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The formation and evolution of stellar clusters is intimately linked to that of their host galaxies. To study this connection, we present the EMP-Pathfinder suite of cosmological zoom-in Milky Way-mass simulations. These simulations contain a sub-grid description for stellar cluster formation and evolution, allowing us to study the simultaneous formation and evolution of stellar clusters alongside their host galaxies across cosmic time. As a key ingredient in these simulations, we include the physics of the multi-phase nature of the interstellar medium (ISM), which enables studies of how the presence of a cold, dense ISM affects cluster formation and evolution. We consider two different star formation prescriptions: a constant star formation efficiency per free-fall time, as well as an environmentally-dependent, turbulence-based prescription. We identify two key results drawn from these simulations. Firstly, we find that tidal shock-driven disruption caused by the graininess of the cold ISM produces old ($\tau>10~$Gyr) stellar cluster populations with properties that are in excellent agreement with the observed populations in the Milky Way and M31. Importantly, the addition of the cold ISM addresses the areas of disagreement found in previous simulations that lacked the cold gas phase. Secondly, the formation of stellar clusters is extremely sensitive to the baryonic physics that govern the properties of the cold, dense gas reservoir in the galaxy. This implies that the demographics of stellar cluster populations represent an important diagnostic tool for constraining baryonic physics models in upcoming galaxy formation simulations that also include a description of the cold ISM., Comment: 30 pages + appendices, 12 figures. MNRAS submitted, comments and suggestions welcome!

We explore how diffuse stellar light and globular clusters (GCs) can be used to trace the matter distribution of their host halo using an observational methodology. For this, we use 117 simulated dark matter (DM) haloes from the $(34.4~\rm cMpc)^3$ periodic volume of the E-MOSAICS project. For each halo, we compare the stellar surface brightness and GC projected number density maps to the surface densities of DM and total mass. We find that the dominant structures identified in the stellar light and in the GCs correspond closely with those from the DM and total mass. Our method is unaffected by the presence of satellites and its precision improves with fainter GC samples. We recover tight relations between the profiles of stellar surface brightness and GC number density to those of the DM, suggesting that the profile of DM can be accurately recovered from the stars and GCs ($\sigma\leq0.5~$dex). We quantify the projected morphology of DM, stars and GCs, and find that the stars and GCs are more flattened than the DM. Additionally, the semi-major axes of the distribution of stars and GCs are typically misaligned by $\sim 10~$degrees from that of DM. We demonstrate that deep imaging of diffuse stellar light and GCs can place constraints on the shape, profile and orientation of their host halo. These results extend down to haloes with central galaxies $M_{\star}\geq10^{10}~M_{\odot}$, and the analysis will be applicable to future data from the Euclid, Roman and the Rubin observatories., Comment: 17 pages, 15 figures; submitted to MNRAS (25/04/2022) - comments and suggestions welcome!

The formation and evolution of stellar clusters is intimately linked to that of their host galaxies. To study this connection, we present the EMP-Pathfinder suite of cosmological zoom-in Milky Way-mass simulations. These simulations contain a sub-grid description for stellar cluster formation and evolution, allowing us to study the simultaneous formation and evolution of stellar clusters alongside their host galaxies across cosmic time. As a key ingredient in these simulations, we include the physics of the multi-phase nature of the interstellar medium (ISM), which enables studies of how the presence of a cold, dense ISM affects cluster formation and evolution. We consider two different star formation prescriptions: a constant star formation efficiency per free-fall time, as well as an environmentally-dependent, turbulence-based prescription. We identify two key results drawn from these simulations. Firstly, we find that tidal shock-driven disruption caused by the graininess of the cold ISM produces old ($\tau>10~$Gyr) stellar cluster populations with properties that are in excellent agreement with the observed populations in the Milky Way and M31. Importantly, the addition of the cold ISM addresses the areas of disagreement found in previous simulations that lacked the cold gas phase. Secondly, the formation of stellar clusters is extremely sensitive to the baryonic physics that govern the properties of the cold, dense gas reservoir in the galaxy. This implies that the demographics of stellar cluster populations represent an important diagnostic tool for constraining baryonic physics models in upcoming galaxy formation simulations that also include a description of the cold ISM., Comment: 30 pages + appendices, 12 figures. MNRAS submitted, comments and suggestions welcome!

The mass function of globular cluster (GC) populations is a fundamental observable that encodes the physical conditions under which these massive stellar clusters formed and evolved. The high-mass end of star cluster mass functions are commonly described using a Schechter function, with an exponential truncation mass $M_{c,*}$. For the GC mass functions in the Virgo galaxy cluster, this truncation mass increases with galaxy mass ($M_{*}$). In this paper we fit Schechter mass functions to the GCs in the most massive galaxy group ($M_{\mathrm{200}} = 5.14 \times 10^{13} M_{\odot}$) in the E-MOSAICS simulations. The fiducial cluster formation model in E-MOSAICS reproduces the observed trend of $M_{c,*}$ with $M_{*}$ for the Virgo cluster. We therefore examine the origin of the relation by fitting $M_{c,*}$ as a function of galaxy mass, with and without accounting for mass loss by two-body relaxation, tidal shocks and/or dynamical friction. In the absence of these mass-loss mechanisms, the $M_{c,*}$-$M_{*}$ relation is flat above $M_* > 10^{10} M_{\odot}$. It is therefore the disruption of high-mass GCs in galaxies with $M_{*}\sim 10^{10} M_{\odot}$ that lowers the $M_{c,*}$ in these galaxies. High-mass GCs are able to survive in more massive galaxies, since there are more mergers to facilitate their redistribution to less-dense environments. The $M_{c,*}-M_*$ relation is therefore a consequence of both the formation conditions of massive star clusters and their environmentally-dependent disruption mechanisms., Comment: Accepted to MNRAS

We analyse the surface brightness profiles of disc-type galaxies in the EAGLE simulations in order to investigate the effects of galaxy mass and environment on galaxy profile types. Following observational works, we classify the simulated galaxies by their disc surface brightness profiles into single exponential (Type I), truncated (Type II) and anti-truncated (Type III) profiles. In agreement with previous observation and theoretical work, we find that Type II discs result from truncated star-forming discs that drive radial gradients in the stellar populations. In contrast, Type III profiles result from galaxy mergers, extended star-forming discs or the late formation of a steeper, inner disc. We find that the EAGLE simulations qualitatively reproduce the observed trends found between profile type frequency and galaxy mass, morphology and environment, such as the fraction of Type III galaxies increasing with galaxy mass, and the the fraction of Type II galaxies increasing with Hubble type. We investigate the lower incidence of Type II galaxies in galaxy clusters, finding, in a striking similarity to observed galaxies, that almost no S0-like galaxies in clusters have Type II profiles. Similarly, the fraction of Type II profiles for disc-dominated galaxies in clusters is significantly decreased relative to field galaxies. This difference between field and cluster galaxies is driven by star formation quenching. Following the cessation of star formation upon entering a galaxy cluster, the young stellar populations of Type II galaxies simply fade, leaving behind Type I galaxies., Comment: 11 pages, 10 figures. Accepted for publication in MNRAS

Globular clusters (GCs) are bright objects that span a wide range of galactocentric distances, and are thus probes of the structure of dark matter (DM) haloes. In this work, we explore whether the projected radial profiles of GCs can be used to infer the structural properties of their host DM haloes. We use the simulated GC populations in a sample of 166 central galaxies from the $(34.4~\rm cMpc)^3$ periodic volume of the E-MOSAICS project. We find that more massive galaxies host stellar and GC populations with shallower density profiles that are more radially extended. In addition, the metal-poor GC subpopulations tend to have shallower and more extended profiles than the metal-rich subsamples, which we relate to the preferentially accreted origin of the metal-poor GCs. We find strong correlations between the slopes and effective radii of the radial profiles of the GC populations and the structural properties of the DM haloes, such as their power-law slopes, scale radii, and concentration parameters. Accounting for a dependence on the galaxy stellar mass decreases the scatter of the two-dimensional relations. This suggests that the projected number counts of GCs, combined with their galaxy mass, trace the density profile of the DM halo of their host galaxy. When applied to extragalactic GC systems, we recover the scale radii and the extent of the DM haloes of a sample of ETGs with uncertainties smaller than $0.2~\rm dex$. Thus, extragalactic GC systems provide a novel avenue to explore the structure of DM haloes beyond the Local Group., Comment: 19 pages, 11 figures and 2 tables; submitted to MNRAS, comments and/or suggestions are welcomed!

The mass function of globular cluster (GC) populations is a fundamental observable that encodes the physical conditions under which these massive stellar clusters formed and evolved. The high-mass end of star cluster mass functions are commonly described using a Schechter function, with an exponential truncation mass $M_{c,*}$. For the GC mass functions in the Virgo galaxy cluster, this truncation mass increases with galaxy mass ($M_{*}$). In this paper we fit Schechter mass functions to the GCs in the most massive galaxy group ($M_{\mathrm{200}} = 5.14 \times 10^{13} M_{\odot}$) in the E-MOSAICS simulations. The fiducial cluster formation model in E-MOSAICS reproduces the observed trend of $M_{c,*}$ with $M_{*}$ for the Virgo cluster. We therefore examine the origin of the relation by fitting $M_{c,*}$ as a function of galaxy mass, with and without accounting for mass loss by two-body relaxation, tidal shocks and/or dynamical friction. In the absence of these mass-loss mechanisms, the $M_{c,*}$-$M_{*}$ relation is flat above $M_* > 10^{10} M_{\odot}$. It is therefore the disruption of high-mass GCs in galaxies with $M_{*}\sim 10^{10} M_{\odot}$ that lowers the $M_{c,*}$ in these galaxies. High-mass GCs are able to survive in more massive galaxies, since there are more mergers to facilitate their redistribution to less-dense environments. The $M_{c,*}-M_*$ relation is therefore a consequence of both the formation conditions of massive star clusters and their environmentally-dependent disruption mechanisms., Comment: Accepted to MNRAS

We analyse the surface brightness profiles of disc-type galaxies in the EAGLE simulations in order to investigate the effects of galaxy mass and environment on galaxy profile types. Following observational works, we classify the simulated galaxies by their disc surface brightness profiles into single exponential (Type I), truncated (Type II) and anti-truncated (Type III) profiles. In agreement with previous observation and theoretical work, we find that Type II discs result from truncated star-forming discs that drive radial gradients in the stellar populations. In contrast, Type III profiles result from galaxy mergers, extended star-forming discs or the late formation of a steeper, inner disc. We find that the EAGLE simulations qualitatively reproduce the observed trends found between profile type frequency and galaxy mass, morphology and environment, such as the fraction of Type III galaxies increasing with galaxy mass, and the the fraction of Type II galaxies increasing with Hubble type. We investigate the lower incidence of Type II galaxies in galaxy clusters, finding, in a striking similarity to observed galaxies, that almost no S0-like galaxies in clusters have Type II profiles. Similarly, the fraction of Type II profiles for disc-dominated galaxies in clusters is significantly decreased relative to field galaxies. This difference between field and cluster galaxies is driven by star formation quenching. Following the cessation of star formation upon entering a galaxy cluster, the young stellar populations of Type II galaxies simply fade, leaving behind Type I galaxies., Comment: 11 pages, 10 figures. Accepted for publication in MNRAS

Globular clusters (GCs) are bright objects that span a wide range of galactocentric distances, and are thus probes of the structure of dark matter (DM) haloes. In this work, we explore whether the projected radial profiles of GCs can be used to infer the structural properties of their host DM haloes. We use the simulated GC populations in a sample of 166 central galaxies from the $(34.4~\rm cMpc)^3$ periodic volume of the E-MOSAICS project. We find that more massive galaxies host stellar and GC populations with shallower density profiles that are more radially extended. In addition, the metal-poor GC subpopulations tend to have shallower and more extended profiles than the metal-rich subsamples, which we relate to the preferentially accreted origin of the metal-poor GCs. We find strong correlations between the slopes and effective radii of the radial profiles of the GC populations and the structural properties of the DM haloes, such as their power-law slopes, scale radii, and concentration parameters. Accounting for a dependence on the galaxy stellar mass decreases the scatter of the two-dimensional relations. This suggests that the projected number counts of GCs, combined with their galaxy mass, trace the density profile of the DM halo of their host galaxy. When applied to extragalactic GC systems, we recover the scale radii and the extent of the DM haloes of a sample of ETGs with uncertainties smaller than $0.2~\rm dex$. Thus, extragalactic GC systems provide a novel avenue to explore the structure of DM haloes beyond the Local Group., Comment: 19 pages, 11 figures and 2 tables; submitted to MNRAS, comments and/or suggestions are welcomed!

Dynamical models allow us to connect the motion of a set of tracers to the underlying gravitational potential, and thus to the total (luminous and dark) matter distribution. They are particularly useful for understanding the mass and spatial distribution of dark matter (DM) in a galaxy. Globular clusters (GCs) are an ideal tracer population in dynamical models, since they are bright and can be found far out into the halo of galaxies. We aim to test how well Jeans-Anisotropic-MGE (JAM) models using GCs (positions and line-of-sight velocities) as tracers can constrain the mass and radial distribution of DM halos. For this, we use the E-MOSAICS suite of 25 zoom-in simulations of L* galaxies. We find that the DM halo properties are reasonably well recovered by the JAM models. There is, however, a strong correlation between how well we recover the mass and the radial distribution of the DM and the number of GCs in the galaxy: the constraints get exponentially worse with fewer GCs, and at least 150 GCs are needed in order to guarantee that the JAM model will perform well. We find that while the data quality (uncertainty on the radial velocities) can be important, the number of GCs is the dominant factor in terms of the accuracy and precision of the measurements. This work shows promising results for these models to be used in extragalactic systems with a sample of more than 150 GCs., Comment: 18 pages, 13 figures. Accepted for publication in MNRAS

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using $z=0$ snapshots from the 100cMpc$^3$ and 25cMpc$^3$ EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2$\times$10$^{7}$ - 1.9$\times$10$^{12}$ M$_{\odot}$. For those galaxies of mass M$_*$>5$\times$10$^{8}$M$_{\odot}$, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be the result of high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies., Comment: 16 pages, 11 figures. Accepted for publication in MNRAS

Globular clusters (GCs) formed when the Milky Way experienced a phase of rapid assembly. We use the wealth of information contained in the Galactic GC population to quantify the properties of the satellite galaxies from which the Milky Way assembled. To achieve this, we train an artificial neural network on the E-MOSAICS cosmological simulations of the co-formation and co-evolution of GCs and their host galaxies. The network uses the ages, metallicities, and orbital properties of GCs that formed in the same progenitor galaxies to predict the stellar masses and accretion redshifts of these progenitors. We apply the network to Galactic GCs associated with five progenitors: {\it Gaia}-Enceladus, the Helmi streams, Sequoia, Sagittarius, and the recently discovered, `low-energy' GCs, which provide an excellent match to the predicted properties of the enigmatic galaxy `Kraken'. The five galaxies cover a narrow stellar mass range [$M_\star=(0.6{-}4.6)\times10^8~{\rm M}_\odot$], but have widely different accretion redshifts ($z_{\rm acc}=0.57{-}2.65$). All accretion events represent minor mergers, but Kraken likely represents the most major merger ever experienced by the Milky Way, with stellar and virial mass ratios of $r_{M_\star}=1$:$31^{+34}_{-16}$ and $r_{M_{\rm h}}=1$:$7^{+4}_{-2}$, respectively. The progenitors match the $z=0$ relation between GC number and halo virial mass, but have elevated specific frequencies, suggesting an evolution with redshift. Even though these progenitors likely were the Milky Way's most massive accretion events, they contributed a total mass of only $\log{(M_{\rm \star,tot}/{\rm M}_\odot)}=9.0\pm0.1$, similar to the stellar halo. This implies that the Milky Way grew its stellar mass mostly by in-situ star formation. We conclude by organising these accretion events into the most detailed reconstruction to date of the Milky Way's merger tree., Comment: 20 pages, 9 figures, 2 tables; submitted to MNRAS (March 1, 2020); Figures 4, 5, and 9 show the main results of the paper

The ages and metallicities of globular clusters (GCs) are known to be powerful tracers of the properties of their progenitor galaxies, enabling their use in determining the merger histories of galaxies. However, while useful in separating GCs into individual accretion events, the orbits of GC groups themselves have received less attention as probes of their progenitor galaxy properties. In this work, we use simulations of galaxies and their GC systems from the E-MOSAICS project to explore how the present-day orbital properties of GCs are related to the properties of their progenitor galaxies. We find that the orbits of GCs deposited by accretion events are sensitive to the mass and merger redshift of the satellite galaxy. Earlier mergers and larger galaxy masses deposit GCs at smaller median apocentres and lower total orbital energy. The orbital properties of accreted groups of GCs can therefore be used to infer the properties of their progenitor galaxy, though there exists a degeneracy between galaxy mass and accretion time. Combining GC orbits with other tracers (GC ages, metallicities) will help to break the galaxy mass/accretion time degeneracy, enabling stronger constraints on the properties of their progenitor galaxy. In situ GCs generally orbit at lower energies (small apocentres) than accreted GCs, however they exhibit a large tail to high energies and even retrograde orbits (relative to the present-day disc), showing significant overlap with accreted GCs. Applying the results to Milky Way GCs groups suggests a merger redshift $z \sim 1.5$ for the Gaia Sausage/Enceladus and $z>2$ for the `low-energy'/Kraken group, adding further evidence that the Milky Way had two significant mergers in its past., Comment: 13 pages, 7 figures. Accepted for publication in MNRAS (21 September 2020)

We present a detailed comparison of the Milky Way (MW) globular cluster (GC) kinematics with the 25 Milky Way-mass cosmological simulations from the E-MOSAICS project. While the MW falls within the kinematic distribution of GCs spanned by the simulations, the relative kinematics of its metal-rich ($[\rm{Fe/H}]>-1.2$) versus metal-poor ($[\rm{Fe/H}]<-1.2$), and inner ($r<8\rm{kpc}$) versus outer ($r>8\rm{kpc}$) populations are atypical for its mass. To understand the origins of these features, we perform a comprehensive statistical analysis of the simulations, and find 18 correlations describing the assembly of $L^*$ galaxies and their dark matter haloes based on their GC population kinematics. The correlations arise because the orbital distributions of accreted and in-situ GCs depend on the masses and accretion redshifts of accreted satellites, driven by the combined effects of dynamical fraction, tidal stripping, and dynamical heating. Because the kinematics of in-situ/accreted GCs are broadly traced by the metal-rich/metal-poor and inner/outer populations, the observed GC kinematics are a sensitive probe of galaxy assembly. We predict that relative to the population of $L^*$ galaxies, the MW assembled its dark matter and stellar mass rapidly through a combination of in-situ star formation, more than a dozen low-mass mergers, and $1.4\pm1.2$ early ($z=3.1\pm1.3$) major merger. The rapid assembly period ended early, limiting the fraction of accreted stars. We conclude by providing detailed quantitative predictions for the assembly history of the MW., Comment: 24 pages, 20 figures. Published in MNRAS

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using z = 0 snapshots from the 100cMpc3 and 25cMpc3 EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2× 107 - 1.9× 1012 M⊙. For those galaxies of mass M*>5× 108M⊙, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be due to high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies.

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using z = 0 snapshots from the 100cMpc3 and 25cMpc3 EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2× 107 - 1.9× 1012 M⊙. For those galaxies of mass M*>5× 108M⊙, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be due to high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies.

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using z = 0 snapshots from the 100cMpc3 and 25cMpc3 EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2× 107 - 1.9× 1012 M⊙. For those galaxies of mass M*>5× 108M⊙, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be due to high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies.

We set out to compare the age-metallicity relation (AMR) of massive clusters from Magellanic Cloud mass galaxies in the E-MOSAICS suite of numerical cosmological simulations with an amalgamation of observational data of massive clusters in the Large and Small Magellanic Clouds (LMC/SMC). We aim to test if: i) star cluster formation proceeds according to universal physical processes, suggestive of a common formation mechanism for young-massive clusters (YMCs), intermediate-age clusters (IACs), and ancient globular clusters (GCs); ii) massive clusters of all ages trace a continuous AMR; iii) the AMRs of smaller mass galaxies show a shallower relation when compared to more massive galaxies. Our results show that, within the uncertainties, the predicted AMRs of L/SMC-mass galaxies with similar star formation histories to the L/SMC follow the same relation as observations. We also find that the metallicity at which the AMR saturates increases with galaxy mass, which is also found for the field star AMRs. This suggests that relatively low-metallicity clusters can still form in dwarfs galaxies. Given our results, we suggest that ancient GCs share their formation mechanism with IACs and YMCs, in which GCs are the result of a universal process of star cluster formation during the early episodes of star formation in their host galaxies., Comment: Accepted for publication in MNRAS

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using $z=0$ snapshots from the 100cMpc$^3$ and 25cMpc$^3$ EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2$\times$10$^{7}$ - 1.9$\times$10$^{12}$ M$_{\odot}$. For those galaxies of mass M$_*$>5$\times$10$^{8}$M$_{\odot}$, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be the result of high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies., Comment: 16 pages, 11 figures. Accepted for publication in MNRAS

We present a detailed comparison of the Milky Way (MW) globular cluster (GC) kinematics with the 25 Milky Way-mass cosmological simulations from the E-MOSAICS project. While the MW falls within the kinematic distribution of GCs spanned by the simulations, the relative kinematics of its metal-rich ($[\rm{Fe/H}]>-1.2$) versus metal-poor ($[\rm{Fe/H}]<-1.2$), and inner ($r<8\rm{kpc}$) versus outer ($r>8\rm{kpc}$) populations are atypical for its mass. To understand the origins of these features, we perform a comprehensive statistical analysis of the simulations, and find 18 correlations describing the assembly of $L^*$ galaxies and their dark matter haloes based on their GC population kinematics. The correlations arise because the orbital distributions of accreted and in-situ GCs depend on the masses and accretion redshifts of accreted satellites, driven by the combined effects of dynamical fraction, tidal stripping, and dynamical heating. Because the kinematics of in-situ/accreted GCs are broadly traced by the metal-rich/metal-poor and inner/outer populations, the observed GC kinematics are a sensitive probe of galaxy assembly. We predict that relative to the population of $L^*$ galaxies, the MW assembled its dark matter and stellar mass rapidly through a combination of in-situ star formation, more than a dozen low-mass mergers, and $1.4\pm1.2$ early ($z=3.1\pm1.3$) major merger. The rapid assembly period ended early, limiting the fraction of accreted stars. We conclude by providing detailed quantitative predictions for the assembly history of the MW., Comment: 24 pages, 20 figures. Published in MNRAS

The ages and metallicities of globular clusters (GCs) are known to be powerful tracers of the properties of their progenitor galaxies, enabling their use in determining the merger histories of galaxies. However, while useful in separating GCs into individual accretion events, the orbits of GC groups themselves have received less attention as probes of their progenitor galaxy properties. In this work, we use simulations of galaxies and their GC systems from the E-MOSAICS project to explore how the present-day orbital properties of GCs are related to the properties of their progenitor galaxies. We find that the orbits of GCs deposited by accretion events are sensitive to the mass and merger redshift of the satellite galaxy. Earlier mergers and larger galaxy masses deposit GCs at smaller median apocentres and lower total orbital energy. The orbital properties of accreted groups of GCs can therefore be used to infer the properties of their progenitor galaxy, though there exists a degeneracy between galaxy mass and accretion time. Combining GC orbits with other tracers (GC ages, metallicities) will help to break the galaxy mass/accretion time degeneracy, enabling stronger constraints on the properties of their progenitor galaxy. In situ GCs generally orbit at lower energies (small apocentres) than accreted GCs, however they exhibit a large tail to high energies and even retrograde orbits (relative to the present-day disc), showing significant overlap with accreted GCs. Applying the results to Milky Way GCs groups suggests a merger redshift $z \sim 1.5$ for the Gaia Sausage/Enceladus and $z>2$ for the `low-energy'/Kraken group, adding further evidence that the Milky Way had two significant mergers in its past., Comment: 13 pages, 7 figures. Accepted for publication in MNRAS (21 September 2020)

Globular clusters (GCs) formed when the Milky Way experienced a phase of rapid assembly. We use the wealth of information contained in the Galactic GC population to quantify the properties of the satellite galaxies from which the Milky Way assembled. To achieve this, we train an artificial neural network on the E-MOSAICS cosmological simulations of the co-formation and co-evolution of GCs and their host galaxies. The network uses the ages, metallicities, and orbital properties of GCs that formed in the same progenitor galaxies to predict the stellar masses and accretion redshifts of these progenitors. We apply the network to Galactic GCs associated with five progenitors: {\it Gaia}-Enceladus, the Helmi streams, Sequoia, Sagittarius, and the recently discovered, `low-energy' GCs, which provide an excellent match to the predicted properties of the enigmatic galaxy `Kraken'. The five galaxies cover a narrow stellar mass range [$M_\star=(0.6{-}4.6)\times10^8~{\rm M}_\odot$], but have widely different accretion redshifts ($z_{\rm acc}=0.57{-}2.65$). All accretion events represent minor mergers, but Kraken likely represents the most major merger ever experienced by the Milky Way, with stellar and virial mass ratios of $r_{M_\star}=1$:$31^{+34}_{-16}$ and $r_{M_{\rm h}}=1$:$7^{+4}_{-2}$, respectively. The progenitors match the $z=0$ relation between GC number and halo virial mass, but have elevated specific frequencies, suggesting an evolution with redshift. Even though these progenitors likely were the Milky Way's most massive accretion events, they contributed a total mass of only $\log{(M_{\rm \star,tot}/{\rm M}_\odot)}=9.0\pm0.1$, similar to the stellar halo. This implies that the Milky Way grew its stellar mass mostly by in-situ star formation. We conclude by organising these accretion events into the most detailed reconstruction to date of the Milky Way's merger tree., Comment: 20 pages, 9 figures, 2 tables; submitted to MNRAS (March 1, 2020); Figures 4, 5, and 9 show the main results of the paper

Modern observational and analytic techniques now enable the direct measurement of star formation histories and the inference of galaxy assembly histories. However, current theoretical predictions of assembly are not ideally suited for direct comparison with such observational data. We therefore extend the work of prior examinations of the contribution of ex-situ stars to the stellar mass budget of simulated galaxies. Our predictions are specifically tailored for direct testing with a new generation of observational techniques by calculating ex-situ fractions as functions of galaxy mass and morphological type, for a range of surface brightnesses. These enable comparison with results from large FoV IFU spectrographs, and increasingly accurate spectral fitting, providing a look-up method for the estimated accreted fraction. We furthermore provide predictions of ex-situ mass fractions as functions of galaxy mass, galactocentric radius and environment. Using z = 0 snapshots from the 100cMpc3 and 25cMpc3 EAGLE simulations we corroborate the findings of prior studies, finding that ex-situ fraction increases with stellar mass for central and satellite galaxies in a stellar mass range of 2× 107 - 1.9× 1012 M⊙. For those galaxies of mass M*>5× 108M⊙, we find that the total ex-situ mass fraction is greater for more extended galaxies at fixed mass. When categorising satellite galaxies by their parent group/cluster halo mass we find that the ex-situ fraction decreases with increasing parent halo mass at fixed galaxy mass. This apparently counter-intuitive result may be due to high passing velocities within large cluster halos inhibiting efficient accretion onto individual galaxies.

The {\alpha}-element abundances of the globular cluster (GC) and field star populations of galaxies encode information about the formation of each of these components. We use the E-MOSAICS cosmological simulations of ~L* galaxies and their GCs to investigate the [{\alpha}/Fe]-[Fe/H] distribution of field stars and GCs in 25 Milky Way-mass galaxies. The [{\alpha}/Fe]-[Fe/H] distribution go GCs largely follows that of the field stars and can also therefore be used as tracers of the [{\alpha}/Fe]-[Fe/H] evolution of the galaxy. Due to the difference in their star formation histories, GCs associated with stellar streams (i.e. which have recently been accreted) have systematically lower [{\alpha}/Fe] at fixed [Fe/H]. Therefore, if a GC is observed to have low [{\alpha}/Fe] for its [Fe/H] there is an increased probability that this GC was accreted recently alongside a dwarf galaxy. There is a wide range of shapes for the field star [{\alpha}/Fe]-[Fe/H] distribution, with a notable subset of galaxies exhibiting bimodal distributions, in which the high [{\alpha}/Fe] sequence is mostly comprised of stars in the bulge, a high fraction of which are from disrupted GCs. We calculate the contribution of disrupted GCs to the bulge component of the 25 simulated galaxies and find values between 0.3-14 per cent, where this fraction correlates with the galaxy's formation time. The upper range of these fractions is compatible with observationally-inferred measurements for the Milky Way, suggesting that in this respect the Milky Way is not typical of L* galaxies, having experienced a phase of unusually rapid growth at early times.

Globular clusters (GCs) have been posited, alongside dwarf galaxies, as significant contributors to the field stellar population of the Galactic halo. In order to quantify their contribution, we examine the fraction of halo stars formed in stellar clusters in the suite of 25 present-day Milky Way-mass cosmological zoom simulations from the E-MOSAICS project. We find that a median of $2.3$ and $0.3$ per cent of the mass in halo field stars formed in clusters and GCs, defined as clusters more massive than $5\times 10^3$ and $10^5~M_{\odot}$, respectively, with the $25$-$75$th percentiles spanning $1.9$-$3.0$ and $0.2$-$0.5$ per cent being caused by differences in the assembly histories of the host galaxies. Under the extreme assumption that no stellar cluster survives to the present day, the mass fractions increase to a median of $5.9$ and $1.8$ per cent. These small fractions indicate that the disruption of GCs plays a sub-dominant role in the build-up of the stellar halo. We also determine the contributed halo mass fraction that would present signatures of light-element abundance variations considered to be unique to GCs, and find that clusters and GCs would contribute a median of $1.1$ and $0.2$ per cent, respectively. We estimate the contributed fraction of GC stars to the Milky Way halo, based on recent surveys, and find upper limits of $2$-$5$ per cent (significantly lower than previous estimates), suggesting that models other than those invoking strong mass loss are required to describe the formation of chemically enriched stellar populations in GCs., Comment: 7 pages, 2 figures; submitted to MNRAS (Oct. 10th 2019)

The formation histories of globular clusters (GCs) are a key diagnostic for understanding their relation to the evolution of the Universe through cosmic time. We use the suite of 25 cosmological zoom-in simulations of present-day Milky Way-mass galaxies from the E-MOSAICS project to study the formation histories of stars, clusters, and GCs, and how these are affected by the environmental dependence of the cluster formation physics. We find that the median lookback time of GC formation in these galaxies is ${\sim}10.73~$Gyr ($z=2.1$), roughly $2.5~$Gyr earlier than that of the field stars (${\sim}8.34~$Gyr or $z=1.1$). The epoch of peak GC formation is mainly determined by the time evolution of the maximum cluster mass, which depends on the galactic environment and largely increases with the gas pressure. Different metallicity subpopulations of stars, clusters and GCs present overlapping formation histories, implying that star and cluster formation represent continuous processes. The metal-poor GCs ($-2.5<[\rm Fe/H]<-1.5$) of our galaxies are older than the metal-rich GC subpopulation ($-1.0<[\rm Fe/H]<-0.5$), forming $12.13~$Gyr and $10.15~$Gyr ago ($z=3.7$ and $z=1.8$), respectively. The median ages of GCs are found to decrease gradually with increasing metallicity, which suggests different GC metallicity subpopulations do not form independently and their spatial and kinematic distributions are the result of their evolution in the context of hierarchical galaxy formation and evolution. We predict that proto-GC formation is most prevalent at $2\lesssim z \lesssim 3$, which could be tested with observations of lensed galaxies using JWST., Comment: 15 pages, 6 figures; accepted by MNRAS (April 30, 2019)

We present 25 cosmological zoom-in simulations of Milky Way-mass galaxies in the `MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE' (E-MOSAICS) project. E-MOSAICS couples a detailed physical model for the formation, evolution, and disruption of star clusters to the EAGLE galaxy formation simulations. This enables following the co-formation and co-evolution of galaxies and their star cluster populations, thus realising the long-standing promise of using globular clusters (GCs) as tracers of galaxy formation and assembly. The simulations show that the age-metallicity distributions of GC populations exhibit strong galaxy-to-galaxy variations, resulting from differences in their evolutionary histories. We develop a formalism for systematically constraining the assembly histories of galaxies using GC age-metallicity distributions. These distributions are characterised through 13 metrics that we correlate with 30 quantities describing galaxy formation and assembly (e.g. halo properties, formation/assembly redshifts, stellar mass assembly time-scales, galaxy merger statistics), resulting in 20 statistically (highly) significant correlations. The GC age-metallicity distribution is a sensitive probe of the mass growth, metal enrichment, and minor merger history of the host galaxy. No such relation is found between GCs and major mergers, which play a sub-dominant role in GC formation for Milky Way-mass galaxies. Finally, we show how the GC age-metallicity distribution enables the reconstruction of the host galaxy's merger tree, allowing us to identify all progenitors with masses $M_*\gtrsim10^8$ M$_\odot$ for redshifts $1\leq z\leq2.5$. These results demonstrate that cosmological simulations of the co-formation and co-evolution of GCs and their host galaxies successfully unlock the potential of GCs as quantitative tracers of galaxy formation and assembly., Comment: 44 pages (including appendices), 13 figures, 14 tables; accepted by MNRAS (April 2, 2019). Figures 3, 8, 10, and 11 show the main results of the paper

The formation histories of globular clusters (GCs) are a key diagnostic for understanding their relation to the evolution of the Universe through cosmic time. We use the suite of 25 cosmological zoom-in simulations of present-day Milky Way-mass galaxies from the E-MOSAICS project to study the formation histories of stars, clusters, and GCs, and how these are affected by the environmental dependence of the cluster formation physics. We find that the median lookback time of GC formation in these galaxies is ${\sim}10.73~$Gyr ($z=2.1$), roughly $2.5~$Gyr earlier than that of the field stars (${\sim}8.34~$Gyr or $z=1.1$). The epoch of peak GC formation is mainly determined by the time evolution of the maximum cluster mass, which depends on the galactic environment and largely increases with the gas pressure. Different metallicity subpopulations of stars, clusters and GCs present overlapping formation histories, implying that star and cluster formation represent continuous processes. The metal-poor GCs ($-2.5<[\rm Fe/H]<-1.5$) of our galaxies are older than the metal-rich GC subpopulation ($-1.0<[\rm Fe/H]<-0.5$), forming $12.13~$Gyr and $10.15~$Gyr ago ($z=3.7$ and $z=1.8$), respectively. The median ages of GCs are found to decrease gradually with increasing metallicity, which suggests different GC metallicity subpopulations do not form independently and their spatial and kinematic distributions are the result of their evolution in the context of hierarchical galaxy formation and evolution. We predict that proto-GC formation is most prevalent at $2\lesssim z \lesssim 3$, which could be tested with observations of lensed galaxies using JWST., Comment: 15 pages, 6 figures; accepted by MNRAS (April 30, 2019)

We present 25 cosmological zoom-in simulations of Milky Way-mass galaxies in the `MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE' (E-MOSAICS) project. E-MOSAICS couples a detailed physical model for the formation, evolution, and disruption of star clusters to the EAGLE galaxy formation simulations. This enables following the co-formation and co-evolution of galaxies and their star cluster populations, thus realising the long-standing promise of using globular clusters (GCs) as tracers of galaxy formation and assembly. The simulations show that the age-metallicity distributions of GC populations exhibit strong galaxy-to-galaxy variations, resulting from differences in their evolutionary histories. We develop a formalism for systematically constraining the assembly histories of galaxies using GC age-metallicity distributions. These distributions are characterised through 13 metrics that we correlate with 30 quantities describing galaxy formation and assembly (e.g. halo properties, formation/assembly redshifts, stellar mass assembly time-scales, galaxy merger statistics), resulting in 20 statistically (highly) significant correlations. The GC age-metallicity distribution is a sensitive probe of the mass growth, metal enrichment, and minor merger history of the host galaxy. No such relation is found between GCs and major mergers, which play a sub-dominant role in GC formation for Milky Way-mass galaxies. Finally, we show how the GC age-metallicity distribution enables the reconstruction of the host galaxy's merger tree, allowing us to identify all progenitors with masses $M_*\gtrsim10^8$ M$_\odot$ for redshifts $1\leq z\leq2.5$. These results demonstrate that cosmological simulations of the co-formation and co-evolution of GCs and their host galaxies successfully unlock the potential of GCs as quantitative tracers of galaxy formation and assembly., Comment: 44 pages (including appendices), 13 figures, 14 tables; accepted by MNRAS (April 2, 2019). Figures 3, 8, 10, and 11 show the main results of the paper

The {\alpha}-element abundances of the globular cluster (GC) and field star populations of galaxies encode information about the formation of each of these components. We use the E-MOSAICS cosmological simulations of ~L* galaxies and their GCs to investigate the [{\alpha}/Fe]-[Fe/H] distribution of field stars and GCs in 25 Milky Way-mass galaxies. The [{\alpha}/Fe]-[Fe/H] distribution go GCs largely follows that of the field stars and can also therefore be used as tracers of the [{\alpha}/Fe]-[Fe/H] evolution of the galaxy. Due to the difference in their star formation histories, GCs associated with stellar streams (i.e. which have recently been accreted) have systematically lower [{\alpha}/Fe] at fixed [Fe/H]. Therefore, if a GC is observed to have low [{\alpha}/Fe] for its [Fe/H] there is an increased probability that this GC was accreted recently alongside a dwarf galaxy. There is a wide range of shapes for the field star [{\alpha}/Fe]-[Fe/H] distribution, with a notable subset of galaxies exhibiting bimodal distributions, in which the high [{\alpha}/Fe] sequence is mostly comprised of stars in the bulge, a high fraction of which are from disrupted GCs. We calculate the contribution of disrupted GCs to the bulge component of the 25 simulated galaxies and find values between 0.3-14 per cent, where this fraction correlates with the galaxy's formation time. The upper range of these fractions is compatible with observationally-inferred measurements for the Milky Way, suggesting that in this respect the Milky Way is not typical of L* galaxies, having experienced a phase of unusually rapid growth at early times.

Globular clusters (GCs) have been posited, alongside dwarf galaxies, as significant contributors to the field stellar population of the Galactic halo. In order to quantify their contribution, we examine the fraction of halo stars formed in stellar clusters in the suite of 25 present-day Milky Way-mass cosmological zoom simulations from the E-MOSAICS project. We find that a median of $2.3$ and $0.3$ per cent of the mass in halo field stars formed in clusters and GCs, defined as clusters more massive than $5\times 10^3$ and $10^5~M_{\odot}$, respectively, with the $25$-$75$th percentiles spanning $1.9$-$3.0$ and $0.2$-$0.5$ per cent being caused by differences in the assembly histories of the host galaxies. Under the extreme assumption that no stellar cluster survives to the present day, the mass fractions increase to a median of $5.9$ and $1.8$ per cent. These small fractions indicate that the disruption of GCs plays a sub-dominant role in the build-up of the stellar halo. We also determine the contributed halo mass fraction that would present signatures of light-element abundance variations considered to be unique to GCs, and find that clusters and GCs would contribute a median of $1.1$ and $0.2$ per cent, respectively. We estimate the contributed fraction of GC stars to the Milky Way halo, based on recent surveys, and find upper limits of $2$-$5$ per cent (significantly lower than previous estimates), suggesting that models other than those invoking strong mass loss are required to describe the formation of chemically enriched stellar populations in GCs., Comment: 7 pages, 2 figures; submitted to MNRAS (Oct. 10th 2019)

Several models have been advanced to explain the multiple stellar populations observed in globular clusters (GCs). Most models necessitate a large initial population of unenriched stars that provide the pollution for an enriched population, and which are subsequently lost from the cluster. This scenario generally requires clusters to lose $>90$ per cent of their birth mass. We use a suite of 25 cosmological zoom-in simulations of present-day Milky Way-mass galaxies from the \emosaics project to study whether dynamical disruption by evaporation and tidal shocking provides the necessary mass loss. We find that GCs with present-day masses $M>10^5~M_{\odot}$ were only $2$-$4$ times more massive at birth, in conflict with the requirements of the proposed models. This factor correlates weakly with metallicity, gas pressure at birth, or galactocentric radius, but increases towards lower GC masses. To reconcile our results with observational data, either an unphysically steep cluster mass-size relation must be assumed, or the initial enriched fractions must be similar to their present values. We provide the required relation between the initial enriched fraction and cluster mass. Dynamical cluster mass loss cannot reproduce the high observed enriched fractions nor their trend with cluster mass., Comment: 6 pages, 4 figures; accepted by MNRAS (September 4, 2018)

We use the age-metallicity distribution of 96 Galactic globular clusters (GCs) to infer the formation and assembly history of the Milky Way (MW), culminating in the reconstruction of its merger tree. Based on a quantitative comparison of the Galactic GC population to the 25 cosmological zoom-in simulations of MW-mass galaxies in the E-MOSAICS project, which self-consistently model the formation and evolution of GC populations in a cosmological context, we find that the MW assembled quickly for its mass, reaching $\{25,50\}\%$ of its present-day halo mass already at $z=\{3,1.5\}$ and half of its present-day stellar mass at $z=1.2$. We reconstruct the MW's merger tree from its GC age-metallicity distribution, inferring the number of mergers as a function of mass ratio and redshift. These statistics place the MW's assembly $\textit{rate}$ among the 72th-94th percentile of the E-MOSAICS galaxies, whereas its $\textit{integrated}$ properties (e.g. number of mergers, halo concentration) match the median of the simulations. We conclude that the MW has experienced no major mergers (mass ratios $>$1:4) since $z\sim4$, sharpening previous limits of $z\sim2$. We identify three massive satellite progenitors and constrain their mass growth and enrichment histories. Two are proposed to correspond to Sagittarius (few $10^8~{\rm M}_\odot$) and the GCs formerly associated with Canis Major ($\sim10^9~{\rm M}_\odot$). The third satellite has no known associated relic and was likely accreted between $z=0.6$-$1.3$. We name this enigmatic galaxy $\textit{Kraken}$ and propose that it is the most massive satellite ($M_*\sim2\times10^9~{\rm M}_\odot$) ever accreted by the MW. We predict that $\sim40\%$ of the Galactic GCs formed ex-situ (in galaxies with masses $M_*=2\times10^7$-$2\times10^9~{\rm M}_\odot$), with $6\pm1$ being former nuclear clusters., Comment: 24 pages (including appendices), 6 figures, 5 tables; accepted by MNRAS (June 12, 2018), originally submitted on March 25, 2018; Figures 4 and 6 show the main results of the paper. Updated with published version, clarifying the intended historical use of "Canis Major" as referring to a group of GCs rather than a galaxy

Several models have been advanced to explain the multiple stellar populations observed in globular clusters (GCs). Most models necessitate a large initial population of unenriched stars that provide the pollution for an enriched population, and which are subsequently lost from the cluster. This scenario generally requires clusters to lose $>90$ per cent of their birth mass. We use a suite of 25 cosmological zoom-in simulations of present-day Milky Way-mass galaxies from the \emosaics project to study whether dynamical disruption by evaporation and tidal shocking provides the necessary mass loss. We find that GCs with present-day masses $M>10^5~M_{\odot}$ were only $2$-$4$ times more massive at birth, in conflict with the requirements of the proposed models. This factor correlates weakly with metallicity, gas pressure at birth, or galactocentric radius, but increases towards lower GC masses. To reconcile our results with observational data, either an unphysically steep cluster mass-size relation must be assumed, or the initial enriched fractions must be similar to their present values. We provide the required relation between the initial enriched fraction and cluster mass. Dynamical cluster mass loss cannot reproduce the high observed enriched fractions nor their trend with cluster mass., Comment: 6 pages, 4 figures; accepted by MNRAS (September 4, 2018)

We use the age-metallicity distribution of 96 Galactic globular clusters (GCs) to infer the formation and assembly history of the Milky Way (MW), culminating in the reconstruction of its merger tree. Based on a quantitative comparison of the Galactic GC population to the 25 cosmological zoom-in simulations of MW-mass galaxies in the E-MOSAICS project, which self-consistently model the formation and evolution of GC populations in a cosmological context, we find that the MW assembled quickly for its mass, reaching $\{25,50\}\%$ of its present-day halo mass already at $z=\{3,1.5\}$ and half of its present-day stellar mass at $z=1.2$. We reconstruct the MW's merger tree from its GC age-metallicity distribution, inferring the number of mergers as a function of mass ratio and redshift. These statistics place the MW's assembly $\textit{rate}$ among the 72th-94th percentile of the E-MOSAICS galaxies, whereas its $\textit{integrated}$ properties (e.g. number of mergers, halo concentration) match the median of the simulations. We conclude that the MW has experienced no major mergers (mass ratios $>$1:4) since $z\sim4$, sharpening previous limits of $z\sim2$. We identify three massive satellite progenitors and constrain their mass growth and enrichment histories. Two are proposed to correspond to Sagittarius (few $10^8~{\rm M}_\odot$) and the GCs formerly associated with Canis Major ($\sim10^9~{\rm M}_\odot$). The third satellite has no known associated relic and was likely accreted between $z=0.6$-$1.3$. We name this enigmatic galaxy $\textit{Kraken}$ and propose that it is the most massive satellite ($M_*\sim2\times10^9~{\rm M}_\odot$) ever accreted by the MW. We predict that $\sim40\%$ of the Galactic GCs formed ex-situ (in galaxies with masses $M_*=2\times10^7$-$2\times10^9~{\rm M}_\odot$), with $6\pm1$ being former nuclear clusters., Comment: 24 pages (including appendices), 6 figures, 5 tables; accepted by MNRAS (June 12, 2018), originally submitted on March 25, 2018; Figures 4 and 6 show the main results of the paper. Updated with published version, clarifying the intended historical use of "Canis Major" as referring to a group of GCs rather than a galaxy