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We present a comprehensive analysis of globular cluster (GC) formation and evolution across the $34^3$ Mpc$^3$ volume of the E-MOSAICS galaxy formation simulations. Defining GCs as surviving, high-mass ($>10^5$ M$_\odot$) clusters, we analyse their formation histories as a function of their metallicity and host galaxy mass, also distinguishing between central and satellite galaxies. The redshift of peak GC formation rate increases weakly with galaxy mass, decreases with metallicity, and does not differ between centrals and satellites. The epoch of peak GC formation precedes that of the stars by a factor of $1.1{-}1.6$, primarily due to `downsizing', i.e. low-mass galaxies form their stars later. Consequently, this offset decreases with galaxy mass, leading to nearly coeval stellar and GC populations in massive galaxies ($>10^{11}$ M$_\odot$). GCs themselves do not exhibit strong downsizing, because they predominantly formed at early cosmic epochs conducive to the formation (through high gas pressures) and survival (through high galaxy merger and GC migration rates) of massive, compact stellar systems. The total GC formation rate in the volume peaks at $z\approx 2.5$, shortly before star formation peaks at $z\approx 2$, but well after the general cluster formation rate at $z\approx 4$, reflecting a survivor bias where surviving GCs formed more recently. We find that GC formation commenced early, at $z>10$, such that the results of this work may provide a framework for interpreting direct observations of proto-GC formation with the JWST, especially as these observations accumulate to enable statistical studies., Comment: 12 pages, 7 figures, 3 tables; submitted to The Open Journal of Astrophysics (December 6, 2024); Figures 6 and 7 show the Madau plot for GCs

Most of the dynamical mass loss from star clusters is thought to be caused by the time-variability of the tidal field (``tidal shocks''). Systematic studies of tidal shocks have been hampered by the fact that each tidal history is unique, implying both a reproducibility and a generalisation problem. Here we address these issues by investigating how star cluster evolution depends on the statistical properties of its tidal history. We run a large suite of direct N-body simulations of clusters with tidal histories generated from power spectra of a given slope and with different normalisations, which determine the time-scales and amplitudes of the shocks, respectively. At fixed normalisation (i.e. the same median tidal field strength), the dissolution time-scale is nearly independent of the power spectrum slope. However, the dispersion in dissolution time-scales, obtained by repeating simulations for different realisations of statistically identical tidal histories, increases with the power spectrum slope. This result means that clusters experiencing high-frequency shocks have more similar mass loss histories than clusters experiencing low-frequency shocks. The density-mass relationship of the simulated clusters follows a power-law with slope between 1.08 and 1.45, except for the lowest normalisations (for which clusters effectively evolve in a static tidal field). Our findings suggest that star cluster evolution can be described statistically from a time-series analysis of its tidal history, which is an important simplification for describing the evolution of the star cluster population during galaxy formation and evolution., Comment: 15 pages, 10 figures, 1 table, accepted for publication in The Astrophysical Journal

Stellar clusters are critical constituents within galaxies: they are the result of highest-density star formation, and through their spatially and temporally correlated feedback they regulate their host galaxy evolution. We present a novel numerical method to model star clusters as individual units of star formation using sink particles. In our method, star clusters grow via gas accretion and via merging with less massive clusters. We describe the implementation in the radiation hydrodynamics code GIZMO and run a large grid of marginally bound, turbulent clouds of $10^7~{\rm M}_{\odot}$ to explore the effect of modeling ingredients on the evolution of the clouds and the star clusters. We find both gas accretion and mergers to be critical processes to form star clusters of masses up to $\sim10^5$-$10^6~{\rm M}_{\odot}$, while ionising radiation is the main feedback mechanism regulating the growth of star clusters. The majority of our star clusters assemble their mass in $0.3$-$2.6~{\rm Myr}$, and the most massive ones take $\sim10~{\rm Myr}$. By removing high density gas by accretion, our sink-based cluster formation prescription allows the newly-formed star clusters to inject their stellar feedback in less dense environments. This makes feedback more efficient at ionising and disrupting the cloud than if we were to use a standard star formation approach, indicating that our numerical method is the missing critical step to model the interplay between star clusters and their host galaxies., Comment: 16 + 7 pages, 11 + 1 figures. Submitted to ApJ, comments welcome!

Deep JWST imaging of the giant galaxy cluster Abell 2744, at redshift $z=0.308$, is used to explore the features of its rich population of globular clusters (GCs), building on our initial survey of the system (Harris & Reina-Campos 2023). We use the photometry of more than $10,000$ GCs over a three-magnitude range to construct the GC luminosity function (GCLF) and color distribution (CDF). These results now specifically account for photometric incompleteness as a function of location relative to the five giant galaxies that dominate the gravitational potential of A2744. The total GC population in A2744 is estimated at $N_{\rm GC} \geq 1.1 \times 10^5$, consistent with its high total mass. We also directly compare the observed distributions with theoretical predictions for GC populations drawn from the recent EMP-Pathfinder simulations (Reina-Campos et al. 2022), viewed at the same 3.5 Gyr lookback time as the cluster. The simulations match the observations well, with the only notable disagreement being that the simulations predict larger numbers of GCs at high metallicity formed after $z\simeq2$ than are seen in the data., Comment: 15 pages, 9 figures; submitted to ApJ

Observations of caustic-crossing galaxies at redshift $0.72$ and the number density of events is greater around substructureand the number density of events is greater around substructures, and (ii) negative imaging regime where $\beta<2$. We study the particular case of seven microlensing events found by HST in the Dragon arc (at z=0.725). We find that a population of supergiant stars with a steep LF with $\beta=2.55$ fits the distribution of these events. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of $\sim 1.3 \times 10^8\,\Msun$ (within its Einstein radius)., Comment: 23 pages, 16 figures

The advent of JWST (the James Webb Space Telescope) now allows entire star cluster populations to be imaged in galaxies at cosmologically significant redshifts, bringing with it the need to apply K-corrections to their magnitudes and colour indices. Since the stellar populations within star clusters can be well approximated by a single age and metallicity, their spectral energy distributions are very different from those of galaxies or supernovae, and their K-corrections behave differently. We derive the photometric K-corrections versus redshift for model star clusters that cover a wide range of ages and metallicities, illustrating the results particularly for the broadband filters on the HST/ACS and the JWST/NIRCam cameras that are most commonly being used for imaging of populations of star clusters in distant galaxies. In an Appendix, we introduce a simple webtool called RESCUER that can generate K-values for any user-defined combination of cluster properties., Comment: 9 pages, 7 figures, submitted to MNRAS, comments are welcomed! The RESCUER webtool is available here: https://rescuer.streamlit.app

Understanding what shapes the cold gas component of galaxies, which both provides the fuel for star formation and is strongly affected by the subsequent stellar feedback, is a crucial step towards a better understanding of galaxy evolution. Here, we analyse the HI properties of a sample of 46 Milky Way halo-mass galaxies, drawn from cosmological simulations (EMP-Pathfinder and FIREbox). This set of simulations comprises galaxies evolved self-consistently across cosmic time with different baryonic sub-grid physics: three different star formation models [constant star formation efficiency (SFE) with different star formation eligibility criteria, and an environmentally-dependent, turbulence-based SFE] and two different feedback prescriptions, where only one sub-sample includes early stellar feedback. We use these simulations to assess the impact of different baryonic physics on the HI content of galaxies. We find that the galaxy-wide HI properties agree with each other and with observations. However, differences appear for small-scale properties. The thin HI discs observed in the local Universe are only reproduced with a turbulence-dependent SFE and/or early stellar feedback. Furthermore, we find that the morphology of HI discs is particularly sensitive to the different physics models: galaxies simulated with a turbulence-based SFE have discs that are smoother and more rotationally symmetric, compared to those simulated with a constant SFE; galaxies simulated with early stellar feedback have more regular discs than supernova-feedback-only galaxies. We find that the rotational asymmetry of the HI discs depends most strongly on the underlying physics model, making this a promising observable for understanding the physics responsible for shaping the interstellar medium of galaxies., Comment: 13 pages, 10 figures + appendices (7 pages, 10 figures); updated to version accepted by MNRAS

The presence or absence of star clusters in galaxies, and the properties of star cluster populations compared to their host galaxy properties, are important observables for validating models of cluster formation, galaxy formation, and galaxy assembly. In this work, we apply a Bayesian approach to fit two models to data from surveys of young clusters in star forming galaxies. The first model is a logistic regression, which allows us to include galaxies which do not have any young clusters. The second model is a hurdle model, which includes galaxies with zero clusters and also incorporates information about the total mass in the cluster system. We investigate two predictors (star formation rate and total stellar mass in the galaxy) and look at clusters younger than 10 or 100 Myr. We find that in all cases, star formation rate is the better predictor for both the probability of hosting clusters and the total mass in the cluster system. We compare our results to similar models for old globular clusters, and conclude that star cluster formation was more abundant and more efficient at higher redshifts, likely because of the high gas content of galaxies at that time., Comment: 10 pages, 5 figures, accepted by MNRAS

JWST imaging of the rich galaxy cluster Abell 2744 at $z=0.308$ has been used by the UNCOVER team (Bezanson et al. 2022) to construct mosaic images in the NIRCAM filters. The exceptionally deep images in the ($F115W$, $F150W$, $F200W$) bands reveal a large population of unresolved pointlike sources across the field, the vast majority of which are globular clusters (GCs). To the limits of our photometry, more than 10,000 such objects were measured, most of which are in the halos of the five largest A2744 galaxies but which also include GCs around some satellite galaxies and throughout the IntraCluster Medium. Their luminosity function follows a lognormal shape, with the data reaching to within one magnitude of the classic GCLF turnover point. The colour index ($F115W-F200W$) in particular covers a range of $0.5$ mag, clearly resolving the expected internal spread of GC metallicities. The estimated GC masses are systematically higher than in present-day galaxies, consistent with a large, normal GC population seen at a $3.5~$Gyr earlier stage of dynamical evolution. Lastly, the spatial distribution of the bluer (more metal-poor) GCs resembles the gravitational lensing map of the cluster, consistent with recent theoretical suggestions., Comment: 13 pages and 13 figures. Accepted by MNRAS (September 18th 2023)

Massive star clusters are often used as tracers of galaxy formation and assembly. In order to do so, we must understand their properties at formation, and how those properties change with time, galactic environment, and galaxy assembly history. The two most important intrinsic properties that govern star cluster evolution are mass and radius. In this paper, we investigate 10 theoretically and observationally motivated initial size-mass relations for star clusters, and evolve populations of clusters through galaxy formation models. We compare our results to each other and to observations of cluster populations in M83, M31, and the Milky Way. We find that none of our size-mass relations agree with the observations after 6-10 Gyr of evolution. We can successfully reproduce the cluster mass functions with models that have a small range of initial radii, and which do not allow cluster radii to change with time. However, these models do not agree with our understanding of cluster evolution, which does involve radius evolution, and do not match the observed distributions of radii. We note that there is a region of parameter space where clusters are optimally protected from both tidal shocks and evaporation due to two-body relaxation. Clusters which are allowed to evolve into this parameter space will likely survive. An improved understanding of both mass and radius evolution of star clusters in realistic, time-varying galactic potentials is necessary to appropriately make the connection between present-day cluster properties and their use as tracers of galaxy formation and assembly., Comment: Accepted by MNRAS

The Vera C. Rubin Observatory will undertake the Legacy Survey of Space and Time, providing an unprecedented, volume-limited catalog of star clusters in the Southern Sky, including Galactic and extragalactic star clusters. The Star Clusters subgroup of the Stars, Milky Way and Local Volume Working Group has identified key areas where Rubin Observatory will enable significant progress in star cluster research. This roadmap represents our science cases and preparation for studies of all kinds of star clusters from the Milky Way out to distances of tens of megaparsecs., Comment: accepted to PASP

The Nancy Grace Roman Telescope's High Latitude Wide Area Survey will have a number of synergies with the Vera Rubin Observatory's Legacy Survey of Space and Time (LSST), particularly for extragalactic star clusters. Understanding the nature of star clusters and star cluster systems are key topics in many areas of astronomy, chief among them stellar evolution, high energy astrophysics, galaxy assembly/dark matter, the extragalactic distance scale, and cosmology. One of the challenges will be disentangling the age/metallicity degeneracy because young ($\sim$Myr) metal-rich clusters have similar SEDs to old ($\sim$Gyr) metal-poor clusters. Rubin will provide homogeneous, $ugrizy$ photometric coverage, and measurements in the red Roman filters will help break the age-metallicity and age-extinction degeneracies, providing the first globular cluster samples that cover wide areas while essentially free of contamination from Milky Way stars. Roman's excellent spatial resolution will also allow measurements of cluster sizes. We advocate for observations of a large sample of galaxies with a range of properties and morphologies in the Rubin/LSST footprint matching the depth of the LSST Wide-Fast-Deep field $i$ band limit (26.3 mag), and recommend adding the F213 filter to the survey., Comment: white paper submitted for Roman CCS input

Globular clusters (GCs) are powerful tracers of the galaxy assembly process, and have already been used to obtain a detailed picture of the progenitors of the Milky Way. Using the E-MOSAICS cosmological simulation of a (34.4 Mpc)$^3$ volume that follows the formation and co-evolution of galaxies and their star cluster populations, we develop a method to link the origin of GCs to their observable properties. We capture this complex link using a supervised deep learning algorithm trained on the simulations, and predict the origin of individual GCs (whether they formed in the main progenitor or were accreted from satellites) based solely on extragalactic observables. An artificial neural network classifier trained on $\sim50,000$ GCs hosted by $\sim 700$ simulated galaxies successfully predicts the origin of GCs in the test set with a mean accuracy of $89$ per cent for the objects with [Fe/H]<-0.5 that have unambiguous classifications. The network relies mostly on the alpha-element abundances, metallicities, projected positions, and projected angular momenta of the clusters to predict their origin. A real-world test using the known progenitor associations of the Milky Way GCs achieves up to $90$ per cent accuracy, and successfully identifies as accreted most of the GCs in the inner Galaxy associated to the Kraken progenitor, as well as all the Gaia-Enceladus GCs. We demonstrate that the model is robust to observational uncertainties, and develop a method to predict the classification accuracy across observed galaxies. The classifier can be optimized for available observables (e.g. to improve the accuracy by including GC ages), making it a valuable tool to reconstruct the assembly histories of galaxies in upcoming wide-field surveys., Comment: 21 pages, 22 figures. Submitted to MNRAS. Comments 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

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!

In addition to their low stellar densities, ultra-diffuse galaxies (UDGs) have a broad variety of dynamical mass-to-light ratios, ranging from dark matter (DM) dominated systems to objects nearly devoid of DM. To investigate the origin of this diversity, we develop a simple, semi-empirical model that predicts the structural evolution of galaxies, driven by feedback from massive star clusters, as a function of their departure from the mean SMHM relation. The model predicts that a galaxy located $\gtrsim 0.5$ dex above the mean relation at $M_{\rm halo}=10^{10}M_{\odot}$ will host a factor of $\sim 10-100$ larger globular cluster (GC) populations, and that feedback from these GCs drives a significant expansion of the stellar component and loss of DM compared to galaxies on the SMHM relation. This effect is stronger in haloes that collapse earlier and have enhanced star formation rates at $z\gtrsim2$, which leads to increased gas pressures, stellar clustering, and mean cluster masses, and significantly enhances the energy loading of galactic winds and its impact on the DM and stellar orbits. The impact on galaxy size and DM content can be large enough to explain observed galaxies that contain nearly the universal baryon fraction, as well as NGC1052-DF2 and DF4 and other isolated UDGs that contain almost no DM. The trend of increasing galaxy size with GC specific frequency observed in galaxy clusters also emerges naturally in the model. Our predictions can be tested with large and deep surveys of the stellar and GC populations in dwarfs and UDGs. Because stellar clustering drives the efficiency of galactic winds, it may be a dominant factor in the structural evolution of galaxies and should be included as an essential ingredient in galaxy formation models., Comment: 23 pages, 17 figures. Accepted for publication in MNRAS (November 5)

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

It has long been argued that the radial distribution of globular clusters (GCs) in the Fornax dwarf galaxy requires its dark matter halo to have a core of size $\sim 1$ kpc. We revisit this argument by investigating analogues of Fornax formed in E-MOSAICS, a cosmological hydrodynamical simulation that self-consistently follows the formation and evolution of GCs in the EAGLE galaxy formation model. In EAGLE, Fornax-mass haloes are cuspy and well described by the Navarro-Frenk-White profile. We post-process the E-MOSAICS to account for GC orbital decay by dynamical friction, which is not included in the original model. Dynamical friction causes 33 per cent of GCs with masses $M_{\rm GC}\geq4\times10^4 {~\rm M_\odot}$ to sink to the centre of their host where they are tidally disrupted. Fornax has a total of five GCs, an exceptionally large number compared to other galaxies of similar stellar mass. In the simulations, we find that only 3 per cent of the Fornax analogues have five or more GCs, while 30 per cent have only one and 35 per cent have none. We find that GC systems in satellites are more centrally concentrated than in field dwarfs, and that those formed in situ (45 per cent) are more concentrated than those that were accreted. The survival probability of a GC increases rapidly with the radial distance at which it formed ($r_{\rm init}$): it is 37 per cent for GCs with $r_{\rm init} \leq 1$ kpc and 92 per cent for GCs with $r_{\rm init} \geq 1$ kpc. The present-day radial distribution of GCs in E-MOSAICS turns out to be indistinguishable from that in Fornax, demonstrating that, contrary to claims in the literature, the presence of five GCs in the central kiloparsec of Fornax does not exclude a cuspy DM halo., Comment: 15 pages, 13 figures. submitted to MNRAS, comments welcome!

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

The ultra-diffuse galaxy (UDG) NGC1052-DF2 has a low dark matter content and hosts a very unusual globular cluster (GC) population, with a median luminosity $\sim4$ times higher than in most galaxies and containing about 5~per~cent of the galaxy's stars. We apply a theoretical model that predicts the initial cluster mass function as a function of the galactic environment to investigate the origin of DF2's peculiar GC system. Using the GC mass function, the model constrains the star-forming conditions in the galaxy during the formation of its GCs, $\sim9~\rm{Gyr}$ ago. We predict that the GCs formed in an environment with very high gas surface density, $\Sigma_{\rm ISM} \gtrsim 10^3 M_{\odot} \rm{pc}^{-2}$, and strong centrifugal support, $\Omega \gtrsim 0.7~\rm{Myr}^{-1}$, similar to nearby circum-nuclear starbursts and the central region of the Milky Way. These extreme conditions required to form the observed GC population imply a very high cluster formation efficiency of $\gtrsim 78$ per cent, and contrast strongly with the current diffuse nature of the galaxy. Since a nuclear starburst would lead to the rapid in-spiral of the GCs and is ruled out by the absence of a nuclear star cluster, we propose that the GCs plausibly formed during a major merger at $z\sim1.3$. The merger remnant must have undergone significant expansion of its stellar (and perhaps also its dark matter) component to reach its low present surface brightness, leading to the interesting possibility that it was the formation of DF2's extreme GC population that caused it to become a UDG. If true, this strong structural evolution would have important implications for understanding the origins of UDGs., Comment: 14 pages, 6 figures; Accepted for publication in MNRAS (June 17, 2021)

Linking globular clusters (GCs) to the assembly of their host galaxies is an overarching goal in GC studies. The inference of tight scaling relations between GC system properties and the mass of both the stellar and dark halo components of their host galaxies are indicative of an intimate physical connection, yet have also raised fundamental questions about how and when GCs form. Specifically, the inferred correlation between the mass of a GC system (Mgc) and the dark matter halo mass (Mhalo) of a galaxy has been posited as a consequence of a causal relation between the formation of dark matter mini-haloes and GC formation during the early epochs of galaxy assembly. We present the first results from a new simulation of a cosmological volume ($L=34.4$~cMpc on a side) from the E-MOSAICS suite, which includes treatments of the formation and evolution of GCs within the framework of a detailed galaxy formation model. The simulated Mgc-Mhalo relation is linear for halo masses $>5\times10^{11}~Msun$, and is driven by the hierarchical assembly of galaxies. Below this halo mass, the simulated relation features a downturn, which we show is consistent with observations, and is driven by the underlying stellar mass-halo mass relation of galaxies. Our fiducial model reproduces the observed Mgc-Mstar relation across the full mass range, which we argue is more physically relevant than the Mgc-Mhalo relation. We also explore the physical processes driving the observed constant value of $Mgc / Mhalo \sim 5\times10^{-5}$ and find that it is the result of a combination of cluster formation physics and cluster disruption., Comment: 13 pages, 9 figures, accepted for publication in MNRAS

Globular clusters (GCs) are typically old, with most having formed at z >~ 2. This makes understanding their birth environments difficult, as they are typically too distant to observe with sufficient angular resolution to resolve GC birth sites. Using 25 cosmological zoom-in simulations of Milky Way-like galaxies from the E-MOSAICS project, with physically-motivated models for star formation, feedback, and the formation, evolution, and disruption of GCs, we identify the birth environments of present-day GCs. We find roughly half of GCs in these galaxies formed in-situ (52.0 +/- 1.0 per cent) between z ~ 2 - 4, in turbulent, high-pressure discs fed by gas that was accreted without ever being strongly heated through a virial shock or feedback. A minority of GCs form during mergers (12.6 +/- 0.6 per cent in major mergers, and 7.2 +/- 0.5 per cent in minor mergers), but we find that mergers are important for preserving the GCs seen today by ejecting them from their natal, high density interstellar medium (ISM), where proto-GCs are rapidly destroyed due to tidal shocks from ISM substructure. This chaotic history of hierarchical galaxy assembly acts to mix the spatial and kinematic distribution of GCs formed through different channels, making it difficult to use observable GC properties to distinguish GCs formed in mergers from ones formed by smooth accretion, and similarly GCs formed in-situ from those formed ex-situ. These results suggest a simple picture of GC formation, in which GCs are a natural outcome of normal star formation in the typical, gas-rich galaxies that are the progenitors of present-day galaxies., Comment: 20 pages, 20 figures, resubmitted to MNRAS after accounting for referee's comments

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

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)

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)

It has been a long-standing open question why observed globular cluster (GC) populations of different metallicities differ in their ages and spatial distributions, with metal-poor GCs being the older and radially more extended of the two. We use the suite of 25 Milky Way-mass cosmological zoom-in simulations from the E-MOSAICS project, which self-consistently model the formation and evolution of stellar clusters and their host galaxies, to understand the properties of observed GC populations. We find that the different ages and spatial distributions of metal-poor and metal-rich GCs are the result of regular cluster formation at high redshift in the context of hierarchical galaxy assembly. We also find that metallicity on its own is not a good tracer of accretion, and other properties, such as kinematics, need to be considered., Comment: 4 pages, 2 figures, to appear in Proceedings IAU Symposium n. 351, "Star Clusters: From the Milky Way to the Early Universe", 2019

We present an analysis of young star clusters (YSCs) that form in the E-MOSAICS cosmological, hydrodynamical simulations of galaxies and their star cluster populations. Through comparisons with observed YSC populations, this work aims to test models for YSC formation and obtain an insight into the formation processes at work in part of the local galaxy population. We find that the models used in E-MOSAICS for the cluster formation efficiency and high-mass truncation of the initial cluster mass function ($M_\mathrm{c,\ast}$) both quantitatively reproduce the observed values of cluster populations in nearby galaxies. At higher redshifts ($z \geq 2$, near the peak of globular cluster formation) we find that, at a constant star formation rate (SFR) surface density, $M_\mathrm{c,\ast}$ is larger than at $z=0$ by a factor of four due to the higher gas fractions in the simulated high-redshift galaxies. Similar processes should be at work in local galaxies, offering a new way to test the models. We find that cluster age distributions may be sensitive to variations in the cluster formation rate (but not SFR) with time, which may significantly affect their use in tests of cluster mass loss. By comparing simulations with different implementations of cluster formation physics, we find that (even partially) environmentally-independent cluster formation is inconsistent with the brightest cluster-SFR and specific luminosity-$\Sigma_\mathrm{SFR}$ relations, whereas these observables are reproduced by the fiducial, environmentally-varying model. This shows that models in which a constant fraction of stars form in clusters are inconsistent with observations., Comment: 20 pages, 17 figures, accepted for publication in MNRAS

We present a simple physical model for the minimum mass of bound stellar clusters as a function of the galactic environment. The model evaluates which parts of a hierarchically-clustered star-forming region remain bound given the time-scales for gravitational collapse, star formation, and stellar feedback. We predict the initial cluster mass functions (ICMFs) for a variety of galaxies and we show that these predictions are consistent with observations of the solar neighbourhood and nearby galaxies, including the Large Magellanic Cloud and M31. In these galaxies, the low minimum cluster mass of $\sim10^2~\rm{M}_{\odot}$ is caused by sampling statistics, representing the lowest mass at which massive (feedback-generating) stars are expected to form. At the high gas density and shear found in the Milky Way's Central Molecular Zone and the nucleus of M82, the model predicts that a mass $>10^2~\rm{M}_{\odot}$ must collapse into a single cluster prior to feedback-driven dispersal, resulting in narrow ICMFs with elevated characteristic masses. We find that the minimum cluster mass is a sensitive probe of star formation physics due to its steep dependence on the star formation efficiency per free-fall time. Finally, we provide predictions for globular cluster (GC) populations, finding a narrow ICMF for dwarf galaxy progenitors at high redshift, which can explain the high specific frequency of GCs at low metallicities observed in Local Group dwarfs like Fornax and WLM. The predicted ICMFs in high-redshift galaxies constitute a critical test of the model, ideally-suited for the upcoming generation of telescopes., Comment: 24 pages, 14 figures. Accepted to MNRAS

We present the evolution of the rest-frame ultraviolet (UV) properties of the globular cluster (GC) populations and their host galaxies formed in the E-MOSAICS suite of cosmological hydrodynamical simulations. We compute the luminosities of all clusters associated with 25 simulated Milky Way-mass galaxies, discussed in previous works, in the rest-frame UV and optical bands by combining instantaneous cluster properties (age, mass, metallicity) with simple stellar population models, from redshifts $z=0$ to 10. Due to the rapid fading of young stellar populations in the UV, most of the simulated galaxies do not host GCs bright enough to be individually identified in deep Hubble Space Telescope (HST) observations, even in highly magnified systems. The median age of the most UV-luminous GCs is $<10$ Myr (assuming no extinction), increasing to $\gtrsim 100$ Myr for red optical filters. We estimate that these GCs typically only contribute a few per cent of the total UV luminosity of their host galaxies at any epoch. We predict that the number density of UV-bright proto-GCs (or cluster clumps) will peak between redshifts $z=1-3$. In the main progenitors of Milky Way-mass galaxies, $10$-$20$ per cent of the galaxies at redshifts $1 \lesssim z \lesssim 3$ have clusters brighter than $M_{\rm UV} < -15$, and less than $10$ per cent at other epochs. The brightest cluster in the galaxy sample at $z>2$ is typically $M_{\rm UV} \sim -16$, consistent with the luminosities of observed compact, high-redshift sources., Comment: 15 pages, 9 figures, accepted for publication in MNRAS (4 June 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)

Understanding the evolution of stellar clusters in an evolving tidal field is critical for studying the disruption of stellar clusters in a cosmological context. We systematically characterise the response of stellar clusters to tidal shocks using controlled N-body simulations of clusters with various properties that are subjected to different types of shocks. We find that the strength of the shock and the density of the cluster within the half-mass radius are the dominant properties that drive the amount of mass lost by the cluster, with the shape of the cluster profile being of minor influence. When the shock is applied as two separate sub-shocks, the amount of mass loss during the second sub-shock is sensitive to the gap time between them. Clusters that experience successive sub-shocks separated by less than their crossing time attain the same masses and sizes at the end of the simulation. However, clusters subjected to sub-shocks separated by more than a crossing time experience different evolutionary histories. The amount of mass lost in the N-body models and its scaling with shock and cluster properties differs from that predicted by classical tidal disruption theory. We demonstrate that the discrepancy is alleviated by including a dependence on the escape time-scale of unbound stars, analogously to mass loss driven by two-body relaxation. With our new theoretical model for shock-driven mass loss, the predicted relative amounts of mass loss agree with the results of the N-body simulations to ~0.3 dex across the full suite of simulations., Comment: 14 pages, 12 figures, 1 table, Accepted for publication in MNRAS

Stellar haloes encode a fossil record of a galaxy's accretion history, generally in the form of structures of low surface brightness, such as stellar streams. While their low surface brightness makes it challenging to determine their age, metallicity, kinematics and spatial structure, the infalling galaxies also deposit globular clusters (GCs) in the halo, which are bright and therefore easier to observe and characterise. To understand how GCs associated with stellar streams can be used to estimate the stellar mass and the infall time of their parent galaxy, we examine a subset of 15 simulations of galaxies and their star clusters from the E-MOSAICS project. E-MOSAICS is a suite of hydrodynamical simulations incorporating a sub-grid model for GC formation and evolution. We find that more massive accreted galaxies typically contribute younger and more metal rich GCs. This lower age results from a more extended cluster formation history in more massive galaxies. In addition, at fixed stellar mass, galaxies that are accreted later host younger clusters, because they can continue to form GCs without being subjected to environmental influences for longer. This explains the large range of ages observed for clusters associated with the Sagittarius dwarf galaxy in the halo of the Milky Way compared to clusters which are thought to have formed in satellites accreted early in the Milky Way's formation history. Using the ages of the GCs associated with the Sagittarius dwarf, we estimate a virial radius crossing lookback time (infall time) of $9.3 \pm 1.8 Gyr$., Comment: Accepted to MNRAS

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)

The metal-poor sub-population of globular cluster (GC) systems exhibits a correlation between the GC average colour and luminosity, especially in those systems associated with massive elliptical galaxies. More luminous (more massive) GCs are typically redder and hence more metal-rich. This 'blue tilt' is often interpreted as a mass-metallicity relation stemming from GC self-enrichment, whereby more massive GCs retain a greater fraction of the enriched gas ejected by their evolving stars, fostering the formation of more metal-rich secondary generations. We examine the E-MOSAICS simulations of the formation and evolution of galaxies and their GC populations, and find that their GCs exhibit a colour-luminosity relation similar to that observed in local galaxies, without the need to invoke mass-dependent self-enrichment. We find that the blue tilt is most appropriately interpreted as a dearth of massive, metal-poor GCs: the formation of massive GCs requires high interstellar gas surface densities, conditions that are most commonly fostered by the most massive, and hence most metal rich, galaxies, at the peak epoch of GC formation. The blue tilt is therefore a consequence of the intimate coupling between the small-scale physics of GC formation and the evolving properties of interstellar gas hosted by hierarchically-assembling galaxies., Comment: 24 pages, 11 figures. Accepted for publication in the Monthly Notices of the Royal Astronomical Society

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

We present a simple, self-consistent model to predict the maximum masses of giant molecular clouds (GMCs), stellar clusters and high-redshift clumps as a function of the galactic environment. Recent works have proposed that these maximum masses are set by shearing motions and centrifugal forces, but we show that this idea is inconsistent with the low masses observed across an important range of local-Universe environments, such as low-surface density galaxies and galaxy outskirts. Instead, we propose that feedback from young stars can disrupt clouds before the global collapse of the shear-limited area is completed. We develop a shear-feedback hybrid model that depends on three observable quantities: the gas surface density, the epicylic frequency, and the Toomre parameter. The model is tested in four galactic environments: the Milky Way, the Local Group galaxy M31, the spiral galaxy M83, and the high-redshift galaxy zC406690. We demonstrate that our model simultaneously reproduces the observed maximum masses of GMCs, clumps and clusters in each of these environments. We find that clouds and clusters in M31 and in the Milky Way are feedback-limited beyond radii of 8.4 and 4 kpc, respectively, whereas the masses in M83 and zC406690 are shear-limited at all radii. In zC406690, the maximum cluster masses decrease further due to their inspiral by dynamical friction. These results illustrate that the maximum masses change from being shear-limited to being feedback-limited as galaxies become less gas-rich and evolve towards low shear. This explains why high-redshift clumps are more massive than GMCs in the Local Universe., Comment: 17 pages, 12 figures; accepted by MNRAS (March 27, 2017)