arXiv subjects

Federico Marinacci

Publications and source records attributed to Federico Marinacci.

At least 181 records · Page 10Linked to original sources

arXiv2019

Atomic and molecular gas in IllustrisTNG galaxies at low redshift

We have recently developed a post-processing framework to estimate the abundance of atomic and molecular hydrogen (HI and H2, respectively) in galaxies in large-volume cosmological simulations. Here we compare the HI and H2 content of IllustrisTNG galaxies to observations. We mostly restrict this comparison to $z \approx 0$ and consider six observational metrics: the overall abundance of HI and H2, their mass functions, gas fractions as a function of stellar mass, the correlation between H2 and star formation rate, the spatial distribution of gas, and the correlation between gas content and morphology. We find generally good agreement between simulations and observations, particularly for the gas fractions and the HI mass-size relation. The H2 mass correlates with star formation rate as expected, revealing an almost constant depletion time that evolves up to z = 2 as observed. However, we also discover a number of tensions with varying degrees of significance, including an overestimate of the total neutral gas abundance at z = 0 by about a factor of two and a possible excess of satellites with no or very little neutral gas. These conclusions are robust to the modelling of the HI/H2 transition. In terms of their neutral gas properties, the IllustrisTNG simulations represent an enormous improvement over the original Illustris run. All data used in this paper are publicly available as part of the IllustrisTNG data release.

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arXiv2019

On the correlation between the local dark matter and stellar velocities

The dark matter velocity distribution in the Solar neighbourhood is an important astrophysical input which enters in the predicted event rate of dark matter direct detection experiments. It has been recently suggested that the local dark matter velocity distribution can be inferred from that of old or metal-poor stars in the Milky Way. We investigate this potential relation using six high resolution magneto-hydrodynamical simulations of Milky Way-like galaxies of the Auriga project. We do not find any correlation between the velocity distributions of dark matter and old stars in the Solar neighbourhood. Likewise, there are no strong correlations between the local velocity distributions of dark matter and metal-poor stars selected by applying reasonable cuts on metallicity. In some simulated galaxies, extremely metal-poor stars have a velocity distribution that is statistically consistent with that of the dark matter, but the sample of such stars is so small that we cannot draw any strong conclusions.

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arXiv2019

The effects of dynamical substructure on Milky Way mass estimates from the high velocity tail of the local stellar halo

We investigate the impact of dynamical streams and substructure on estimates of the local escape speed and total mass of Milky Way-mass galaxies from modelling the high velocity tail of local halo stars. We use a suite of high-resolution, magneto-hydrodynamical cosmological zoom-in simulations, which resolve phase space substructure in local volumes around solar-like positions. We show that phase space structure varies significantly between positions in individual galaxies and across the suite. Substructure populates the high velocity tail unevenly and leads to discrepancies in the mass estimates. We show that a combination of streams, sample noise and truncation of the high velocity tail below the escape speed leads to a distribution of mass estimates with a median that falls below the true value by $\sim 20 \%$, and a spread of a factor of 2 across the suite. Correcting for these biases, we derive a revised value for the Milky Way mass presented in Deason et al. of $1.29 ^{+0.37}_{-0.47} \times 10^{12}$ $\rm M_{\odot}$.

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arXiv2019

No cores in dark matter-dominated dwarf galaxies with bursty star formation histories

Measurements of the rotation curves of dwarf galaxies are often interpreted as requiring a constant density core at the centre, at odds with the "cuspy" inner profiles predicted by $N$-body simulations of cold dark matter (CDM) haloes. It has been suggested that this conflict could be resolved by fluctuations in the inner gravitational potential caused by the periodic removal of gas following bursts of star formation. Earlier work has suggested that core formation requires a bursty and extended star formation history (SFH). Here we investigate the structure of CDM haloes of dwarf galaxies ($M_{\rm DM} \sim 10^9-5\times10^{10}\,{\rm M}_\odot$) formed in the APOSTLE ('A Project of Simulating the Local Environment') and AURIGA cosmological hydrodynamic simulations. Our simulations have comparable or better resolution than others that make cores ($M_{\rm gas} \sim 10^4\,{\rm M}_\odot$, gravitational softening $\sim 150$ pc). Yet, we do not find evidence of core formation at {\it any} mass or any correlation between the inner slope of the DM density profile and temporal variations in the SFH. APOSTLE and AURIGA dwarfs display a similar diversity in their cumulative SFHs to available data for Local Group dwarfs. Dwarfs in both simulations are DM-dominated on all resolved scales at all times, likely limiting the ability of gas outflows to alter significantly the central density profiles of their haloes. We conclude that recurrent bursts of star formation are not sufficient to cause the formation of cores, and that other conditions must also be met for baryons to be able to modify the central DM cusp.

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arXiv2019

A study of stellar orbit fractions: simulated IllustrisTNG galaxies compared to CALIFA observations

Motivated by the recently discovered kinematic "Hubble sequence" shown by the stellar orbit-circularity distribution of 260 CALIFA galaxies, we make use of a comparable galaxy sample at z = 0 with a stellar mass range from 5E9 to 5E11 solar masses, selected from the IllustrisTNG simulation and study their stellar orbit compositions in relation to a number of other fundamental galaxy properties.We find that the TNG100 simulation broadly reproduces the observed fractions of different orbital components and their stellar mass dependencies. In particular, the mean mass dependencies of the luminosity fractions for the kinematically warm and hot orbits are well reproduced within model uncertainties of the observed galaxies. The simulation also largely reproduces the observed peak and trough features at a stellar mass of 1-2E10 solar masses, in the mean distributions of the cold- and hot-orbit fractions, respectively, indicating fewer cooler orbits and more hotter orbits in both more- and less-massive galaxies beyond such a mass range. Several marginal disagreements are seen between the simulation and observations: the average cold-orbit (counter-rotating) fractions of the simulated galaxies below (above) a stellar mass of 6E10 solar masses, are systematically higher than the observational data by < 10% (absolute orbital fraction); the simulation also seems to produce more scatter for the cold-orbit fraction and less so for the non-cold orbits at any given galaxy mass. Possible causes that stem from the adopted heating mechanisms are discussed.

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arXiv2019

The Supersonic Project: Shining Light on SIGOs - a New Formation Channel for Globular Clusters

Supersonically induced gas objects (SIGOs) with little to no dark matter component are predicted to exist in patches of the Universe with non-negligible relative velocity between baryons and the dark matter at the time of recombination. Using {\sc arepo} hydrodynamic simulations we find that the gas densities inside these objects are high enough to allow stars to form. An estimate of the luminosity of the first star clusters formed within these SIGOs suggests that they may be observed at high redshift using future HST and JWST observations. Furthermore, our simulations indicate that SIGOs lie in a distinct place in the luminosity-radius parameter space, which can be used observationally to distinguish SIGOs from dark-matter hosting gas systems. Finally, as a proof-of-concept, we model star formation before reionization and evolve these systems to current times. We find that SIGOs occupy a similar part of the magnitude-radius parameter space as globular clusters. These results suggest that SIGOs may be linked with present-day metal-poor local globular clusters. Since the relative velocity between the baryons and dark matter is coherent over a few Mpc scales, we predict that if this is the dominant mechanism for the formation of globular clusters, their abundance should vary significantly over these scales.

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arXiv2019

Revealing the galaxy-halo connection in IllustrisTNG

We use the IllustrisTNG (TNG) simulations to explore the galaxy-halo connection as inferred from state-of-the-art cosmological, magnetohydrodynamical simulations. With the high mass resolution and large volume achieved by combining the 100 Mpc (TNG100) and 300 Mpc (TNG300) volumes, we establish the mean occupancy of central and satellite galaxies and their dependence on the properties of the dark matter haloes hosting them. We derive best-fitting HOD parameters from TNG100 and TNG300 for target galaxy number densities of $\bar{n}_g = 0.032\,h^3$Mpc$^{-3}$ and $\bar{n}_g = 0.016\,h^3$Mpc$^{-3}$, respectively, corresponding to a minimum galaxy stellar mass of $M_\star\sim1.9\times10^9\,{\rm M}_\odot$ and $M_\star\sim3.5\times10^9\,{\rm M}_\odot$, respectively, in hosts more massive than $10^{11}\,{\rm M}_\odot$. Consistent with previous work, we find that haloes located in dense environments, with low concentrations, later formation times, and high angular momenta are richest in their satellite population. At low mass, highly-concentrated haloes and those located in overdense regions are more likely to contain a central galaxy. The degree of environmental dependence is sensitive to the definition adopted for the physical boundary of the host halo. We examine the extent to which correlations between galaxy occupancy and halo properties are independent and demonstrate that HODs predicted by halo mass and present-day concentration capture the qualitative dependence on the remaining halo properties. At fixed halo mass, concentration is a strong predictor of the stellar mass of the central galaxy, which may play a defining role in the fate of the satellite population. The radial distribution of satellite galaxies, which exhibits a universal form across a wide range of host halo mass, is described accurately by the best-fit NFW density profile of their host haloes.

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arXiv2019

Disruption of giant molecular clouds and formation of bound star clusters under the influence of momentum stellar feedback

Energetic feedback from star clusters plays a pivotal role in shaping the dynamical evolution of giant molecular clouds (GMCs). To study the effects of stellar feedback on the star formation efficiency of the clouds and the dynamical response of embedded star clusters, we perform a suite of isolated GMC simulations with star formation and momentum feedback subgrid models using the moving-mesh hydrodynamics code \textsc{Arepo}. The properties of our simulated GMCs span a wide range of initial mass, radius, and velocity configurations. We find that the ratio of the final stellar mass to the total cloud mass, $ε_{\rm int}$, scales strongly with the initial cloud surface density and momentum feedback strength. This correlation is explained by an analytic model that considers force balancing between gravity and momentum feedback. For all simulated GMCs, the stellar density profiles are systematically steeper than that of the gas at the epochs of the peaks of star formation, suggesting a centrally concentrated stellar distribution. We also find that star clusters are always in a sub-virial state with a virial parameter $\sim0.6$ prior to gas expulsion. Both the sub-virial dynamical state and steeper stellar density profiles prevent clusters from dispersal during the gas removal phase of their evolution. The final cluster bound fraction is a continuously increasing function of $ε_{\rm int}$. GMCs with star formation efficiency smaller than 0.5 are still able to form clusters with large bound fractions.

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arXiv2019

Baryons in the CosmicWeb of IllustrisTNG - I: Gas in Knots, Filaments, Sheets and Voids

We analyze the IllustrisTNG simulations to study the mass, volume fraction and phase distribution of gaseous baryons embedded in the knots, filaments, sheets and voids of the Cosmic Web from redshift $z=8$ to redshift $z=0$. We find that filaments host more star-forming gas than knots, and that filaments also have a higher relative mass fraction of gas in this phase than knots. We also show that the cool, diffuse Intergalactic Medium (IGM; $T<10^5 \, {\rm K}$, $ n_{\rm H}<10^{-4}(1+z) \, {\rm cm^{-3}}$) and the Warm-Hot Intergalactic Medium (WHIM; $ 10^5 \, {\rm K} <T<10^7 \, {\rm K}$, $ n_{\rm H} <10^{-4}(1+z)\, {\rm cm^{-3}}$) constitute $\sim 39\%$ and $\sim 46\%$ of the baryons at redshift $z=0$, respectively. Our results indicate that the WHIM may constitute the largest reservoir of {\it missing} baryons at redshift $z=0$. Using our Cosmic Web classification, we predict the WHIM to be the dominant baryon mass contribution in filaments and knots at redshift $z=0$, but not in sheets and voids where the cool, diffuse IGM dominates. We also characterise the evolution of WHIM and IGM from redshift $z=4$ to redshift $z=0$, and find that the mass fraction of WHIM in filaments and knots evolves only by a factor $\sim 2$ from redshift $z=0$ to $z=1$, but declines faster at higher redshift. The WHIM only occupies $4-11\%$ of the volume at redshift $0\leq z \leq 1$. We predict the existence of a significant number of currently undetected OVII and NeIX absorption systems in cosmic filaments which could be detected by future X-ray telescopes like Athena.

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arXiv2019

High redshift JWST predictions from IllustrisTNG: Dust modelling and galaxy luminosity functions

The James Webb Space Telescop (JWST) promises to revolutionise our understanding of the early Universe, and contrasting its upcoming observations with predictions of the $Λ$CDM model requires detailed theoretical forecasts. Here, we exploit the large dynamic range of the IllustrisTNG simulation suite, TNG50, TNG100, and TNG300, to derive multi-band galaxy luminosity functions from $z=2$ to $z=10$. We put particular emphasis on the exploration of different dust attenuation models to determine galaxy luminosity functions for the rest-frame ultraviolet (UV), and apparent wide NIRCam bands. Our most detailed dust model is based on continuum Monte Carlo radiative transfer calculations employing observationally calibrated dust properties. This calibration results in constraints on the redshift evolution of the dust attenuation normalisation and dust-to-metal ratios yielding a stronger redshift evolution of the attenuation normalisation compared to most previous theoretical studies. Overall we find good agreement between the rest-frame UV luminosity functions and observational data for all redshifts, also beyond the regimes used for the dust-model calibrations. Furthermore, we also recover the observed high redshift ($z=4-6$) UV luminosity versus stellar mass relation, the H$α$ versus star formation rate relation, and the H$α$ luminosity function at $z=2$. The bright end ($M_{\rm UV}>-19.5$) cumulative galaxy number densities are consistent with observational data. For the F200W NIRCam band, we predict that JWST will detect $\sim 80$ ($\sim 200$) galaxies with a signal-to-noise ratio of $10$ ($\sim 5$) within the NIRCam field of view, $2.2\times2.2 \,{\rm arcmin}^{2}$, for a total exposure time of $10^5{\rm s}$ in the redshift range $z=8 \pm 0.5$. These numbers drop to $\sim 10$ ($\sim 40$) for an exposure time of $10^4{\rm s}$.

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arXiv2019

The morphology and kinematics of the gaseous circumgalactic medium of Milky Way mass galaxies -- II. comparison of IllustrisTNG and Illustris simulation results

We have carried out a controlled comparison of the structural and kinematic properties of the circumgalactic medium (CGM) around Milky Way mass galaxies in the Illustris and IllustrisTNG simulations. Very striking differences are found. At z=0, gas column density and temperature profiles at large radii ($\sim 100$ kpc) correlate strongly with disk gas mass fraction in Illustris, but not in TNG. The neutral gas at large radii is preferentially aligned in the plane of the disk in TNG, whereas it is much more isotropic in Illustris. The vertical coherence scale of the rotationally supported gas in the CGM is linked to the gas mass fraction of the galaxy in Illustris, but not in TNG. A tracer particle analysis allows us to show how these differences can be understood as a consequence of the different sub-grid models of feedback in the two simulations. A study of spatially matched galaxies in the two simulations shows that in TNG, feedback by supernovae and AGN helps to create an extended smooth reservoir of hot gas at high redshifts, that then cools to form a thin, rotationally-supported disk at later times. In Illustris, AGN dump heat in the form of hot gas bubbles that push diffuse material at large radii out of the halo. The disk is formed by accretion of colder, recycled material, and this results in more vertically extended gas distributions above and below the Galactic plane. We conclude that variations in the structure of gas around Milky Way mass galaxies are a sensitive probe of feedback physics in simulations and are worthy of more observational consideration in future.

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arXiv2019

The ALMA Spectroscopic Survey in the HUDF: the molecular gas content of galaxies and tensions with IllustrisTNG and the Santa Cruz SAM

The ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS) provides new constraints for galaxy formation models on the molecular gas properties of galaxies. We compare results from ASPECS to predictions from two cosmological galaxy formation models: the IllustrisTNG hydrodynamical simulations and the Santa Cruz semi-analytic model (SC SAM). We explore several recipes to model the H$_2$ content of galaxies, finding them to be consistent with one another, and take into account the sensitivity limits and survey area of ASPECS. For a canonical CO-to-H$_2$ conversion factor of $α_{\rm CO} = 3.6\,\rm{M}_\odot/(\rm{K}\,\rm{km/s}\,\rm{pc}^{2})$ the results of our work include: (1) the H$_2$ mass of $z>1$ galaxies predicted by the models as a function of their stellar mass is a factor of 2-3 lower than observed; (2) the models do not reproduce the number of H$_2$-rich ($M_{\rm H2} > 3\times 10^{10}\,\rm{M}_\odot$) galaxies observed by ASPECS; (3) the H$_2$ cosmic density evolution predicted by IllustrisTNG (the SC SAM) is in tension (only just agrees) with the observed cosmic density, even after accounting for the ASPECS selection function and field-to-field variance effects. The tension between models and observations at $z>1$ can be alleviated by adopting a CO-to-H$_2$ conversion factor in the range $α_{\rm CO} = 2.0 - 0.8\,\rm{M}_\odot/(\rm{K}\,\rm{km/s}\,\rm{pc}^{2})$. Additional work on constraining the CO-to-H$_2$ conversion factor and CO excitation conditions of galaxies through observations and theory will be necessary to more robustly test the success of galaxy formation models.

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arXiv2019

The star-formation activity of IllustrisTNG galaxies: main sequence, UVJ diagram, quenched fractions, and systematics

We select galaxies from the IllustrisTNG hydrodynamical simulations ($M_*>10^9~\rm M_\odot$ at $0\le z\le2$) and characterize the shapes and evolutions of their UVJ and star-formation rate -- stellar mass (SFR-$M_*$) diagrams. We quantify the systematic uncertainties related to different criteria to classify star-forming vs. quiescent galaxies, different SFR estimates, and by accounting for the star formation measured within different physical apertures. The TNG model returns the observed features of the UVJ diagram at $z\leq2$, with a clear separation between two classes of galaxies. It also returns a tight star-forming main sequence (MS) for $M_*<10^{10.5}\,\rm M_\odot$ with a $\sim0.3$ dex scatter at $z\sim0$ in our fiducial choices. If a UVJ-based cut is adopted, the TNG MS exhibits a downwardly bending at stellar masses of about $10^{10.5-10.7}~\rm M_\odot$. Moreover, the model predicts that $\sim80\,(50)$ per cent of $10^{10.5-11}~\rm M_\odot$ galaxies at $z=0~(z=2)$ are quiescent and the numbers of quenched galaxies at intermediate redshifts and high masses are in better agreement with observational estimates than previous models. However, shorter SFR-averaging timescales imply higher normalizations and scatter of the MS, while smaller apertures lead to underestimating the galaxy SFRs: overall we estimate the inspected systematic uncertainties to sum up to about $0.2-0.3$ dex in the locus of the MS and to about 15 percentage points in the quenched fractions. While TNG color distributions are clearly bimodal, this is not the case for the SFR logarithmic distributions in bins of stellar mass (SFR$\geq 10^{-3}~\rm M_\odot$yr$^{-1}$). Finally, the slope and $z=0$ normalization of the TNG MS are consistent with observational findings; however, the locus of the TNG MS remains lower by about $0.2-0.5$ dex at $0.75\le z<2$ than the available observational estimates taken at face value.

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arXiv2019

The local high velocity tail and the Galactic escape speed

We model the fastest moving (v_tot > 300 km/s) local (D < 3 kpc) halo stars using cosmological simulations and 6-dimensional Gaia data. Our approach is to use our knowledge of the assembly history and phase-space distribution of halo stars to constrain the form of the high velocity tail of the stellar halo. Using simple analytical models and cosmological simulations, we find that the shape of the high velocity tail is strongly dependent on the velocity anisotropy and number density profile of the halo stars --- highly eccentric orbits and/or shallow density profiles have more extended high velocity tails. The halo stars in the solar vicinity are known to have a strongly radial velocity anisotropy, and it has recently been shown the origin of these highly eccentric orbits is the early accretion of a massive (M_star ~ 10^9 M_Sun) dwarf satellite. We use this knowledge to construct a prior on the shape of the high velocity tail. Moreover, we use the simulations to define an appropriate outer boundary of 2r_200, beyond which stars can escape. After applying our methodology to the Gaia data, we find a local (r_0=8.3 kpc) escape speed of v_esc(r_0) = 528(+24,-25) km/s. We use our measurement of the escape velocity to estimate the total Milky Way mass, and dark halo concentration: M_200,tot = 1.00(+0.31,-0.24) x 10^12 M_Sun, c_200 = 10.9(+4.4,-3.3). Our estimated mass agrees with recent results in the literature that seem to be converging on a Milky Way mass of M_200,tot ~ 10^12 M_Sun.

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arXiv2019

The Auriga Stellar Haloes: Connecting stellar population properties with accretion and merging history

We examine the stellar haloes of the Auriga simulations, a suite of thirty cosmological magneto-hydrodynamical high-resolution simulations of Milky Way-mass galaxies performed with the moving-mesh code AREPO. We study halo global properties and radial profiles out to $\sim 150$ kpc for each individual galaxy. The Auriga haloes are diverse in their masses and density profiles; mean metallicity and metallicity gradients; ages; and shapes, reflecting the stochasticity inherent in their accretion and merger histories. A comparison with observations of nearby late-type galaxies shows very good agreement between most observed and simulated halo properties. However, Auriga haloes are typically too massive. We find a connection between population gradients and mass assembly history: galaxies with few significant progenitors have more massive haloes, possess large negative halo metallicity gradients and steeper density profiles. The number of accreted galaxies, either disrupted or under disruption, that contribute 90% of the accreted halo mass ranges from 1 to 14, with a median of 6.5, and their stellar masses span over three orders of magnitude. The observed halo mass--metallicity relation is well reproduced by Auriga and is set by the stellar mass and metallicity of the dominant satellite contributors. This relationship is found not only for the accreted component but also for the total (accreted + in-situ) stellar halo. Our results highlight the potential of observable halo properties to infer the assembly history of galaxies.

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arXiv2019

AREPO-RT: Radiation hydrodynamics on a moving mesh

We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the unstructured moving-mesh code AREPO. Our method solves the moment-based radiative transfer equations using the M1 closure relation. We achieve second order convergence by using a slope limited linear spatial extrapolation and a first order time prediction step to obtain the values of the primitive variables on both sides of the cell interface. A Harten-Lax-Van Leer flux function, suitably modified for moving meshes, is then used to solve the Riemann problem at the interface. The implementation is fully conservative and compatible with the individual timestepping scheme of AREPO. It incorporates atomic Hydrogen (H) and Helium (He) thermochemistry, which is used to couple the ultra-violet (UV) radiation field to the gas. Additionally, infrared radiation is coupled to the gas under the assumption of local thermodynamic equilibrium between the gas and the dust. We successfully apply our code to a large number of test problems, including applications such as the expansion of ${\rm H_{II}}$ regions, radiation pressure driven outflows and the levitation of optically thick layer of gas by trapped IR radiation. The new implementation is suitable for studying various important astrophysical phenomena, such as the effect of radiative feedback in driving galactic scale outflows, radiation driven dusty winds in high redshift quasars, or simulating the reionisation history of the Universe in a self consistent manner.

astro-ph.IM↗

arXiv2019

The interplay of Self-Interacting Dark Matter and baryons in shaping the halo evolution

We use high-resolution hydrodynamical simulation to test the difference of halo properties in cold dark matter (CDM) and a self-interacting dark matter (SIDM) scenario with a constant cross-section of $σ^\text{T}/m_χ=1\;\text{cm}^{2}\text{g}^{-1}$. We find that the interplay between dark matter self-interaction and baryonic physics induces a complex evolution of the halo properties, which depends on the halo mass and morphological type, as well as on the halo mass accretion history. While high mass haloes, selected as analogues of early-type galaxies, show cored profiles in the SIDM run, systems of intermediate mass and with a significant disk component can develop a profile that is similar or cuspier than in CDM. The final properties of SIDM haloes - measured at z=0.2 - correlate with the halo concentration and formation time, suggesting that the differences between different systems are due to the fact that we are observing the impact self-interaction. We also search for signatures of self-interacting dark matter in the lensing signal of the main haloes and hints of potential differences in the distribution of Einstein radii, which suggests that future wide-field survey might be able to distinguish between CDM and SIDM models on this basis. Finally, we find that the subhalo abundances are not altered in the adopted SIDM model with respect to CDM.

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arXiv2019

The mass of the Milky Way from satellite dynamics

We present and apply a method to infer the mass of the Milky Way (MW) by comparing the dynamics of MW satellites to those of model satellites in the EAGLE cosmological hydrodynamics simulations. A distribution function (DF) for galactic satellites is constructed from EAGLE using specific angular momentum and specific energy, which are scaled so as to be independent of host halo mass. In this 2-dimensional space, the orbital properties of satellite galaxies vary according to the host halo mass. The halo mass can be inferred by calculating the likelihood that the observed satellite population is drawn from this DF. Our method is robustly calibrated on mock EAGLE systems. We validate it by applying it to the completely independent suite of 30 AURIGA high-resolution simulations of MW-like galaxies: the method accurately recovers their true mass and associated uncertainties. We then apply it to ten classical satellites of the MW with 6D phase-space measurements, including updated proper motions from the GAIA satellite. The mass of the MW is estimated to be $M_{200}^{\textnormal{MW}}=1.17_{-0.15}^{+0.21}\times10^{12}M_{\odot}$ (68\% confidence limits). We combine our total mass estimate with recent mass estimates in the inner regions of the Galaxy to infer an inner dark matter (DM) mass fraction $M^\textnormal{DM}(<20~\rm{kpc})/M^\textnormal{DM}_{200}=0.12$ which is typical of ${\sim}10^{12}M_{\odot}$ $Λ$CDM haloes in hydrodynamical galaxy formation simulations. Assuming an NFW profile, this is equivalent to a halo concentration of $c_{200}^{\textnormal{MW}}=10.9^{+2.6}_{-2.0}$.

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