Cluster Mass Function Research Articles

The SRG/eROSITA All-Sky Survey. Constraints on f(R) gravity from cluster abundances

The evolution of the cluster mass function traces the growth of the linear density perturbations and can be utilized to constrain the parameters of cosmological and alternative gravity models. In this context, we present new constraints on potential deviations from general relativity by investigating the Hu-Sawicki parametrization of the $f(R)$ gravity with the first Spectrum Roentgen Gamma (SRG)/ All-Sky Survey ( cluster catalog in the western Galactic hemisphere in combination with the overlapping Dark Energy Survey Year-3, KiloDegree Survey, and Hyper Suprime-Cam data for weak lensing mass calibration. For the first time, we present constraints obtained from cluster abundances only. When we consider massless neutrinos, we find a strict upper limit of $ f_ R0 | < -4.31$ at a 95<!PCT!> confidence level. Massive neutrinos suppress structure growth at small scales, and thus have the opposite effect of $f(R)$ gravity. We consequently investigate the joint fit of the mass of the neutrinos with the modified gravity parameter. We obtain $ f_ R0 | < -4.08$ jointly with $ m_ eV $ at a 95<!PCT!> confidence level, which is tighter than the limits in the literature utilizing cluster counts only. At $ f_ R0 |= - 6$, the number of clusters is not significantly changed by the theory. Consequently, we do not find any statistical deviation from general relativity in the study of eRASS1 cluster abundance. Deeper surveys with eROSITA, increasing the number of detected clusters, will further improve constraints on $ |f_ R0 |$ and investigate alternative gravity theories.

JWST Observations of Starbursts: Massive Star Clusters in the Central Starburst of M82

We present a near-infrared (NIR) candidate star cluster catalog for the central kiloparsec of M82 based on new JWST NIRCam images. We identify star cluster candidates using the F250M filter, finding 1357 star cluster candidates with stellar masses >104 M ⊙. Compared to previous optical catalogs, nearly all (87%) of the candidates we identify are new. The star cluster candidates have a median intrinsic cluster radius of ≈1 pc and stellar masses up to 106 M ⊙. By comparing the color–color diagram to dust-free yggdrasil stellar population models, we estimate that the star cluster candidates have A V ∼ 3−24 mag, corresponding to A 2.5μm ∼ 0.3−2.1 mag. There is still appreciable dust extinction toward these clusters into the NIR. We measure the stellar masses of the star cluster candidates, assuming ages of 0 and 8 Myr. The slope of the resulting cluster mass function is β = 1.9 ± 0.2, in excellent agreement with studies of star clusters in other galaxies.

Spatial segregation of massive clusters in a simulation of colliding dwarf galaxies

The collective properties of star clusters are investigated using a simulation of the collision between two dwarf galaxies. The characteristic power law of the cluster mass function, N(M), with a logarithmic slope dN/dM ~ -1, is present from cluster birth and remains throughout the simulation. The maximum mass of a young cluster scales with the star formation rate (SFR). The relative average minimum separation, R(M)= N(M)^{1/p}D_min(M)/D(M_low), for average minimum distance D_min(M) between clusters of mass M, and for lowest mass, M_low, measured in projection (p=2) or three dimensions (p=3), has a negative slope, d log R/d log M ~ -0.2, for all masses and ages. This agrees with observations of R(M) in low-mass galaxies studied previously. Like the slope of N(M), R(M) is apparently a property of cluster birth for dwarf galaxies that does not depend on SFR or time. The negative slope for R(M) implies that massive clusters are more concentrated relative to lower mass clusters throughout the entire mass range. Cluster growth through coalescence is also investigated. The ratio of the kinetic to potential energy of all near-neighbor clusters is generally large, but a tail of low values in the distribution of this ratio suggests that a fraction of the clusters merge, ~8% by number throughout the ~300 Myr of the simulation and up to 60% by mass for young clusters in their first 10 Myr, scaling with the SFR above a certain threshold.

On the Determination of Stellar Mass and Binary Fraction of Open Clusters within 500 pc from the Sun

We investigated the stellar mass function and the binary fraction of 114 nearby open clusters (OCs) using the high-precision photometric data from Gaia Data Release 3 (Gaia DR3). We estimated the mass of member stars by using a ridge line that is better in line with the observed color–magnitude diagram, thus obtaining more accurate stellar mass and binary mass ratio (q) at the low-mass region. By analyzing the present-day mass function (PDMF) of star clusters, we found that 108 OCs follow a two-stage power-law distribution, whereas six OCs present a single power-law PDMF. Subsequently, we fitted the high(low)-mass index of PDMF ( dN/dm∝m−α ), denoted as α h(α l), and segmentation point m c. For our cluster sample, the median values of α h and α l are 2.65 and 0.95, respectively, which are approximately consistent with the initial mass function results provided by Kroupa. We utilized the cumulative radial number distribution of stars with different masses to quantify the degree of mass segregation. We found a significant positive correlation between the state of dynamical evolution and mass segregation in OCs. We also estimated the fraction of binary stars with q ≥ 0.5, ranging from 6% to 34% with a median of 17%. Finally, we provided a catalog of 114 nearby cluster properties, including the total mass, the binary fraction, the PDMF, and the dynamical state.

Cluster population demographics in NGC 628 derived from stochastic population synthesis models

ABSTRACT The physical properties of star cluster populations offer valuable insights into their birth, evolution, and disruption. However, individual stars in clusters beyond the nearest neighbours of the Milky Way are unresolved, forcing analyses of star cluster demographics to rely on integrated light, a process fraught with uncertainty. Here, we infer the demographics of the cluster population in the benchmark galaxy NGC 628 using data from the Legacy Extra-galactic UV Survey (LEGUS) coupled to a novel Bayesian forward-modelling technique. Our method analyses all 1178 clusters in the LEGUS catalogue, $\sim 4$ times more than prior studies severely affected by completeness cuts. Our results indicate that the cluster mass function is either significantly steeper than the commonly observed slope of $-2$ or is truncated at $\approx 10^{4.5}$ M$_\odot$; the latter possibility is consistent with proposed relations between truncation mass and star formation surface density. We find that cluster disruption is relatively mild for the first $\approx 200$ Myr of cluster evolution; no evidence for mass-dependent disruption is found. We find suggestive but not incontrovertible evidence that inner galaxy clusters may be more prone to disruption and outer galaxy clusters have a more truncated mass function, but confirming or refuting these findings will require larger samples from future observations of outer galaxy clusters. Finally, we find that current stellar track and atmosphere models, along with common forms for cluster mass and age distributions, cannot fully capture all features in the multidimensional photometric distribution of star clusters. While our forward-modelling approach outperforms earlier backward-modelling approaches, some systematic differences persist between observed and modelled photometric distributions.

Merge and strip: Dark matter-free dwarf galaxies in clusters can be formed by galaxy mergers

Context. Recent observations of galaxy mergers inside galaxy cluster environments, such as NGC 5291 in the vicinity of Abell 3574, report high star formation rates in the ejected tidal tails, which point towards currently developing tidal dwarf galaxies. This prompts the intriguing question whether these newly formed stellar structures could get stripped from the galaxy potential by the cluster and thus populate it with dwarf galaxies. Aims. We verify whether environmental stripping of tidal dwarf galaxies from galaxy mergers inside galaxy cluster environments is a possible evolutionary channel to populate a galaxy cluster with low-mass and low surface brightness galaxies. Methods. We performed three high-resolution hydrodynamical simulations of mergers between spiral galaxies in a cluster environment, implementing a stellar mass ratio of 2:1 with M200 = 9.5 × 1011 M⊙ for the more massive galaxy. Between the three different simulations, we varied the initial orbit of the infalling galaxies with respect to the cluster center. Results. We demonstrate that cluster environments are capable of stripping tidal dwarf galaxies from the host potential independently of the infall orbit of the merging galaxy pair, without instantly destroying the tidal dwarfs. Starting to evolve separately from their progenitor, these newly formed dwarf galaxies reach total masses of Mtot ≈ 107 − 9 M⊙ within the limits of our resolution. In the three tested orbit scenarios, we find three, seven, and eight tidal dwarf galaxies per merger, respectively, which survive longer than 1 Gyr after the merger event. Exposed to ram pressure, these gas dominated dwarf galaxies exhibit high star formation rates while also losing gas to the environment. Experiencing a strong headwind due to their motion through the intracluster medium, they quickly lose momentum and start spiraling towards the cluster center, reaching distances on the order of 1 Mpc from their progenitor. About 4 Gyr after the merger event, we still find three and four intact dwarf galaxies in two of the tested scenarios, respectively. The other stripped tidal dwarf galaxies either evaporate in the hostile cluster environment due to their low initial mass, or are disrupted as soon as they reach the cluster center. Conclusions. The dwarf production rate due to galaxy mergers is elevated when the interaction with a cluster environment is taken into account. Comparing their contribution to the observed galaxy mass function in clusters, our results indicate that ∼30% of dwarf galaxies in clusters could have been formed by stripping from galaxy mergers.

The Present-day Mass Function of Star Clusters in the Solar Neighborhood

This work analyzes the present-day mass function (PDMF) of 93 star clusters utilizing Gaia Data Release 3 data, with membership determined by the StarGo machine-learning algorithm. The impact of unresolved binary systems on mass estimation is rigorously assessed, adopting three mass ratio profiles for correction. The PDMF is characterized by the power-law index, α, derived through a robust maximum likelihood method that avoids biases associated with data binning. The value of α for stars between the completeness limited mass of Gaia (with a mean 0.3 M ⊙ for our cluster samples) and 2 M ⊙ exhibits stability for clusters younger than 200 Myr, decreasing for older clusters, particularly when considering stars within the half-mass radius. The PDMF of these star clusters is consistent with a dynamically evolved Kroupa initial mass function via the loss of low-mass stars. Cluster morphology shows a correlation with α, as α values exhibit a decreasing trend from filamentary to tidal-tail clusters, mirroring the sequence of increasing cluster age. The dependence of α on the total cluster mass is weak, with a subtle increase for higher-mass clusters, especially outside the half-mass radius. We do not observe a correlation between α and the mean metallicity of the clusters. Younger clusters have lower metallicity compared to their older counterparts, which indicates that the older clusters might have migrated to the solar neighborhood from the inner disk. A comparison with numerical models incorporating a black hole population suggests the need for observations of distant, older, massive open clusters to determine whether or not they contain black holes.

A Tale of Three Dwarfs: Cluster-based Star Formation Histories of Blue Compact Dwarf Galaxies

We present a new study of the cluster populations in the blue compact dwarf galaxies (BCD) ESO185-IG13, ESO338-IG04, and Haro11, based on new and archival high-resolution images taken by the Hubble Space Telescope, and the first to probe the populations older than ≈100 Myr. BCDs are believed to experience intense bursts of star formation (including at the present day) after long periods of quiescence, but little is known about the timing, frequency, duration, and strength of these bursts or about their star formation histories in general. We find that the cluster population in each of the three galaxies studied here has its own unique distribution of colors and hence a unique cluster and star formation history. From an assumed correlation between the normalization of the cluster mass function and the star formation rate of the host galaxy, we construct cluster-based star formation histories over the past ≈few × Gyr and find that only Haro11 is currently experiencing a burst (≈factor of 10 increase in the rate of star formation for the last ≈20 Myr), whereas ESO185 experienced enhanced star formation (by a factor ≈4) between 10 and 40 Myr ago, and ESO338 has had a fairly constant SFH over the past few Gyr. These findings indicate that not all BCDs are experiencing a burst of star formation at the present day, and that some have been forming stars and clusters at a fairly steady rate (within a factor of ≈2–3) over the past few Gyr. This scenario is similar to the histories of dwarf irregular and dwarf starburst galaxies, which have star formation rates that are 10–1000 times lower than those in BCDs.

Pre-supernova feedback sets the star cluster mass function to a power law and reduces the cluster formation efficiency

Context. The star cluster initial mass function is observed to have an inverse power law exponent around 2, yet there is no consensus on what determines this distribution, and why some variation is observed in different galaxies. Furthermore, the cluster formation efficiency (CFE) covers a range of values, particularly when considering different environments. These clusters are often used to empirically constrain star formation and as fundamental units for stellar feedback models. Detailed galaxy models must therefore accurately capture the basic properties of observed clusters to be considered predictive. Aims. We study how feedback mechanisms acting on different timescales and with different energy budgets affect the star cluster mass function and CFE. Methods. We use hydrodynamical simulations of a dwarf galaxy as a laboratory to study star cluster formation. We test different combinations of stellar feedback mechanisms, including stellar winds, ionizing radiation, and supernovae (SNe). Results. Each feedback mechanism affects the CFE and cluster mass function. Increasing the feedback budget by combining the different types of feedback decreases the CFE by reducing the number of massive clusters. Ionizing radiation is found to be especially influential. This effect depends on the timing of feedback initiation, as shown by comparing early and late feedback. Early feedback occurs from ionizing radiation and stellar winds with onset immediately after a massive star is formed. Late feedback occurs when energy injection only starts after the main-sequence lifetime of the most massive SN progenitor, a timing that is further influenced by the choice of the most massive SN progenitor. Late feedback alone results in a broad, flat mass function, approaching a log-normal shape in the complete absence of feedback. Early feedback, on the other hand, produces a power-law cluster mass function with lower CFE, albeit with a steeper slope than that usually observed.

Variation of the High-mass Slope of the Stellar Initial Mass Function: Theory Meets Observations

We present observational evidence of a correlation between the high-mass slope of the stellar initial mass function (IMF) in young star clusters and their stellar surface density, σ *. When the high-mass end of the IMF is described by a power law of the form , the value of Γ is seen to decrease weakly with increasing σ *, following a relation. We also present a model that can explain these observations. The model is based on the idea that the coalescence of protostellar cores in a protocluster-forming clump is more efficient in high-density environments where cores are more closely packed. The efficiency of the coalescence process is calculated as a function of the parental clump properties, in particular the relation between its mass and radius as well as its core formation efficiency. The main result of this model is that the increased efficiency of the coalescence process leads to shallower slopes of the IMF, in agreement with the observations of young clusters, and the observations are best reproduced with compact protocluster-forming clumps. These results have significant implications for the shape of the IMF in different Galactic and extragalactic environments and have very important consequences for galactic evolution.

The cluster mass function and the σ8 tension

ABSTRACT We use a large set of halo mass function (HMF) models in order to investigate their ability to represent the observational cluster mass function (CMF), derived from the $\tt {GalWCat19}$ cluster catalogue, within the Lambda cold dark matter (ΛCDM) cosmology. We apply the χ2 minimization procedure to constrain the free parameters of the models, namely Ωm and σ8. We find that all HMF models fit well the observational CMF, while the Bocquet et al. model provides the best fit, with the lowest χ2 value. Utilizing the index of inconsistency (IOI) measure, we further test the possible inconsistency of the models with respect to a variety of Planck 2018 ΛCDM cosmologies, resulting from the combination of different probes (CMB–BAO or CMB–DES). We find that the HMF models that fitted well the observed CMF provide consistent cosmological parameters with those of the Planck CMB analysis, except for the Press and Schechter, Yahagi et al., and Despali et al. models that return large IOI values. The inverse $\chi _{\rm min}^2$-weighted average values of Ωm and σ8, overall 23 theoretical HMF models are ${\bar{\Omega }_{m,0}}=0.313\pm 0.022$ and ${\bar{\sigma }_8}=0.798\pm 0.040$, which are clearly consistent with the results of Planck–CMB, providing S8 = σ8(Ωm/0.3)1/2 = 0.815 ± 0.05. Within the ΛCDM paradigm and independently of the selected HMF model in the analysis, we find that the current CMF shows no σ8 tension with the corresponding Planck–CMB results.

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.

Painting baryons on to N-body simulations of galaxy clusters with image-to-image deep learning

ABSTRACT Galaxy cluster mass functions are a function of cosmology, but mass is not a direct observable, and systematic errors abound in all its observable proxies. Mass-free inference can bypass this challenge, but it requires large suites of simulations spanning a range of cosmologies and models for directly observable quantities. In this work, we devise a U-net – an image-to-image machine learning algorithm – to ‘paint’ the illustristng model of baryons on to dark matter-only (DMO) simulations of galaxy clusters. Using 761 galaxy clusters with M200c ≳ 1014 M⊙ from the TNG300 simulation at z < 1, we train the algorithm to read in maps of projected dark matter mass and output maps of projected gas density, temperature, and X-ray flux. Despite being trained on individual images, the model reproduces the true scaling relation and scatter for the MDM–LX, as well as the distribution functions of the cluster X-ray luminosity and gas mass. For just one decade in cluster mass, the model reproduces three orders of magnitude in LX. The model is biased slightly high when using dark matter maps from the DMO simulation. The model performs well on inputs from TNG300-2, whose mass resolution is eight times coarser; further degrading the resolution biases the predicted luminosity function high. We conclude that U-net-based baryon painting is a promising technique to build large simulated cluster catalogues, which can be used to improve cluster cosmology by combining existing full-physics and large N-body simulations.

The cluster initial mass function of the M82 disc super star clusters

ABSTRACT The presence of a population of a large number (∼400) of almost coeval (100–300 Myr) super star clusters (SSCs) in the disc of M82 offers an opportunity to construct the Cluster Initial Mass Function (CIMF) from the observed present-day Cluster Mass Function (CMF). We carry out the dynamical and photometric evolution of the CMF assuming that the clusters move in circular orbits under the gravitational potential of the host galaxy using the semi-analytical simulation code Evolve Me a Cluster of StarS. We explore power-law and lognormal functions for the CIMFs, and populate the clusters in the disc assuming uniform, power-law, and exponential radial distribution functions. We find that the observed CMF is best produced by a CIMF that is power law in form with an index of 1.8, for a power-law radial distribution function. More importantly, we establish that the observed turn-over in the present-day CMF is the result of observational incompleteness rather than due to dynamically induced effects, or an intrinsically lognormal CIMF, as was proposed for the fossil starburst region B of this galaxy. Our simulations naturally reproduce the mass–radius relation observed for a sub-sample of M82 SSCs.

Universal Upper End of the Stellar Initial Mass Function in the Young and Compact LEGUS Clusters

We investigate the variation in the upper end of the stellar initial mass function (uIMF) in 375 young and compact star clusters in five nearby galaxies within ∼5 Mpc. All the young stellar clusters (YSCs) in the sample have ages ≲ 4 Myr and masses above 500 M ⊙, according to standard stellar models. The YSC catalogs were produced from Hubble Space Telescope images obtained as part of the Legacy ExtraGalactic UV Survey (LEGUS) Hubble treasury program. They are used here to test whether the uIMF is universal or changes as a function of the cluster’s stellar mass. We perform this test by measuring the Hα luminosity of the star clusters as a proxy for their ionizing photon rate, and charting its trend as a function of cluster mass. Large cluster numbers allow us to mitigate the stochastic sampling of the uIMF. The advantage of our approach relative to previous similar attempts is the use of cluster catalogs that have been selected independently of the presence of Hα emission, thus removing a potential sample bias. We find that the uIMF, as traced by the Hα emission, shows no dependence on cluster mass, suggesting that the maximum stellar mass that can be produced in star clusters is universal, in agreement with previous findings.

CODEX: Role of velocity substructure in the scaling relations of galaxy clusters

Context. The use of galaxy clusters as cosmological probes relies on a detailed understanding of their properties. They define cluster selection and ranking linked to a cosmologically significant cluster mass function. Previous studies have employed small samples of clusters, concentrating on achieving the first calibrations of cluster properties with mass, while the diversity of cluster properties has been revealed via detailed studies. Aims. The large spectroscopic follow-up on the CODEX cluster sample with SDSS and NOT enables a detailed study of hundreds of clusters, lifting the limitations of previous samples. We aim to update the spectroscopic cluster identification of CODEX by running the spectroscopic group finder on the follow-up spectroscopy results and connecting the dynamical state of clusters to their scaling relations. Methods. We implemented a reproducible spectroscopic membership determination and cleaning procedures, based on the redMaPPer membership, running the spectroscopic group finder on the follow-up spectroscopy results and cleaning the membership for spectroscopic outliers. We applied the Anderson-Darling test for velocity substructure and analysed its influence on the scaling relations. We also tested the effect of the X-ray-to-optical centre offset on the scaling relations. Results. We report on the scaling relations between richness, X-ray luminosity, and velocity dispersion for a complete sample of clusters with at least 15 members. Clusters with velocity substructure exhibit enhanced velocity dispersion for a given richness and are characterized by 2.5 times larger scatter. Clusters that have a strong offset in X-ray-to-optical centres have comparable scaling relations as clusters with substructure. We demonstrate that there is a consistency in the parameters of the scaling relations for the low- and high-richness galaxy clusters. Splitting the clusters by redshift, we note a decrease in scatter with redshift in all scaling relations. We localize the redshift range where a high scatter is observed to z < 0.15, which is in agreement with the literature results on the scatter. We note that the increase in scatter for both high- and low-luminosity clusters is z < 0.15, suggesting that both cooling and the resulting active galactic nucleus feedback are at the root of this scatter.

Dynamically Forming Extremely Low-mass White Dwarf Binaries in Wide Orbits

The detection of a 0.2 M ⊙ extremely low-mass white dwarf (EW) in a wide orbit (P orb ≈ 450 days) with a 1.1 M ⊙ main-sequence companion, KIC 8145411, challenges our current understanding of how EWs form. The traditional channel for EW formation, via mass transfer from the EW’s progenitor, is expected to form EW binaries in tight orbits. Indeed, the majority of known EWs are found in tight binaries with a median P orb ≈ 5.4 hr. Using numerical scattering experiments, we find that binary–binary strong encounters in star clusters can sufficiently widen the orbit of a typical EW binary, to explain the observed wide orbit of the KIC 8145411 system. The P orb distribution for EW binaries produced through binary–binary encounters is bimodal: one mode corresponds to the initial orbital period of the EW binary, while the other is near P orb ∼ few 102 days, similar to the orbital period of the KIC 8145411 system. We find that the production of wide EW binaries that are also ejected from the cluster peaks at a star cluster mass of ∼105 M ⊙ with a rate of ∼10−3 Gyr−1. Assuming that 50% of all stars form in star clusters and an initial cluster mass function ∝m −2, we estimate a galactic formation rate of ∼4.16 × 103 Gyr−1 for wide EW binaries.

The mass-loss rates of star clusters with stellar-mass black holes: implications for the globular cluster mass function

ABSTRACT Stellar-mass black holes (BHs) can be retained in globular clusters (GCs) until the present. Simulations of GC evolution find that the relaxation driven mass-loss rate is elevated if BHs are present, especially near dissolution. We capture this behaviour in a parametrized mass-loss rate, bench marked by results from N-body simulations, and use it to evolve an initial GC mass function (GCMF), similar to that of young massive clusters in the Local Universe, to an age of 12 Gyr. Low-metallicity GCs ([Fe/H] ≲ −1.5) have the highest mass-loss rates, because of their relatively high BH masses, which combined with their more radial orbits and stronger tidal field in the past explains the high turnover mass of the GCMF ($\sim 10^5\, {\rm M}_\odot$ ) at large Galactic radii ($\gtrsim 10\, {\rm kpc}$ ). The turnover mass at smaller Galactic radii is similar because of the upper mass truncation of the initial GCMF and the lower mass-loss rate due to the higher metallicities. The density profile in the Galaxy of mass lost from massive GCs ($\gtrsim 10^{5}\, {\rm M}_\odot$ ) resembles that of nitrogen-rich stars in the halo, confirming that these stars originated from GCs. We conclude that two-body relaxation is the dominant effect in shaping the GCMF from a universal initial GCMF, because including the effect of BHs reduces the need for additional disruption mechanisms.

Star cluster formation and survival in the first galaxies

ABSTRACT Using radiation-hydrodynamic cosmological simulations, we present a detailed (0.1 pc resolution), physically motivated portrait of a typical-mass dwarf galaxy before the epoch of reionization, resolving the formation, and evolution of star clusters into individual 10 M⊙ star particles. In the rest-frame ultraviolet, the galaxy has an irregular morphology with no bulge or disc, dominated by light emitted from numerous, compact, and gravitationally-bound star clusters. This is especially interesting in light of recent James Webb Space Telescope observations that − aided by the magnifying power of gravitational lenses – have imaged, at parsec-scale resolution, individual young star clusters forming in similar galaxies at z> 6. Because of their low metallicities and high temperatures, star-forming gas clouds in this galaxy have densities ∼100 times higher than typical giant molecular clouds; hence, their expected star formation efficiencies (SFEs) are high enough (around 10 − 70 per cent) to produce a sizeable population of potential globular cluster progenitors, but typically smaller (a few 100 − 2 ×104M⊙, half-mass radii of up to 3 pc) and of lower metallicities (10−3.5– 10−2.5 Z⊙). The initial mass function of the star-forming clouds is log-normal, whereas the bound star cluster mass function is a power-law with a slope that depends mainly on SFE but also on the temporal proximity to a major starburst. We find slopes between −0.5 and −2.5 depending on the assumed sub-grid SFE. Star formation is self-regulated on galactic scales; however, the multimodal metallicity distribution of the star clusters and the fraction of stars locked into surviving bound star clusters depends on SFE.

Global survey of star clusters in the Milky Way

Aims. We built Galactic open star cluster mass functions (CMFs) for different age sub-samples and spatial locations in the wider solar neighbourhood. Here, we present a simple cluster formation and evolution model to reproduce the main features of the CMFs. Methods. We used an unbiased working sample of 2227 clusters of the Milky Way Star Cluster (MWSC) catalogue, which occupy the heliocentric cylinders with magnitude-dependent completeness radii of 1–5 kpc. The MWSC survey provides an extended set of open star cluster parameters, including tidal radii, distances, and ages. From an analytic three-component Galaxy model, we derived tidal masses of clusters with a typical accuracy of about 70%. Our simple model includes a two-section cluster initial mass function, constant cluster formation rate, supervirial phase after a sudden expulsion of the remaining gas, and cluster mass loss due to stellar evolution and the clusters’ gradual destruction in the Galactic tidal field. The dynamical evolution model is based on previous N-body simulations. Results. The obtained tidal masses have been added to the MWSC catalogue. A general CMF (GCMF), built for all cluster ages around the Sun, has a bell-like shape and extends over four decades in mass. The high-mass slope found for tidal mass log mt/M⊙ ≥ 2.3 is equal to 1.14 ± 0.07. The CMFs for different age groups show the same high-mass slopes, while the low-mass slope is nearly flat for the youngest sub-sample (clusters younger than 20 Myr) and about −0.7 for the others. The inner and outer sub-samples covering Galactocentric radii R = 4.2–8.1 kpc and 8.9–13.5 kpc, respectively, are consistent with the GCMF, once the exponential decline of the Galactic disc density is taken into account. The model suggests star formation with low efficiency of 15–20%, where only 10% of stars remain bound in a cluster after gas expulsion and subsequent violent relaxation. The cluster formation rate required to reproduce the observed distributions in age and mass is about 0.4 M⊙ pc−2 Gyr−1. Conclusions. The obtained high-mass slope of the GCMF for the wide neighbourhood of the Sun is similar to slopes determined earlier in nearby galaxies for more luminous clusters with log m/M⊙ > 3.8. The MWSC catalogue supports models with a low star-formation efficiency, where 90% of stars are lost quickly after gas expulsion. The obtained cluster formation rate corresponds to open clusters’ contribution to the stellar content of the thin disc at the level of 30%.