E-MOSAICS Simulations Research Articles

The ages and metallicities of the globular clusters in the Sparkler

ABSTRACT JWST observations of the strongly lensed galaxy the Sparkler have revealed a population of gravitationally bound globular cluster (GC) candidates. Different analyses have resulted in broadly similar ages but significantly different metallicities, questioning the assembly history that has led to the formation of such a population. In this letter, we reanalyse the two sets of photometry available in the literature with the code mcmame especially tailored to fit physical properties of GCs. We find the ages and metallicities from both data sets are consistent within 1σ uncertainties. A significant group of GCs is consistent with being old and metal poor ([Fe/H] ∼ −1.7). For this group, the ages do not converge, hence, we conclude that they are definitively older than 1 Gyr and can be as old as the age of the Universe. The remaining GCs have younger ages and a metallicity spread. The ages and metallicities distribution of GCs in the Sparkler are consistent with those observed in Local Group’s galaxies at similar lookback times. Comparing with predictions from E-MOSAICS simulations we confirm that the Sparkler GC population traces the self-enrichment history of a galaxy which might become a few times 109 M⊙ massive system at redshift z = 0.

Constraining the shape of dark matter haloes with globular clusters and diffuse stellar light in the E-MOSAICS simulations

ABSTRACTWe 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 density of DM. We find that the dominant structures identified in the stellar light and GCs correspond closely with those from the DM. Our method is unaffected by the presence of satellites and its precision improves with fainter GC samples. We recover tight relations between the dimensionless profiles of stellar-to-DM surface density and GC-to-DM surface density, suggesting that the profile of DM can be accurately recovered from the stars and GCs (σ ≤ 0.5 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 semimajor axes of the distribution of stars and GCs are typically misaligned by ∼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⋆ ≥ 1010 M⊙, and the analysis will be applicable to future data from the Euclid, Roman, and the Rubin observatories

Radial distributions of globular clusters trace their host dark matter halo: insights from the E-MOSAICS simulations

ABSTRACT Globular clusters (GCs) are bright objects that span a wide range of galactocentric distances, and can therefore probe the structure of dark matter (DM) haloes. In this work, we explore whether the projected number density 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, metal-poor GC subpopulations tend to have shallower and more extended profiles than metal-rich subsamples, which we relate to the preferentially accreted origin of metal-poor GCs. We find strong correlations between the power-law 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, Navarro–Frenk–White 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 early-type galaxies 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.

The present-day globular cluster kinematics of lenticular galaxies from the E-MOSAICS simulations and their relation to the galaxy assembly histories

ABSTRACT We study the present-day rotational velocity (Vrot) and velocity dispersion (σ) profiles of the globular cluster (GC) systems in a sample of 50 lenticular (S0) galaxies from the E-MOSAICS galaxy formation simulations. We find that $82{{\ \rm per\ cent}}$ of the galaxies have GCs that are rotating along the photometric major axis of the galaxy (aligned), while the remaining $18{{\ \rm per\ cent}}$ of the galaxies do not (misaligned). This is generally consistent with the observations from the SLUGGS survey. For the aligned galaxies, classified as peaked and outwardly decreasing ($49{{\ \rm per\ cent}}$), flat ($24{{\ \rm per\ cent}}$), and increasing ($27{{\ \rm per\ cent}}$) based on the Vrot/σ profiles out to large radii, we do not find any clear correlation between these present-day Vrot/σ profiles of the GCs and the past merger histories of the S0 galaxies, unlike in previous simulations of galaxy stars. For just over half of the misaligned galaxies, we find that the GC misalignment is the result of a major merger within the last $10\, \mathrm{Gyr}$ so that the ex-situ GCs are misaligned by an angle between 0° (co-rotation) and 180° (counter-rotation), with respect to the in situ GCs, depending on the orbital configuration of the merging galaxies. For the remaining misaligned galaxies, we suggest that the in situ metal-poor GCs, formed at early times, have undergone more frequent kinematic perturbations than the in situ metal-rich GCs. We also find that the GCs accreted early and the in situ GCs are predominantly located within 0.2 virial radii (R200) from the centre of galaxies in 3D phase-space diagrams.

The physics governing the upper truncation mass of the globular cluster mass function

ABSTRACT 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 Mc, *. 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 ($M_{\mathrm{200}} = 5.14 \times 10^{13} \, {\rm M}_{\odot }$) in the E-MOSAICS simulations. The fiducial cluster formation model in E-MOSAICS reproduces the observed trend of Mc, * with M* for the Virgo cluster. We therefore examine the origin of the relation by fitting Mc, * 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 Mc, *-M* relation is flat above $M_* \gt 10^{10}\, {\rm M}_{\odot }$. It is therefore the disruption of high-mass GCs in galaxies with $M_{*}\sim 10^{10} \, {\rm M}_{\odot }$ that lowers the Mc, * 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 Mc, * − M* relation is therefore a consequence of both the formation conditions of massive star clusters and their environmentally dependent disruption mechanisms.

The kinematics of globular cluster populations in the E-MOSAICS simulations and their implications for the assembly history of the Milky Way

ABSTRACT We present a detailed comparison of the Milky Way (MW) globular cluster (GC) kinematics with the 25 MW-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 ($[\rm {Fe}/\rm {H}] \gt -1.2$) versus metal-poor ($[\rm {Fe}/\rm {H}] \lt -1.2$) and inner (r < 8 kpc) versus outer (r > 8 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 ± 1.2 early ($z$ = 3.1 ± 1.3) major mergers. 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.

Predicting accreted satellite galaxy masses and accretion redshifts based on globular cluster orbits in the E-MOSAICS simulations

ABSTRACT 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 MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE 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 ∼ 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.

The globular cluster system mass–halo mass relation in the E-MOSAICS simulations

ABSTRACT 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 × 1011 M⊙, 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–M⋆ 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 $\hbox{$M_{\rm GC}$}/ \hbox{$M_{\rm halo}$}\sim 5\times 10^{-5}$ and find that it is the result of a combination of cluster formation physics and cluster disruption.

Kraken reveals itself – the merger history of the Milky Way reconstructed with the E-MOSAICS simulations

ABSTRACT 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: 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⋆ = (0.6–4.6) × 108 M⊙], but have widely different accretion redshifts ($\mbox{$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 $\mbox{$r_{M_\star }$}=1$:$31^{+34}_{-16}$ and $\mbox{$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⋆, tot/M⊙) = 9.0 ± 0.1, similar to the stellar halo. This implies that the Milky Way grew its stellar mass mostly by in-situ star formation. We conclude by organizing these accretion events into the most detailed reconstruction to date of the Milky Way’s merger tree.

Where did the globular clusters of the Milky Way form? Insights from the E-MOSAICS simulations

ABSTRACT 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.

The mass fraction of halo stars contributed by the disruption of globular clusters in the E-MOSAICS simulations

ABSTRACT 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 × 103 and 105 M⊙, respectively, with the 25–75th 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 subdominant 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.

The [α/Fe]–[Fe/H] relation in the E-MOSAICS simulations: its connection to the birth place of globular clusters and the fraction of globular cluster field stars in the bulge

ABSTRACT The α-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 [α/Fe]–[Fe/H] distribution of field stars and GCs in 25 Milky Way–mass galaxies. The [α/Fe]–[Fe/H] distribution of GCs largely follows that of the field stars and can also therefore be used as tracers of the [α/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 [α/Fe] at fixed [Fe/H]. Therefore, if a GC is observed to have low [α/Fe] for its [Fe/H] there is an increased possibility that this GC was accreted recently alongside a dwarf galaxy. There is a wide range of shapes for the field star [α/Fe]–[Fe/H] distribution, with a notable subset of galaxies exhibiting bimodal distributions, in which the high [α/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 and 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.

Young star cluster populations in the E-MOSAICS simulations

ABSTRACT 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 ($M_\rm {c,\ast }$) both quantitatively reproduce the observed values of cluster populations in nearby galaxies. At higher redshifts (z ≥ 2, near the peak of globular cluster formation) we find that, at a constant star formation rate (SFR) surface density, $M_\rm {c,\ast }$ 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-$\Sigma _\rm {SFR}$ 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.

The evolution of the UV luminosity function of globular clusters in the E-MOSAICS simulations

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.

Formation histories of stars, clusters, and globular clusters in the E-MOSAICS simulations

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.

Fossil stellar streams and their globular cluster populations in the E-MOSAICS simulations

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 $9.3 \pm 1.8 Gyr$.

Dynamical cluster disruption and its implications for multiple population models in the E-MOSAICS simulations

ABSTRACT 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 &amp;gt;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 e-mosaics 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\gt 10^5 $ M⊙ 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.