Globular Cluster Formation Research Articles

Spectro-photometry and radial distribution of multiple stellar populations in globular clusters from gaia XP spectra

Abstract Understanding the formation of multiple populations in globular clusters (GCs) represents a challenge for stellar population studies. Nevertheless, the outermost cluster regions, likely to hold clues about the initial configuration of GC stars, remain underexplored. We use synthetic spectra reflecting the chemical compositions of first- and second-population (1P, 2P) stars in 47 Tucanae to identify spectral regions sensitive to these populations. This led us to define new photometric bands that effectively distinguish 1P and 2P giant stars using Gaia XP spectra. Testing these filters, we constructed the pseudo two-color diagrams dubbed chromosome maps (ChMs) and, for the first time, identified 1P and 2P stars in the cluster’s outermost regions and beyond its tidal radius. We constructed similar diagrams for NGC 3201, NGC 6121, NGC 6752, and NGC 6397, thus exploring GCs with different metallicities. The ChMs effectively distinguished multiple populations in the outer regions of all clusters, except for the metal-poor NGC 6397. Our findings, together with literature results from more-internal regions, show that the 2P stars of 47 Tucanae are more-centrally concentrated than the 1P. A similar pattern is seen for 2P stars with extreme chemical composition of NGC 3201. The multiple populations of NGC 6121, and NGC 6752 share the same radial distributions. These radial behaviors are consistent with the GC formation scenarios where 2P stars originate in the central regions. Noticeably, results on NGC 3201 are in tension with the conclusion from recent work that its 1P is more centrally concentrated than the 2P and might form with more central concentration.

Forecasting the Population of Globular Cluster Streams in Milky Way–type Galaxies

Thin stellar streams originating from globular clusters (GCs) are among the most sensitive tracers of low-mass dark matter subhalos. Joint analysis of the entire population of stellar streams will place the most robust constraints on the dark matter subhalo mass function, and therefore the nature of dark matter. Here we use a hierarchical model of GC formation to forecast the total number, masses, and radial distribution of dissolved GC in Milky Way–like galaxies. Furthermore, we generate mock stellar streams from these progenitors’ orbital histories taking into account the clusters’ formation and accretion times, mass, and metallicity. Out of ∼10,000 clusters more massive than 104 M ⊙, ∼9000 dissolved in the central bulge and are fully phase mixed at the present, while the remaining ∼1000 survive as coherent stellar streams. This suggests that the current census of ∼80 GC streams in the Milky Way is severely incomplete. Beyond 15 kpc from the Galactic center we are missing ∼100 streams, of which the vast majority are from accreted GCs. Deep Rubin photometry (g ≲ 27.5) would be able to detect these streams, even the most distant ones beyond >75 kpc. We also find that M31 will have an abundance of streams at galactocentric radii of 30–100 kpc. We conclude that future surveys will find a multitude of stellar streams from GCs, which can be used for dark matter subhalo searches.

Massive star cluster formation

The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the TORCH framework, which uses the Astrophysical MUltipurpose Software Environment (AMUSE) to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgraded TORCH by implementing the N-body code PETAR, thereby enabling TORCH to handle massive clusters forming from 106 M⊙ clouds with ≥105 individual stars. We present results from TORCH simulations of star clusters forming from 104, 105, and 106 M⊙ turbulent spherical gas clouds (named M4, M5, M6) of radius R = 11.7 pc. We find that star formation is highly efficient and becomes more so at a higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities 2.325 × 101,2,3 M⊙ pc−2, after a free-fall time of tff = 6.7,2.1,0.67 Myr, we find that ∼30%, 40%, and 60% of the cloud mass has formed into stars, respectively. The end of simulation-integrated star formation efficiencies for M4, M5, and M6 are ϵ⋆ = M⋆/Mcloud = 36%, 65%, and 85%. Observations of nearby clusters similar in mass and size to M4 have instantaneous star formation efficiencies of ϵinst ≤ 30%, which is slightly lower than the integrated star formation efficiency of M4. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense (Σ ≥ 102 M⊙ pc−2) and massive (Mcloud ≥ 105 M⊙). In such environments, stellar feedback from winds and radiation is not strong enough to counteract the gravity from gas and stars until a majority of the gas has formed into stars.

Tidal mass loss in the Fornax dwarf spheroidal galaxy through N-body simulations with Gaia DR3-based orbits

Aims. The Fornax dwarf spheroidal galaxy (dSph) represents a challenge for some globular cluster (GC) formation models, because an exceptionally high fraction of its stellar mass is locked in its GC system. In order to shed light on our understanding of GC formation, we aim to constrain the amount of stellar mass that Fornax has lost via tidal interaction with the Milky Way (MW). Methods. Exploiting the flexibility of effective multi-component N-body simulations and relying on state-of-the-art estimates of Fornax’s orbital parameters, we study the evolution of the mass distribution of the Fornax dSph in observationally justified orbits in the gravitational potential of the MW over 12 Gyr. Results. We find that, though the dark-matter mass loss can be substantial, the fraction of stellar mass lost by Fornax to the MW is always negligible, even in the most eccentric orbit considered. Conclusions. We conclude that stellar-mass loss due to tidal stripping is not a plausible explanation for the unexpectedly high stellar mass of the GC system of the Fornax dSph and we discuss quantitatively the implications for GC formation scenarios.

Low-mass Globular Clusters from Stripped Dark Matter Halos

The origin and formation of globular clusters (GCs) has remained a mystery. We present a formation scenario for ancient GC-like objects that form in ultrahigh-resolution simulations (smallest cell size < 0.1 pc, mass resolution M cell = 4 M ⊙). The simulations are cosmological zoom-in simulations of dwarf galaxies within the stellar mass range 106−7 M ⊙ that match Local Group dwarf properties well. Our investigation reveals GCs hosting ancient stellar populations, characterized by a lack of dark matter (DM) in the present epoch. The clusters exhibit short, episodic star formation histories, occasionally marked by the presence of multiple stellar generations. The metallicity distributions show a widening, encompassing stars in the range of 10−4 < Z ⋆/Z ⊙ < 1. The presence of these objects is attributable to star formation occurring within low-mass DM halos (M halo ≈ 106 M ⊙) during the early stages of the Universe, preceding reionization (z ≳ 7). As these clusters are accreted into dwarf galaxies, DM is preferentially subjected to tidal stripping, with an average accretion redshift of z¯≈5 .

Simulations predict intermediate-mass black hole formation in globular clusters.

Intermediate-mass black holes (IMBHs) are those between 100 and 105 solar masses (M⨀); their formation process is debated. One potential origin is the growth of less massive black holes, by merging with stars and compact objects within globular clusters (GCs). However, previous simulations have indicated that this process only produces IMBHs <500 M⨀, before gravitational wave recoil ejects them from the GC. We perform star-by-star simulations of GC formation, finding that high-density star formation in a GC's parent giant molecular cloud can produce sufficient mergers of massive stars to overcome that mass threshold. We conclude that GCs can form with IMBHs ≳103M⨀, which is sufficiently massive to be retained within the GC even with the expected gravitational wave recoil.

The original composition of the gas forming first-generation stars in clusters: Insights from HST and JWST

Globular cluster (GC) stars composed of pristine material, also known as first-generation (1G) stars, are not chemically homogeneous as they exhibit extended sequences in the chromosome map (ChM). Recent studies characterized 1G stars within the center of 55 Galactic GCs, revealing metallicity variations. Despite this progress, several unanswered questions persist, particularly concerning the link between the 1G metallicity spread and factors such as the radial distance from the cluster center or the host GC parameters. Additionally, it remains unclear whether the extended 1G sequence phenomenon is exclusive to old Galactic GCs with multiple populations. This work addresses these open issues, examining 1G stars in different environments. First, we combine Hubble Space Telescope (HST) and James Webb Space Telescope photometry of the GC 47\,Tucanae to study 1G stars at increasing distances from the cluster center. We find that metal-rich 1G stars are more centrally concentrated than metal-poor ones, suggesting a metallicity radial gradient. Additionally, the two groups of 1G stars share similar kinematics. Since our analysis focuses on giant stars in the cluster center and M dwarfs in external fields, we discuss the possibility that the metallicity distribution depends on stellar mass. Subsequently, we analyze HST multi-band photometry of two simple-population clusters, NGC\,6791 and NGC\,1783, revealing elongated sequences in the ChM associated with metallicity variations. Finally, we investigate the 1G color distribution in 51 GCs, finding no connections with the host cluster parameters. These results shed light on the complex nature of 1G stars, providing insights into the GC formation environment.

On the origin of globular clusters in a hierarchical universe

ABSTRACT We present an end-to-end description of the formation of globular clusters (GCs) combining a treatment for their formation and dynamical evolution within galaxy haloes with a state-of-the-art semi-analytic simulation of galaxy formation. Our approach allows us to obtain exquisite statistics to study the effect of the environment and assembly history of galaxies, while still allowing a very efficient exploration of the parameter space. Our reference model, including both efficient cluster disruption during galaxy mergers and dynamical friction of GCs within the galactic potential, accurately reproduces the observed correlation between the total mass in GCs and the parent halo mass. A deviation from linearity is predicted at low-halo masses, which is driven by a strong dependence on morphological type: bulge-dominated galaxies tend to host larger masses of GCs than their later-type counterparts. While the significance of the difference might be affected by resolution at the lowest halo masses considered, this is a robust prediction of our model and a natural consequence of the assumption that cluster migration into the halo is triggered by galaxy mergers. Our model requires an environmental dependence of GC radii to reproduce the observed low-mass mass distribution of GCs in our Galaxy. At GC masses $\gt 10^6\, {\rm M}_\odot$, our model predicts fewer GCs than observed, due to an overly aggressive treatment of dynamical friction. Our model reproduces well the metallicity distribution measured for Galactic GCs, even though we predict systematically younger GCs than observed. We argue that this adds further evidence for an anomalously early formation of the stars in our Galaxy.

Origin of the correlation between stellar kinematics and globular cluster system richness in ultradiffuse galaxies

ABSTRACT Observational surveys have found that the dynamical masses of ultradiffuse 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 lead 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.

Metal-poor star formation at z &amp;gt; 6 with JWST: new insight into hard radiation fields and nitrogen enrichment on 20 pc scales

ABSTRACT Nearly a decade ago, we began to see indications that reionization-era galaxies power hard radiation fields rarely seen at lower redshift. Most striking were detections of nebular C iv emission in what appeared to be typical low-mass galaxies, requiring an ample supply of 48 eV photons to triply ionize carbon. We have obtained deep JWST/NIRSpec R = 1000 spectroscopy of the two z &amp;gt; 6 C iv-emitting galaxies known prior to JWST. Here, we present a rest-UV to optical spectrum of one of these two systems, the multiply-imaged z = 6.1 lensed galaxy RXCJ2248-ID. NIRCam imaging reveals two compact (&amp;lt;22 pc) clumps separated by 220 pc, with one comprising a dense concentration of massive stars (&amp;gt;10 400 M⊙ yr−1 kpc−2) formed in a recent burst. We stack spectra of 3 images of the galaxy (J = 24.8–25.9), yielding a very deep spectrum providing a high-S/N template of strong emission line sources at z &amp;gt; 6. The spectrum reveals narrow high-ionization lines (He ii, C iv, N iv]) with line ratios consistent with powering by massive stars. The rest-optical spectrum is dominated by very strong emission lines ([O iii] EW = 2800 Å), albeit with weak emission from low-ionization transitions ([O iii]/[O ii] = 184). The electron density is found to be very high (6.4–31.0 × 104 cm−3) based on three UV transitions. The ionized gas is metal poor ($12+\log (\rm O/H)=7.43^{+0.17}_{-0.09}$), yet highly enriched in nitrogen ($\log (\rm N/O)=-0.39^{+0.11}_{-0.10}$). The spectrum appears broadly similar to that of GNz11 at z = 10.6, without showing the same AGN signatures. We suggest that the hard radiation field and rapid nitrogen enrichment may be a short-lived phase that many z &amp;gt; 6 galaxies go through as they undergo strong bursts of star formation. We comment on the potential link of such spectra to globular cluster formation.

Towards a holistic view of the origin of multiple stellar populations in globular clusters

The presence of multiple stellar populations in globular clusters is now well accepted, however, very little is known regarding how they formed. Answering this question is one of the major challenges of stellar astrophysics, yet of great interest, given the importance of globular clusters in different fields, from stellar evolution to gravitational wave emission and galaxy assembly. We present a series of 3D hydrodynamic simulations both of isolated clusters and at a cosmological scale aimed at probing the formation of globular clusters and their multiple stellar populations. We focus first on the effects of both rotation and Type Ia supernovae on the formation of the second population with particular attention on the chemical composition of the newborn stars. Then, we present the first simulations of the SImulating the Environment where Globular clusters Emerged project aimed at probing the formation of globular clusters through sub-parsec cosmological zoom-in simulations.

JWST Identification of Extremely Low C/N Galaxies with [N/O] ≳ 0.5 at z ∼ 6–10 Evidencing the Early CNO-cycle Enrichment and a Connection with Globular Cluster Formation

We present chemical abundance ratios of 70 star-forming galaxies at z ∼ 4–10 observed by the JWST/NIRSpec Early Release Observations, GLASS, and CEERS programs. Among the 70 galaxies, we have pinpointed two galaxies, CEERS_01019 at z = 8.68 and GLASS_150008 at z = 6.23, with extremely low C/N ([C/N] ≲ −1), evidenced with C iii]λλ1907,1909, N iii]λ1750, and N iv]λλ1483,1486, which show high N/O ratios ([N/O] ≳ 0.5) comparable with the one of GN-z11, regardless of whether stellar or active galactic nucleus radiation is assumed. Such low C/N and high N/O ratios found in CEERS_01019 and GLASS_150008 (additionally identified in GN-z11) are largely biased toward the equilibrium of the CNO cycle, suggesting that these three galaxies are enriched by metals processed by the CNO cycle. On the C/N versus O/H plane, these three galaxies do not coincide with Galactic H ii regions, normal star-forming galaxies, and nitrogen-loud quasars with asymptotic giant branch stars, but with globular-cluster (GC) stars, indicating a connection with GC formation. We compare the C/O and N/O of these three galaxies with those of theoretical models and find that these three galaxies are explained by scenarios with dominant CNO-cycle materials, i.e., Wolf–Rayet stars, supermassive (103–105 M ⊙) stars, and tidal disruption events, interestingly with a requirement of frequent direct collapses. For all the 70 galaxies, we present measurements of Ne/O, S/O, and Ar/O, together with C/O and N/O. We identify four galaxies with very low Ne/O, log(Ne/O) < −1.0, indicating abundant massive (≳30 M ⊙) stars.

Globular clusters contribute to the nuclear star clusters and galaxy centre γ-ray excess, moderated by galaxy assembly history

ABSTRACT Two unresolved questions at galaxy centres, namely the formation of the nuclear star cluster (NSC) and the origin of the γ-ray excess in the Milky Way (MW) and Andromeda (M31), are both related to the formation and evolution of globular clusters (GCs). They migrate towards the galaxy centre due to dynamical friction, and get tidally disrupted to release the stellar mass content including millisecond pulsars (MSPs), which contribute to the NSC and γ-ray excess. In this study, we propose a semi-analytical model of GC formation and evolution that utilizes the Illustris cosmological simulation to accurately capture the formation epochs of GCs and simulate their subsequent evolution. Our analysis confirms that our GC properties at z = 0 are consistent with observations, and our model naturally explains the formation of a massive NSC in a galaxy similar to the MW and M31. We also find a remarkable similarity in our model prediction with the γ-ray excess signal in the MW. However, our predictions fall short by approximately an order of magnitude in M31, indicating distinct origins for the two γ-ray excesses. Meanwhile, we utilize the catalogue of Illustris haloes to investigate the influence of galaxy assembly history. We find that the earlier a galaxy is assembled, the heavier and spatially more concentrated its GC system behaves at z = 0. This results in a larger NSC mass and brighter γ-ray emission from deposited MSPs.

Catalogue of model star clusters in the Milky Way and M31 galaxies

ABSTRACT Detailed understanding of the formation and evolution of globular clusters (GCs) has been recently advanced through a combination of numerical simulations and analytical models. We employ a state-of-the-art model to create a comprehensive catalogue of simulated clusters in three Milky Way (MW) and three Andromeda (M31) analogue galaxies. Our catalogue aims to connect the chemical and kinematic properties of GCs to the assembly histories of their host galaxies. We apply the model to a selected sample of simulated galaxies that closely match the virial mass, circular velocity profile, and defining assembly events of the MW and M31. The resulting catalogue has been calibrated to successfully reproduce key characteristics of the observed GC systems, including total cluster mass, mass function, metallicity distribution, radial profile, and velocity dispersion. We find that clusters in M31 span a wider range of age and metallicity, relative to the MW, possibly due to M31’s recent major merger. Such a merger also heated up the in-situ GC population to higher orbital energy and introduced a large number of ex-situ clusters at large radii. Understanding the impacts of galaxy mergers and accretion on the GC populations is crucial for uncovering the galaxy assembly histories.

The influence of globular cluster evolution on the specific frequency in dwarf galaxies

ABSTRACT Dwarf galaxies are known to exhibit an unusual richness in numbers of globular clusters (GCs), property quantified by the specific frequency (SN), which is high for dwarf and giant elliptical galaxies, but with a minimum for intermediate-mass galaxies. In this work we study the role that GC evolution has in setting this trend, for which we use N-body simulations to evolve GCs in dwarf galaxies and quantify their disruption efficiency. We selected five individual dwarf galaxies from a high-resolution cosmological simulation, which includes GC formation and follow-up of their paths inside the host galaxy. Then, the tidal history of each GC is coupled to nbody6++gpu to produce N-body models that account for both, the interaction of GCs with their galactic environment and their internal dynamics. This results in a GC mass-loss parametrization to estimate dissolution times and mass-loss rates after a Hubble time. GC evolution is sensitive to the particular orbital histories within each galaxy, but the overall result is that the amount of mass that GC systems lose scales with the mass (and density) of the host galaxy, i.e. the GC mass-loss efficiency is lowest in low-mass dwarfs. After a 12 Gyr evolution all simulated GC systems retain an important fraction of their initial mass (up to 25 per cent), in agreement with the high GC to field star ratios observed in some dwarfs, and supports the scenario in which GC disruption mechanisms play an important role in shaping the GC specific frequency in dwarf galaxies.

A transient overcooling in the early Universe? Clues from globular clusters formation

ABSTRACT The mere existence of multiple stellar generations in Milky Way globular clusters indicates that each generation was unable to stop star formation, that instead persisted unimpeded for several million years. This evidence argues for an extended stage of star formation within a forming globular cluster, during which stellar feedback was substantially ineffective and the nascent globular cluster was able to accrete processed gas from its surrounding, and efficiently convert it into successive stellar generations. It has been argued that such delayed feedback results from core collapse in most massive stars failing to trigger an energetic supernova explosion, but rather leading directly to black hole formation. Thus, globular clusters offer a concrete phenomenological example for the lack of feedback in young starbursts, an option that has been widely advocated to account for the unexpected abundance of ultraviolet-luminous galaxies at z = 9–16, as revealed by JWST observations. The paper is meant to attract attention to this opportunity for a synergic cooperation of globular cluster and high-redshift research.

The formation of globular clusters with top-heavy initial mass functions

ABSTRACT We study the formation of globular clusters (GCs) in massive compact clouds with the low metallicity of Z = 10−3 Z⊙ by performing three-dimensional radiative-hydrodynamic simulations. Considering the uncertainty of the initial mass function (IMF) of stars formed in low-metallicity and high-density clouds, we investigate the impacts of the IMF on the cloud condition for the GC formation with the range of the power-law index of IMF as γ = 1−2.35. We find that the threshold surface density (Σthr) for the GC formation increases from 800 M⊙ pc−2 at γ = 2.35 to 1600 M⊙ pc−2 at γ = 1.5 in the cases of clouds with Mcl = 106 M⊙ because the emissivity of ionizing photons per stellar mass increases as γ decreases. For γ &amp;lt; 1.5, Σthr saturates with ∼2000 M⊙ pc−2 that is quite rare and observed only in local starburst galaxies due to e.g. merger processes. Thus, we suggest that formation sites of low-metallicity GCs could be limited only in the very high-surface density regions. We also find that Σthr can be modelled by a power-law function with the cloud mass (Mcl) and the emissivity of ionizing photons (s*) as $\propto M_{\rm cl}^{-1/5} s_{*}^{2/5}$. Based on the relation between the power-law slope of IMF and Σthr, future observations with e.g. the JWST can allow us to constrain the IMF of GCs.

Globular cluster formation histories, masses, and radii inferred from gravitational waves

ABSTRACT Globular clusters (GCs) are found in all types of galaxies and harbour some of the most extreme stellar systems, including black holes that may dynamically assemble into merging binary black holes (BBHs). Uncertain GC properties, including when they formed, their initial masses and sizes, affect their production rate of BBH mergers. Using the gravitational-wave transient catalogue (GWTC-3), we measure that dynamically assembled BBHs – those that are consistent with isotropic spin directions – make up ${61^{+29}_{-44}\%}$ of the total merger rate, with a local merger rate of ${10.9^{+16.8}_{-9.3}}$ Gpc−3 yr−1 rising to ${58.9^{+149.4}_{-46.0}}$ Gpc−3 yr−1 at z = 1. We assume that this inferred rate describes the contribution from GCs and compare it against the Cluster Monte Carlo (cmc) simulation catalogue to directly fit for the GC initial mass function, virial radius distribution, and formation history. We find that GC initial masses are consistent with a Schechter function with slope ${\beta _m = -1.9^{+0.8}_{-0.8}}$ . Assuming a mass function slope of βm = −2 and a mass range between 104–$10^8\, \mathrm{ M}_\odot$ , we infer a GC formation rate at z = 2 of ${5.0^{+9.4}_{-4.0}}$ Gpc−3 yr−1, or ${2.1^{+3.9}_{-1.7}}\times 10^6\, \mathrm{ M}_\odot$ Gpc−3 yr−1 in terms of mass density. We find that the GC formation rate probably rises more steeply than the global star formation rate between z = 0 and z = 3 (82 per cent credibility) and implies a local number density that is ${f_\mathrm{ev} = 22.6^{+29.9}_{-16.2}}$ times higher than the observed density of survived GCs. This is consistent with expectations for cluster evaporation, but may suggest that other environments contribute to the rate of BBH mergers with significantly tilted spins.

Formation of globular clusters in dwarf galaxies of the Local Group

ABSTRACT The existence of globular clusters (GCs) in a few satellite galaxies, and their absence in majority of dwarf galaxies, present a challenge for models attempting to understand the origins of GCs. In addition to GC presence appearing stochastic and difficult to describe with average trends, in the smallest satellite galaxies GCs contribute a substantial fraction of total stellar mass. We investigate the stochasticity and number of GCs in dwarf galaxies using an updated version of our model that links the formation of GCs to the growth of the host galaxy mass. We find that more than 50 per cent of dwarf galaxies with stellar mass $M_{\star }\lesssim 2\times 10^7\, \mathrm{M}_\odot$ do not host GCs, whereas dwarfs with $M_{\star }\sim 10^8\, \mathrm{M}_\odot$ almost always contain some GCs, with a median number ∼10 at z = 0. These predictions are in agreement with the observations of the Local Volume dwarfs. We also confirm the near-linear GC system mass–halo mass relation down to $M_{\mathrm{h}}\simeq 10^8\, \mathrm{M}_\odot$ under the assumption that GC formation and evolution in galaxies of all mass can be described by the same physical model. A detailed case study of two model dwarfs that resemble the Fornax dwarf spheroidal galaxy shows that observational samples can be notably biased by incompleteness below detection limit and at large radii.

On the Reionization-era Globular Cluster in the Low-mass Galaxy Eridanus II

Using color–magnitude diagrams from deep archival Hubble Space Telescope imaging, we self-consistently measure the star formation history of Eridanus II (Eri II), the lowest-mass galaxy (M ⋆(z = 0) ∼ 105 M ⊙) known to host a globular cluster (GC), and the age, mass, and metallicity of its GC. The GC (∼13.2 ± 0.4 Gyr, 〈[Fe/H]〉 = −2.75 ± 0.2 dex) and field (mean age ∼13.5 ± 0.3 Gyr, 〈[Fe/H]〉 = −2.6 ± 0.15 dex) have similar ages and metallicities. Both are reionization-era relics that formed before the peak of cosmic star and GC formation (z ∼ 2–4). The ancient star formation properties of Eri II are not extreme and appear similar to z = 0 dwarf galaxies. We find that the GC was ≲4 times more massive at birth than today and was ∼10% of the galaxy's stellar mass at birth. At formation, we estimate that the progenitor of Eri II and its GC had M UV ∼ −7 to −12, making it one of the most common type of galaxy in the early universe, though it is fainter than direct detection limits, absent gravitational lensing. Archaeological studies of GCs in nearby low-mass galaxies may be the only way to constrain GC formation in such low-mass systems. We discuss the strengths and limitations in comparing archaeological and high-redshift studies of cluster formation, including challenges stemming from the Hubble Tension, which introduces uncertainties into the mapping between age and redshift.