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Jean P. Brodie

Publications and source records attributed to Jean P. Brodie.

At least 37 records · Page 2Linked to original sources

Comparing E-MOSAICS predictions of high-redshift proto-globular clusters with JWST observations in lensed galaxies

High-resolution imaging and strong gravitational lensing of high-redshift galaxies have enabled the detection of compact sources with properties similar to nearby massive star clusters. Often found to be very young, these sources may be globular clusters detected in their earliest stages. In this work, we compare predictions of high-redshift ($z \sim 1$--$10$) star cluster properties from the E-MOSAICS simulation of galaxy and star cluster formation with those of the star cluster candidates in strongly lensed galaxies from James Webb (JWST) and Hubble Space Telescope (HST) imaging. We select galaxies in the simulation that match the luminosities of the majority of lensed galaxies with star cluster candidates observed with JWST. We find that the luminosities, ages and masses of the brightest star cluster candidates in the high-redshift galaxies are consistent with the E-MOSAICS model. In particular, the brightest cluster ages are in excellent agreement. The results suggest that star clusters in both low- and high-redshift galaxies may form via common mechanisms. However, the brightest clusters in the lensed galaxies tend to be $\approx 1$--$1.5$ mag brighter and $\approx 0.5$ dex more massive than the median E-MOSAICS predictions. We discuss the large number of effects that could explain the discrepancy, including simulation and observational limitations, stellar population models, cluster detection biases and nuclear star clusters. Understanding these limitations would enable stronger tests of globular cluster formation models.

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A census of dwarf galaxy satellites around LMC-mass galaxy NGC 2403

We present the first comprehensive census of the satellite population around a Large Magellanic Cloud (LMC) stellar-mass galaxy, as part of the Magellanic Analog Dwarf Companions and Stellar Halos (MADCASH) survey. We have surveyed NGC 2403 (D=3.0 Mpc) with the Subaru/Hyper Suprime-Cam imager out to a projected radius of 90 kpc (with partial coverage extending out to ~110 kpc, or ~80% of the virial radius of NGC 2403), resolving stars in the uppermost ~2.5 mags of its red giant branch. By looking for stellar overdensities in the red giant branch spatial density map, we identify 149 satellite candidates, of which only the previously discovered MADCASH J074238+65201-dw is a bona fide dwarf, together with the more massive and disrupting satellite DDO 44. We carefully assess the completeness of our search via injection of artificial dwarf galaxies into the images, finding that we are reliably sensitive to candidates down to M_V ~ -7.5 mag (and somewhat sensitive to even fainter satellites). A comparison of the satellite luminosity function of NGC 2403 down to this magnitude limit to theoretical expectations shows overall good agreement. This is the first of a full sample of 11 Magellanic Cloud-mass host galaxies we will analyze, creating a statistical sample that will provide the first quantitative constraints on hierarchical models of galaxy formation around low-mass hosts.

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The PIPER Survey. II. The Globular Cluster Systems of Low Surface Brightness Galaxies in the Perseus Cluster

We present Hubble Space Telescope ACS/WFC and WFC3/UVIS imaging for a sample of 50 low surface brightness (LSB) galaxies in the $\sim$10$^{15}$ M$_{\odot}$ Perseus cluster, which were originally identified in ground-based imaging. We measure the structural properties of these galaxies and estimate the total number of globular clusters (GCs) they host. Around half of our sample galaxies meet the strict definition of an ultra-diffuse galaxy (UDG), while the others are UDG-like but are either somewhat more compact or slightly brighter. A small number of galaxies reveal systems with many tens of GCs, rivalling some of the richest GC systems known around UDGs in the Coma cluster. We find the sizes of rich GC systems, in terms of their half-number radii, extending to $\sim$1.2 times the half-light radii of their host galaxy on average. The mean colours of the GC systems are the same, within the uncertainties, as those of their host galaxy stars. This suggests that GCs and galaxy field stars may have formed at the same epoch from the same enriched gas. It may also indicate a significant contribution from disrupted GCs to the stellar component of the host galaxy as might be expected in the 'failed galaxy' formation scenario for UDGs.

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Keck/KCWI Spectroscopy of Globular Clusters in Local Volume Dwarf Galaxies

A number of nearby dwarf galaxies have globular cluster (GC) candidates that require spectroscopic confirmation. Here we present Keck telescope spectra for 15 known GCs and GC candidates that may be associated with a host dwarf galaxy, and an additional 3 GCs in the halo of M31 that are candidates for accretion from a now disrupted dwarf galaxy. We confirm 6 star clusters (of intermediate-to-old age) to be associated with NGC~247. The vast bulk of its GC system remains to be studied spectroscopically. We also confirm the GC candidates in F8D1 and DDO190, finding both to be young star clusters. The 3 M31 halo GCs all have radial velocities consistent with M31, are old and very metal-poor. Their ages and metallicities are consistent with accretion from a low mass satellite galaxy. Finally, three objects are found to be background galaxies -- two are projected near NGC~247 and one (candidate GCC7) is near the IKN dwarf. The IKN dwarf thus has only 5 confirmed GCs but still a remarkable specific frequency of 124.

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Analysis of Galaxies at the Extremes: A Kinematic Analysis of the Virgo Cluster Dwarfs VCC 9 and VCC 1448 using the Keck Cosmic Web Imager

We present spatially resolved Keck Cosmic Web Imager stellar spectroscopy of the Virgo cluster dwarf galaxies VCC 9 and VCC 1448. These galaxies have similar stellar masses and large half-light radii but very different globular cluster (GC) system richness ($\sim$25 vs. $\sim$99 GCs). Using the KCWI data, we spectroscopically confirm 10 GCs associated with VCC 1448 and one GC associated with VCC 9. We make two measurements of dynamical mass for VCC 1448 based on the stellar and GC velocities respectively. VCC 1448's mass measurements suggest that it resides in a halo in better agreement with the expectation of the stellar mass -- halo mass relationship than the expectation from its large GC counts. For VCC 9, the dynamical mass we measure agrees with the expected halo mass from both relationships. We compare VCC 1448 and VCC 9 to the GC-rich galaxy Dragonfly 44 ($\sim74$ GCs), which is similar in size but has $\sim 1$ dex less stellar mass than either Virgo galaxy. In dynamical mass -- GC number space, Dragonfly 44 and VCC 1448 exhibit richer GC systems given their dynamical mass than that of VCC 9 and other `normal' galaxies. We also place the galaxies in kinematics -- ellipticity space finding evidence of an anticorrelation between rotational support and the fraction of a galaxy's stellar mass in its GC system. i.e., VCC 9 is more rotationally supported than VCC 1448, which is more rotationally supported than Dragonfly 44. This trend may be expected if a galaxy's GC content depends on its natal gas properties at formation.

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A Catalogue and Analysis of Ultra-Diffuse Galaxy Spectroscopic Properties

In order to help facilitate the future study of ultra-diffuse galaxies (UDGs) we compile a catalogue of their spectroscopic properties. Using it, we investigate some of the biases inherent in the current UDG sample that have been targeted for spectroscopy. In comparison to a larger sample of UDGs studied via their spectral energy distributions (SED), current spectroscopic targets are intrinsically brighter, have higher stellar mass, are larger, more globular cluster-rich, older, and have a wider spread in their metallicities. In particular, many spectroscopically studied UDGs have a significant fraction of their stellar mass contained within their globular cluster (GC) system. We also search for correlations between parameters in the catalogue. Of note is a correlation between alpha element abundance and metallicity as may be expected for a `failed galaxy' scenario. However, the expected correlations of metallicity with age are not found and it is unclear if this is evidence against a `failed galaxy' scenario or simply due to the low number statistics and the presence of outliers. Finally, we attempt to segment our catalogue into different classes using a machine learning K-means method. We find that the clustering is very weak and that it is currently not warranted to split the catalogue into multiple, distinct sub-populations. Our catalogue is available online and we aim to maintain it beyond the publication of this work.

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Origin of the correlation between stellar kinematics and globular cluster system richness in ultra-diffuse galaxies

Observational surveys have found that the dynamical masses of ultra-diffuse galaxies (UDGs) correlate with the richness of their globular cluster (GC) system. This could be explained if GC-rich galaxies formed in more massive dark matter haloes. We use simulations of galaxies and their GC systems from the E-MOSAICS project to test whether the simulations reproduce such a trend. We find that GC-rich simulated galaxies in galaxy groups have enclosed masses that are consistent with the dynamical masses of observed GC-rich UDGs. However, simulated GC-poor galaxies in galaxy groups have higher enclosed masses than those observed. We argue that GC-poor UDGs with low stellar velocity dispersions are discs observed nearly face on, such that their true mass is underestimated by observations. Using the simulations, we show that galactic star-formation conditions resulting in dispersion-supported stellar systems also leads to efficient GC formation. Conversely, conditions leading to rotationally-supported discs leads to inefficient GC formation. This result may explain why early-type galaxies typically have richer GC systems than late-type galaxies. This is also supported by comparisons of stellar axis ratios and GC specific frequencies in observed dwarf galaxy samples, which show GC-rich systems are consistent with being spheroidal, while GC-poor systems are consistent with being discs. Therefore, particularly for GC-poor galaxies, rotation should be included in dynamical mass measurements from stellar dynamics.

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Constraining the stellar populations of ultra-diffuse galaxies in the MATLAS survey using spectral energy distribution fitting

We use spectral energy distribution (SED) fitting to place constraints on the stellar populations of 59 ultra-diffuse galaxies (UDGs) in the low-to-moderate density fields of the MATLAS survey. We use the routine PROSPECTOR, coupled with archival data in the optical from DECaLS, and near- and mid-infrared imaging from WISE, to recover the stellar masses, ages, metallicities and star formation timescales of the UDGs. We find that a subsample of the UDGs lies within the scatter of the mass-metallicity relation (MZR) for local classical dwarfs. However, another subsample is more metal-poor, being consistent with the evolving MZR at high-redshift. We investigate UDG positioning trends in the mass-metallicity plane as a function of surface brightness, effective radius, axis ratio, local volume density, mass-weighted age, star formation timescale, globular cluster (GC) counts and GC specific frequency. We find that our sample of UDGs can be separated into two main classes. Class A: Comprised of UDGs with lower stellar masses, prolonged star formation histories (SFHs), more elongated, inhabiting less dense environments, hosting fewer GCs, younger, consistent with the classical dwarf MZR, and fainter. Class B: UDGs with higher stellar masses, rapid SFHs, rounder, inhabiting the densest of our probed environments, hosting on average the most numerous GC systems, older, consistent with the high-redshift MZR (i.e., consistent with early-quenching), and brighter. The combination of these properties suggests that UDGs of Class A are consistent with a `puffed-up dwarf' formation scenario, while UDGs of Class B seem to be better explained by `failed galaxy' scenarios.

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The star formation histories of quiescent ultra-diffuse galaxies and their dependence on environment and globular cluster richness

We derive the stellar population parameters of 11 quiescent ultra-diffuse galaxies (UDGs) from Keck/KCWI data. We supplement these with 14 literature UDGs, creating the largest spectroscopic sample of UDGs to date (25). We find a strong relationship between their $α$-enhancement and their star formation histories: UDGs that formed on very short timescales have elevated [Mg/Fe] abundance ratios, whereas those forming over extended periods present lower values. Those forming earlier and faster are overall found in high-density environments, being mostly early infalls into the cluster. No other strong trends are found with infall times. We analyze the stellar mass-metallicity, age-metallicity and [Mg/Fe]-metallicity relations of the UDGs, comparing them to other types of low mass galaxies. Overall, UDGs scatter around the established stellar mass--metallicity relations of classical dwarfs. We find that GC-rich UDGs have intermediate-to-old ages, but previously reported trends of galaxy metallicity and GC richness are not reproduced with this spectroscopic sample due to the existence of GC-rich UDGs with elevated metallicities. In addition, we also find that a small fraction of UDGs could be 'failed-galaxies', supported by their GC richness, high $α$-abundances, fast formation timescales and that they follow the mass-metallicity relation of z~2 galaxies. Finally, we also compare our observations to simulated UDGs. We caution that there is not a single simulation that can produce the diverse UDG properties simultaneously, in particular the low metallicity failed-galaxy like UDGs.

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Initial mass function variability from the integrated light of diverse stellar systems

We present a uniform analysis of the stellar initial mass function (IMF) from integrated light spectroscopy of 15 compact stellar systems (11 globular clusters in M31 and 4 ultra compact dwarfs in the Virgo cluster, UCDs) and two brightest Coma cluster galaxies (BCGs), covering a wide range of metallicities ($-$1.7 $<$ [Fe/H] $<$ 0.01) and velocity dispersions (7.4 km~s$^{-1}$ $< σ<$ 275 km~s$^{-1}$). The S/N $\sim 100$ Å$^{-1}$ Keck LRIS spectra are fitted over the range $4000<λ/\mboxÅ<10,000$ with flexible, full-spectrum stellar population synthesis models. We use the models to fit simultaneously for ages, metallicities, and individual elemental abundances of the population, allowing us to decouple abundance variations from variations in IMF slope. We show that compact stellar systems do not follow the same trends with physical parameters that have been found for early-type galaxies. Most globular clusters in our sample have an IMF consistent with that of the Milky Way, over a wide range of [Fe/H] and [Mg/Fe]. There is more diversity among the UCDs, with some showing evidence for a bottom-heavy IMF, but with no clear correlation with metallicity, abundance, or velocity dispersion. The two Coma BCGs have similar velocity dispersion and metallicity, but we find the IMF of NGC~4874 is consistent with that of the Milky Way while NGC~4889 presents evidence for a significantly bottom-heavy IMF. For this sample, the IMF appears to vary between objects in a way that is not explained by a single metallicity-dependent prescription.

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Keck Spectroscopy of NGC 1052-DF9: Stellar Populations in the Context of the NGC 1052 Group

In this study, we use Keck/KCWI spectroscopy to measure the age, metallicity and recessional velocity of NGC~1052-DF9 (DF9), a dwarf galaxy in the NGC~1052 group. We compare these properties to those of two other galaxies in the group, NGC~1052-DF2 and NGC~1052-DF4, which have low dark matter content. The three galaxies are proposed constituents of a trail of galaxies recently hypothesised to have formed as part of a ``bullet dwarf'' collision. We show that the ages and total metallicities of the three galaxies are within uncertainties of one another which may be expected if they share a related formation pathway. However, the recessional velocity we recover for DF9 (1680 $\pm$ 10 km s$^{-1}$) is higher than predicted for a linearly projected interpretation of the ``bullet dwarf'' trail. DF9 is then either not part of the trail or the correlation of galaxy velocities along the trail is not linear in 2D projection due to their 3D geometry. After examining other proposed formation pathways for the galaxies, none provide a wholly satisfactory explanation for all of their known properties. We conclude further work is required to understand the formation of this interesting group of galaxies.

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The large-scale structure of globular clusters in the NGC 1052 group

Prompted by the many controversial claims involving the NGC 1052 group, including that it hosts two dark matter-free galaxies with overluminous and monochromatic globular cluster (GC) systems, here we map out the large-scale structure (LSS) of GCs over the entire group. To recover the LSS, we use archival optical CFHT imaging data. We recover two GC density maps, one based on universal photometric properties of GCs from simple stellar population models, and one based on the properties of spectroscopically confirmed GCs in DF2 and DF4 (the two dwarf galaxies with overluminous GC populations). Both selection methods reveal overdensities around the massive galaxies in the group, as well as around NGC 1052 itself, that are coincident with the positions of previously identified stellar streams and tidal features. No intragroup GCs are found connecting these structures to any of the dwarf galaxies. We find, however, two other dwarfs in the group hosting GC systems. These include RCP32 with 2 GCs with ages equivalent to the GCs around NGC 1052, and DF9 with 3 GCs with ages similar to the GCs around DF2 and DF4. We conclude that the GC distribution in the group does not strongly support any formation scenario in particular. It favours, nonetheless, scenarios relying on galaxy-galaxy interactions and on the coeval formation of GCs around the DM-free dwarf galaxies. These may include the recently proposed bullet-dwarf formation, as well as high-redshift tidal dwarf galaxy models.

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Keck Spectroscopy of the Coma Cluster Ultra-Diffuse Galaxy Y358: Dynamical Mass in a Wider Context

We examine ultra-diffuse galaxies (UDGs) and their relation to non-UDGs in mass-radius-luminosity space. We begin by publishing Keck/KCWI spectroscopy for the Coma cluster UDG Y358, for which we measure both a recessional velocity and velocity dispersion. Our recessional velocity confirms association with the Coma cluster and Y358's status as a UDG. From our velocity dispersion (19 $\pm$ 3 km s$^{-1}$) we calculate a dynamical mass within the half-light radius which provides evidence for a core in Y358's dark matter halo. We compare this dynamical mass, along with those for globular cluster (GC)-rich/-poor UDGs in the literature, to mass profiles for isolated, gas-rich UDGs and UDGs in the NIHAO/FIRE simulations. We find GC-poor UDGs have dynamical masses similar to isolated, gas-rich UDGs, suggesting an evolutionary pathway may exist between the two. Conversely, GC-rich UDGs have dynamical masses too massive to be easily explained as the evolution of the isolated, gas-rich UDGs. The simulated UDGs match the dynamical masses of the GC-rich UDGs. However, once compared in stellar mass -- halo mass space, the FIRE/NIHAO simulated UDGs do not match the halo masses of either the isolated, gas-rich UDGs or the GC-rich UDGs at the same stellar mass. Finally, we supplement our data for Y358 with other UDGs that have measured velocity dispersions in the literature. We compare this sample to a wide range of non-UDGs in mass-radius-luminosity space, finding UDGs have a similar locus to non-UDGs of similar luminosity with the primary difference being their larger half-light radii.

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The stellar populations of quiescent ultra-diffuse galaxies from optical to mid-infrared spectral energy distribution fitting

We use spectral energy distribution (SED) fitting to place constraints on the stellar population properties of 29 quiescent ultra-diffuse galaxies (UDGs) across different environments. We use the fully Bayesian routine PROSPECTOR coupled with archival data in the optical, near, and mid-infrared from Spitzer and WISE under the assumption of an exponentially declining star formation history. We recover the stellar mass, age, metallicity, dust content, star formation time scales and photometric redshifts (photo-zs) of the UDGs studied. Using the mid-infrared data, we probe the existence of dust in UDGs. Although its presence cannot be confirmed, we find that the inclusion of small amounts of dust in the models brings the stellar populations closer to those reported with spectroscopy. Additionally, we fit the redshifts of all galaxies. We find a high accuracy in recovering photo-zs compared to spectroscopy, allowing us to provide new photo-z estimates for three field UDGs with unknown distances. We find evidence of a stellar population dependence on the environment, with quiescent field UDGs being systematically younger than their cluster counterparts. Lastly, we find that all UDGs lie below the mass--metallicity relation for normal dwarf galaxies. Particularly, the globular cluster (GC)-poor UDGs are consistently more metal-rich than GC-rich ones, suggesting that GC-poor UDGs may be puffed-up dwarfs, while most GC-rich UDGs are better explained by a failed galaxy scenario. As a byproduct, we show that two galaxies in our sample, NGC 1052-DF2 and NGC 1052-DF4, share equivalent stellar population properties, with ages consistent with 8 Gyr. This finding supports formation scenarios where the galaxies were formed together.

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Low-density star cluster formation: discovery of a young faint fuzzy on the outskirts of the low-mass spiral galaxy NGC 247

The classical globular clusters found in all galaxy types have half-light radii of $r_{\rm h} \sim$ 2-4 pc, which have been tied to formation in the dense cores of giant molecular clouds. Some old star clusters have larger sizes, and it is unclear if these represent a fundamentally different mode of low-density star cluster formation. We report the discovery of a rare, young "faint fuzzy" star cluster, NGC 247-SC1, on the outskirts of the low-mass spiral galaxy NGC 247 in the nearby Sculptor group, and measure its radial velocity using Keck spectroscopy. We use Hubble Space Telescope imaging to measure the cluster half-light radius of $r_{\rm h} \simeq 12$ pc and a luminosity of $L_V \simeq 4\times10^5 \mathrm{L}_\odot$. We produce a colour-magnitude diagram of cluster stars and compare to theoretical isochrones, finding an age of $\simeq$ 300 Myr, a metallicity of [$Z$/H] $\sim -0.6$ and an inferred mass of $M_\star \simeq 9\times10^4 \mathrm{M}_\odot$. The narrow width of blue-loop star magnitudes implies an age spread of $\lesssim$ 50 Myr, while no old red-giant branch stars are found, so SC1 is consistent with hosting a single stellar population, modulo several unexplained bright "red straggler" stars. SC1 appears to be surrounded by tidal debris, at the end of a $\sim$ 2 kpc long stellar filament that also hosts two low-mass, low-density clusters of a similar age. We explore a link between the formation of these unusual clusters and an external perturbation of their host galaxy, illuminating a possible channel by which some clusters are born with large sizes.

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The globular clusters and star formation history of the isolated, quiescent ultra-diffuse galaxy DGSAT I

We investigate the isolated, quiescent ultra-diffuse galaxy (UDG) DGSAT I and its globular cluster (GC) system using two orbits of Hubble Space Telescope Advanced Camera for Surveys imaging in the F606W and F814W filters. This is the first study of GCs around a UDG in a low-density environment. DGSAT I was previously found to host an irregular blue low surface brightness clump, that we confirm as very likely belonging to the galaxy rather than being a chance projection, and represents a recent episode of star formation (${\sim}500~\mathrm{Myr}$) that challenges some UDG formation scenarios. We select GC candidates based on colours and magnitudes, and construct a self consistent model of the GC radial surface density profile along with the background. We find a half-number radius of $R_\mathrm{GC} = 2.7\pm0.1~\mathrm{kpc}$ (more compact than the diffuse starlight) and a total of $12 \pm 2$ GCs. The total mass fraction in GCs is relatively high, supporting an overmassive dark matter halo as also implied by the high velocity dispersion previously measured. The GCs extend to higher luminosities than expected, and have colours that are unusually similar to their host galaxy colour, with a very narrow spread--all of which suggest an early, intense burst of cluster formation. The nature and origin of this galaxy remain puzzling, but the most likely scenario is a "failed galaxy" that formed relatively few stars for its halo mass, and could be related to cluster UDGs whose size and quiescence pre-date their infall.

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Low-Metallicity Globular Clusters in the Low-Mass Isolated Spiral Galaxy NGC 2403

The globular cluster (GC) systems of low-mass late-type galaxies, such as NGC 2403, have been poorly studied to date. As a low mass galaxy (M$_{\ast}$ = 7 $\times$ 10$^{9}$ M$_{\odot}$), cosmological simulations predict NGC 2403 to contain few, if any, accreted GCs. It is also isolated, with a remarkably undisturbed HI disk. Based on candidates from the literature, Sloan Digital Sky Survey and Hyper Suprime-Cam imaging, we selected several GCs for follow-up spectroscopy using the Keck Cosmic Web Imager. From their radial velocities, and other properties, we identify 8 bona-fide GCs associated with either the inner halo or the disk of this bulgeless galaxy. A stellar population analysis suggests a wide range of GC ages from shortly after the Big Bang until the present day. We find all of the old GCs to be metal-poor with [Fe/H] $\le$ --1. The age--metallicity relation for the observed GCs suggests that they were formed over many Gyr from gas with a low effective yield, similar to that observed in the SMC. Outflows of enriched material may have contributed to the low yield. With a total system of $\sim$50 GCs expected, our study is the first step in fully mapping the star cluster history of NGC 2403 in both space and time.

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

We study the present-day rotational velocity ($V_{rot}$) 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% of the galaxies have GCs that are rotating along the photometric major axis of the galaxy ($aligned$), while the remaining 18% 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%), $flat$ (24%) and $increasing$ (27%) based on the $V_{rot}/σ$ profiles out to large radii, we do not find any clear correlation between these present-day $V_{rot}/σ$ 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 Gyr so that the $ex$-$situ$ GCs are misaligned by an angle between 0° (co-rotation) to 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 ($R_{200}$) from the centre of galaxies in 3D phase-space diagrams.

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