs in the Auriga cosmological simulations

The stellar disk of the Milky Way shows complex spatial and abundance structure that is central to understanding the key physical mechanisms responsible for shaping our Galaxy. In this study, we use six very high resolution cosmological zoom simulations of Milky Way-sized haloes to study the prevalence and formation of chemically distinct disc components. We find that our simulations develop a clearly bimodal distribution in the $[\rm \alpha/Fe]$ -- $[\rm Fe/H]$ plane. We find two main pathways to creating this dichotomy which operate in different regions of the galaxies: a) an early ($z>1$) and intense high-$\rm[\alpha/Fe]$ star formation phase in the inner region ($R\lesssim 5$ kpc) induced by gas-rich mergers, followed by more quiescent low-$\rm[\alpha/Fe]$ star formation; and b) an early phase of high-$\rm[\alpha/Fe]$ star formation in the outer disc followed by a shrinking of the gas disc owing to a temporarily lowered gas accretion rate, after which disc growth resumes. In process b), a double-peaked star formation history around the time and radius of disc shrinking accentuates the dichotomy. If the early star formation phase is prolonged (rather than short and intense), chemical evolution proceeds as per process a) in the inner region, but the dichotomy is less clear. In the outer region, the dichotomy is only evident if the first intense phase of star formation covers a large enough radial range before disc shrinking occurs; otherwise, the outer disc consists of only low-$\rm[\alpha/Fe]$ sequence stars. We discuss the implication that both processes occurred in the Milky Way.

On the effect of galactic outflows in cosmological simulations of disc galaxies

We investigate the impact of galactic outflow modelling on the formation and evolution of a disc galaxy, by performing a suite of cosmological simulations with zoomed-in initial conditions of a Milky Way-sized halo. We verify how sensitive the general properties of the simulated galaxy are to the way in which stellar feedback triggered outflows are implemented, keeping initial conditions, simulation code and star formation (SF) model all fixed. We present simulations that are based on a version of the GADGET3 code where our sub-resolution model is coupled with an advanced implementation of Smoothed Particle Hydrodynamics that ensures a more accurate fluid sampling and an improved description of gas mixing and hydrodynamical instabilities. We quantify the strong interplay between the adopted hydrodynamic scheme and the sub-resolution model describing SF and feedback. We consider four different galactic outflow models, including the one introduced by Dalla Vecchia and Schaye (2012) and a scheme that is inspired by the Springel and Hernquist (2003) model. We find that the sub-resolution prescriptions adopted to generate galactic outflows are the main shaping factor of the stellar disc component at low redshift. The key requirement that a feedback model must have to be successful in producing a disc-dominated galaxy is the ability to regulate the high-redshift SF (responsible for the formation of the bulge component), the cosmological infall of gas from the large-scale environment, and gas fall-back within the galactic radius at low redshift, in order to avoid a too high SF rate at $z=0$.

Properties of H i discs in the Auriga cosmological simulations

We analyse the properties of the HI gas distribution in the Auriga project, a set of magnetohydrodynamic cosmological simulations performed with the moving-mesh code AREPO and a physics model for galaxy formation that succeeds in forming realistic late-type galaxies in the 30 Milky Way-sized haloes simulated in this project. We use a simple approach to estimate the neutral hydrogen fraction in our simulation set, which treats low-density and star-forming gas separately, and we explore two different prescriptions to subtract the contribution of molecular hydrogen from the total HI content. The HI gas in the vast majority of the systems forms extended discs although more disturbed morphologies are present. Notwithstanding the general good agreement with observed HI properties -- such as radial profiles and the mass-diameter relation -- the Auriga galaxies are systematically larger and more gas-rich than typical nearby galaxies. Interestingly, the amount of HI gas outside the disc plane correlates with the star formation rate, consistent with a picture where most of this extra-planar HI gas originates from a fountain-like flow. Our findings are robust with respect to the different assumptions adopted for computing the molecular hydrogen fraction and do not vary significantly over a wide range of numerical resolution. The HI modelling introduced in this paper can be used in future work to build artificial interferometric HI data cubes, allowing an even closer comparison of the gas dynamics in simulated galaxies with observations.

Baryonic impact on the dark matter orbital properties of Milky Way-sized haloes

We study the orbital properties of dark matter haloes by combining a spectral method and cosmological simulations of Milky Way-sized galaxies. We compare the dynamics and orbits of individual dark matter particles from both hydrodynamic and $N$-body simulations, and find that the fraction of box, tube and resonant orbits of the dark matter halo decreases significantly due to the effects of baryons. In particular, the central region of the dark matter halo in the hydrodynamic simulation is dominated by regular, short-axis tube orbits, in contrast to the chaotic, box and thin orbits dominant in the $N$-body run. This leads to a more spherical dark matter halo in the hydrodynamic run compared to a prolate one as commonly seen in the $N$-body simulations. Furthermore, by using a kernel based density estimator, we compare the coarse-grained phase-space densities of dark matter haloes in both simulations and find that it is lower by $\sim0.5$ dex in the hydrodynamic run due to changes in the angular momentum distribution, which indicates that the baryonic process that affects the dark matter is irreversible. Our results imply that baryons play an important role in determining the shape, kinematics and phase-space density of dark matter haloes in galaxies.

COLD DARK MATTER SUBSTRUCTURES IN EARLY-TYPE GALAXY HALOS

ABSTRACT We present initial results from the “Ponos” zoom-in numerical simulations of dark matter substructures in massive ellipticals. Two very highly resolved dark matter halos with M vir = 1.2 × 1013 and M vir = 6.5 × 1012 and different (“violent” versus “quiescent”) assembly histories have been simulated down to z = 0 in a ΛCDM cosmology with a total of 921,651,914 and 408,377,544 particles, respectively. Within the virial radius, the total mass fraction in self-bound M sub > 106 subhalos at the present epoch is 15% for the violent host and 16.5% for the quiescent one. At z = 0.7, these fractions increase to 19% and 33%, respectively, as more recently accreted satellites are less prone to tidal destruction. In projection, the average fraction of surface mass density in substructure at a distance of R/R vir = 0.02 (∼5–10 kpc) from the two halo centers ranges from 0.6% to ≳2%, significantly higher than that measured in simulations of Milky Way-sized halos. The contribution of subhalos with M sub < 109 to the projected mass fraction is between one-fifth and one-third of the total, with the smallest share found in the quiescent host. We assess the impact of baryonic effects via twin, lower-resolution hydrodynamical simulations that include metallicity-dependent gas cooling, star formation, and a delayed-radiative-cooling scheme for supernova feedback. Baryonic contraction produces a super-isothermal total density profile and increases the number of massive subhalos in the inner regions of the main host. The host density profiles and projected subhalo mass fractions appear to be broadly consistent with observations of gravitational lenses.

Spiral-induced velocity and metallicity patterns in a cosmological zoom simulation of a Milky Way-sized galaxy

Abstract We use a high-resolution cosmological zoom simulation of a Milky Way-sized halo to study the observable features in velocity and metallicity space associated with the dynamical influence of spiral arms. For the first time, we demonstrate that spiral arms, that form in a disc in a fully cosmological environment with realistic galaxy formation physics, drive large-scale systematic streaming motions. In particular, on the trailing edge of the spiral arms the peculiar galactocentric radial and azimuthal velocity field is directed radially outward and azimuthally backward, whereas it is radially inward and azimuthally forward on the leading edge. Owing to the negative radial metallicity gradient, this systematic motion drives, at a given radius, an azimuthal variation in the residual metallicity that is characterized by a metal-rich trailing edge and a metal-poor leading edge. We show that these signatures are theoretically observable in external galaxies with integral field unit instruments such as VLT/MUSE, and if detected, would provide evidence for large-scale systematic radial migration driven by spiral arms.

The kinetic Sunyaev–Zel'dovich tomography – II. Probing the circumgalactic medium

We propose the use of the kinetic Sunyaev-Zel'dovich (kSZ) effect to probe the circumgalactic medium (CGM), with the aid of a spectroscopic survey covering the same area of a SZ survey. One can design an optimal estimator of the kSZ effect of the CGM with a matched filter, and construct the cross correlation between the estimator and the peculiar velocity recovered from the galaxy survey, which can be measured by stacking a number of galaxies. We investigate two compelling profiles for the CGM, the MB profile (Maller & Bullock 2004) and the $\beta$ profile, and estimate the detectability against the synergy of a fiducial galaxy survey with number density $10^{-3}h^3\,$ Mpc$^{-3}$ and an ACT-like SZ survey. We show that the shape of the filter does not change much with redshift for the $\beta$ profile, while there are significant side lobes at $z<0.1$ for the MB profile. By stacking $\sim 10^4$ Milky Way-size halos around z $\sim 0.5$, one can get $\gtrsim$ 1 $\sigma$ signal to noise (S/N) for the both profiles. The S/N increases with decreasing redshift before it reaches a maximum ($\sim$ 7.5 at z $\simeq$ 0.15 for the MB profile, $\sim 19$ at $z\simeq 0.03$ for the $\beta$ profile). Due to the large beam size, a Planck-like CMB survey can marginally detect the kSZ signal by stacking the same number of galaxies at $z<0.1$. The search for the CGM in realistic surveys will involve dividing the galaxies into subsamples with similar redshift and mass of host halos, and scaling the results presented here to obtain the S/N.

Properties of resonantly produced sterile neutrino dark matter subhaloes

The anomalous 3.55 keV X-ray line recently detected towards a number of massive dark matter objects may be interpreted as the radiative decays of 7.1 keV mass sterile neutrino dark matter. Depending on its parameters, the sterile neutrino can range from cold to warm dark matter with small-scale suppression that differs in form from commonly-adopted thermal warm dark matter. Here, we numerically investigate the subhalo properties for 7.1 keV sterile neutrino dark matter produced via the resonant Shi-Fuller mechanism. Using accurate matter power spectra, we run cosmological zoom-in simulations of a Milky Way-sized halo and explore the abundance of massive subhalos, their radial distributions, and their internal structure. We also simulate the halo with thermal 2.0 keV warm dark matter for comparison and discuss quantitative differences. We find that the resonantly produced sterile neutrino model for the 3.55 keV line provides a good description of structures in the Local Group, including the number of satellite dwarf galaxies and their radial distribution, and largely mitigates the too-big-to-fail problem. Future searches for satellite galaxies by deep surveys, such as the Dark Energy Survey, Large Synoptic Survey Telescope, and Wide Field Infrared Survey Telescope, will be a strong direct test of warm dark matter scenarios.

REVERSAL OF FORTUNE: INCREASED STAR FORMATION EFFICIENCIES IN THE EARLY HISTORIES OF DWARF GALAXIES?

On dwarf galaxy scales, the different shapes of the galaxy stellar mass function and the dark halo mass function require a star-formation efficiency (SFE) in these systems that is currently more than 1 dex lower than that of Milky Way-size halos. Here, we argue that this trend may actually be reversed at high redshift. Specifically, by combining the resolved star-formation histories of nearby isolated dwarfs with the simulated mass-growth rates of dark matter halos, we show that the assembly of these systems occurs in two phases: (1) an early, fast halo accretion phase with a rapidly deepening potential well, characterized by a high SFE; and (2) a late slow halo accretion phase where, perhaps as a consequence of reionization, the SFE is low. Nearby dwarfs have more old stars than predicted by assuming a constant or decreasing SFE with redshift, a behavior that appears to deviate qualitatively from the trends seen amongst more massive systems. Taken at face value, the data suggest that, at sufficiently early epochs, dwarf galaxy halos above the atomic cooling mass limit can be among the most efficient sites of star formation in the universe.

Diffuse gas properties and stellar metallicities in cosmological simulations of disc galaxy formation

We analyse the properties of the circum-galactic medium and the metal content of the stars comprising the central galaxy in eight hydrodynamical `zoom-in' simulations of disc galaxy formation. We use these properties as a benchmark for our model of galaxy formation physics implemented in the moving-mesh code AREPO, which succeeds in forming quite realistic late-type spirals in the set of `Aquarius' initial conditions of Milky Way-sized haloes. Galactic winds significantly influence the morphology of the circum-galactic medium and induce bipolar features in the distribution of heavy elements. They also affect the thermodynamic properties of the circum-galactic gas by supplying an energy input that sustains its radiative losses. Although a significant fraction of the heavy elements are transferred from the central galaxy to the halo, and even beyond the virial radius, enough metals are retained by stars to yield a peak in their metallicity distributions at about $Z_{\odot}$. All our default runs overestimate the stellar [O/Fe] ratio, an effect that we demonstrate can be rectified by an increase of the adopted SN type Ia rate. Nevertheless, the models have difficulty in producing stellar metallicity gradients of the same strength as observed in the Milky Way.

The formation of disc galaxies in high-resolution moving-mesh cosmological simulations

We present cosmological hydrodynamical simulations of eight Milky Way-sized haloes that have been previously studied with dark matter only in the Aquarius project. For the first time, we employ the moving-mesh code AREPO in zoom simulations combined with a comprehensive model for galaxy formation physics designed for large0 cosmological simulations. Our simulations form in most of the eight haloes strongly disc-dominated systems with realistic rotation curves, close to exponential surface density profiles, a stellar-mass to halo-mass ratio that matches expectations from abundance matching techniques, and galaxy sizes and ages consistent with expectations from large galaxy surveys in the local Universe. There is no evidence for any dark matter core formation in our simulations, even so they include repeated baryonic outflows by supernova-driven winds and black hole quasar feedback. For one of our haloes, the object studied in the recent `Aquila' code comparison project, we carried out a resolution study with our techniques, covering a dynamic range of 64 in mass resolution. Without any change in our feedback parameters, the final galaxy properties are reassuringly similar, in contrast to other modelling techniques used in the field that are inherently resolution dependent. This success in producing realistic disc galaxies is reached, in the context of our interstellar medium treatment, without resorting to a high density threshold for star formation, a low star formation efficiency, or early stellar feedback, factors deemed crucial for disc formation by other recent numerical studies.

Structure of dark matter halos in warm dark matter models and in models with long-lived charged massive particles

We study the formation of non-linear structures in warm dark matter (WDM) modelsand in a long-lived charged massive particle (CHAMP) model.CHAMPs with a decay lifetime of about 1 yr induce characteristic suppression in the matter power spectrum at subgalactic scales through acoustic oscillations in the thermal background. We explore structure formation in such a model.We also study three WDM models, where the dark matter particles are producedthrough the following mechanisms:i) WDM particles are produced in the thermal background and then kinematically decoupled; ii) WDM particles are fermions produced by the decay of thermal heavy bosons; and iii) WDM particles are produced by the decay of non-relativistic heavy particles.We show that the linear matter power spectra for the three models are all characterised by the comoving Jeans scale at the matter-radiation equality.Furthermore, we can also describe the linear matter power spectrum for the long-lived CHAMP model in terms of a suitably defined characteristic cut-off scale kCh,similarly to the WDM models.We perform large cosmological N-body simulations to study the non-lineargrowth of structures in these four models.We compare the halo mass functions, the subhalo mass functions, and the radial distributions of subhalos in simulated Milky Way-size halos.For the characteristic cut-off scale kcut = 51 h Mpc−1, the subhalo abundance ( ∼ 109Msun) is suppressed by a factor of ∼ 10 compared with the standard ΛCDM model. We then study the models with kcut ≃ 51, 410, 820 h Mpc−1,and confirm that the halo and the subhalo abundances and the radial distributionsof subhalos are indeed similar between the different WDM models and the long-lived CHAMP model.The result suggests that the cut-off scale kcut not only characterises the linearpower spectra but also can be used to predict the non-linear clustering properties.The radial distribution of subhalos in Milky Way-size halos isconsistent with the observed distribution for kcut ∼ 50−800 h Mpc−1; such models resolve the so-called ``missing satellite problem".

Bailing out the Milky Way: variation in the properties of massive dwarfs among galaxy-sized systems

Recent kinematical constraints on the internal densities of the Milky Way's dwarf satellites have revealed a discrepancy with the subhalo populations of simulated Galaxy-scale halos in the standard cold dark matter model of hierarchical structure formation. In particular, the Via Lactea II and Aquarius simulations both have large subhalos with internal densities that are larger than the constraints inferred for any Milky Way dwarf satellites. This has been dubbed the ``too big to fail'' problem, with reference to the improbability of large and invisible companions existing in the Galactic environment.In this paper, we argue that both the Milky Way observations and simulated subhalos are consistent with the predictions of the standard model for structure formation. Specifically, we show that there is significant variation in the properties of subhalos among distinct host halos of fixed mass and suggest that this can reasonably account for the deficit of dense satellites in the Milky Way. We exploit well-tested analytic techniques to predict the properties in a large sample of distinct host halos with a variety of masses spanning the range expected of the Galactic halo. Such techniques render the problem of estimating the variance in subhalo properties computationally feasible. The analytic model produces subhalo populations consistent with both Via Lactea II and Aquarius, and our results suggest that natural variation in subhalo properties suffices to explain the discrepancy between Milky Way satellite kinematics and these numerical simulations. At least ∼ 10% of Milky Way-sized halos host subhalo populations for which there is no ``too big to fail'' problem, even when the host halo mass is as large as Mhost = 1012.2 h−1 M⊙. Follow-up studies consisting of high-resolution simulations of a large number of Milky Way-sized hosts are necessary to confirm our predictions. In the absence of such efforts, the ``too big to fail'' problem does not appear to be a significant challenge to the standard model of cold dark matter halos undergoing hierarchical formation.