Cluster Initial Mass Function Research Articles

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.

Why should models of dwarf galaxy evolution care about the initial mass function at low star-formation rates?

ABSTRACT When star clusters are formed at low star-formation rates (SFRs), their stellar initial mass function (IMF) can hardly be filled continuously with stars at each mass. This lack holds for massive stars and is verified observationally by the correlation between star-cluster mass and its most massive cluster star. Since galaxy evolution is strongly affected by massive stars, numerical models should account for this lack. Because a filled IMF is mostly applied even when only fractions of massive stars form, here we investigate, by means of 3D chemo-dynamical simulations of isolated dwarf galaxies, how deviations from a standard IMF in star clusters affect the evolution. We compare two different IMF recipes, a filled IMF and one truncated at a maximum mass at which a single complete star forms. Attention is given to energetic and chemical feedback by massive stars. Since their energy release is mass-dependent but steeper than the negative IMF slope, the energetic feedback retains a positive mass dependence, so that a filled IMF regulates star formation (SF) more strongly than truncated IMFs, though only stellar number fractions exist. The higher SFR of the truncated IMF in the simulation leads to more Type II supernovae (SNeII), driving galactic winds. Whether this results from the model-inherent larger SFR is questioned and therefore explored analytically. This shows the expected result for the Lyman continuum, but that the total SNII energy release is equal for both IMF modes, while the power is smaller for the truncated IMF. Reasonably, the different IMFs leave fingerprints in the abundance ratios of massive to intermediate-mass star elements.

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.

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.

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%.

Photometric and structural parameters of newly discovered nuclear star clusters in Local Volume galaxies

ABSTRACTWe use high-resolution Hubble Space Telescope imaging data of dwarf galaxies in the Local Volume ($\lesssim {11}\, \mathrm{Mpc}$) to parameterize 19 newly discovered nuclear star clusters (NSCs). Most of the clusters have stellar masses of $M_{\star }^{\mathrm{nsc}} \lesssim 10^{6}{\, {\rm M}_{\odot }}$ and compare to Galactic globular clusters in terms of ellipticity, effective radius, stellar mass, and surface density. The clusters are modelled with a Sérsic profile and their surface brightness evaluated at the effective radius reveals a tight positive correlation to the host galaxy stellar mass. Our data also indicate an increase in slope of the density profiles with increasing mass, perhaps indicating an increasing role for in situ star formation in more massive hosts. We evaluate the scaling relation between the clusters and their host galaxy stellar mass to find an environmental dependence: for NSCs in field galaxies, the slope of the relation is $\alpha = 0.82^{+0.08}_{-0.08}$ whereas $\alpha = 0.55^{+0.06}_{-0.05}$ for dwarfs in the core of the Virgo cluster. Restricting the fit for the cluster to $M_{\star }^{\mathrm{gal}} \ge 10^{6.5}{\, {\rm M}_{\odot }}$ yields $\alpha = 0.70^{+0.08}_{-0.07}$, in agreement with the field environment within the 1σ interval. The environmental dependence is due to the lowest-mass nucleated galaxies and we speculate that this is either due to an increased number of progenitor globular clusters merging to become an NSC, or due to the formation of more massive globular clusters in dense environments, depending on the initial globular cluster mass function. Our results clearly corroborate recent results in that there exists a tight connection between NSCs and globular clusters in dwarf galaxies.

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

The giants that were born swiftly – implications of the top-heavy stellar initial mass function on the birth conditions of globular clusters

ABSTRACT Recent results suggest that the initial mass function (IMF) of globular clusters (GCs) is metallicity and density dependent. Here, it is studied how this variation affects the initial masses and the numbers of core-collapse supernovae (CCSNe) required to reproduce the observed iron spreads in GCs. The IMFs of all of the investigated GCs were top-heavy implying larger initial masses compared to previous results computed assuming an invariant canonical IMF. This leads to more CCSNe being required to explain the observed iron abundance spreads. The results imply that the more massive GCs formed at smaller Galactocentric radii, possibly suggesting in situ formation of the population II halo. The time until star formation ended within a proto-GC is computed to be 3.5–4 Myr, being slightly shorter than the 4 Myr obtained using the canonical IMF. Therefore, the impact of the IMF on the time for which IMF lasts is small.

Constraining the formation of NGC 1052-DF2 from its unusual globular cluster population

ABSTRACT The ultra-diffuse galaxy (UDG) NGC 1052-DF2 has a low dark matter content and hosts a very unusual globular cluster (GC) population, with a median luminosity ∼4 times higher than in most galaxies and containing about 5 per cent of the galaxy’s stars. We apply a theoretical model that predicts the initial cluster mass function as a function of the galactic environment to investigate the origin of DF2’s peculiar GC system. Using the GC mass function, the model constrains the star-forming conditions in the galaxy during the formation of its GCs, ∼9 Gyr ago. We predict that the GCs formed in an environment with very high gas surface density, $\Sigma _{\rm ISM}\gtrsim 10^3\rm \,{M_\odot}\rm \,{pc}^{-2}$, and strong centrifugal support, $\Omega \gtrsim 0.7\rm \,{Myr}^{-1}$, similar to nearby circumnuclear starbursts and the central region of the Milky Way. The extreme conditions required to form the observed GC population imply a very high cluster formation efficiency of ≈87 per cent, and contrast strongly with the current diffuse nature of the galaxy. Since a nuclear starburst would lead to the rapid in-spiral of the GCs and is ruled out by the absence of a nuclear star cluster, we propose that the GCs plausibly formed during a major merger at z ∼ 1.3. The merger remnant must have undergone significant expansion of its stellar (and perhaps also its dark matter) component to reach its low present surface brightness, leading to the interesting possibility that it was the formation of DF2’s extreme GC population that caused it to become a UDG. If true, this strong structural evolution would have important implications for understanding the origins of UDGs.

Low-metallicity Young Clusters in the Outer Galaxy. III. Sh 2-127

Abstract In deep near-infrared imaging of the low-metallicity ([O/H] = −0.7 dex) H ii region Sh 2-127 (S127) with Subaru/MOIRCS, we detected two young clusters with 413 members (S127A) in a slightly extended H ii region and another with 338 members (S127B) in a compact H ii region. The limiting magnitude was K = 21.3 mag (10σ), corresponding to a mass detection limit of ∼0.2 . These clusters are an order of magnitude larger than previously studied young low-metallicity clusters and larger than the majority of solar neighborhood young clusters. Fits to the K-band luminosity functions indicate very young cluster ages of 0.5 Myr for S127A and 0.1–0.5 Myr for S127B, consistent with the large extinction (up to A V ≃ 20 mag) from thick molecular clouds and the presence of a compact H ii region and class I source candidates, and suggest that the initial mass function (IMF) of the low-metallicity clusters is indistinguishable from typical solar neighborhood IMFs. Disk fractions of 28% ± 3% for S127A and 40% ± 4% for S127B are significantly lower than those of similarly aged solar neighborhood clusters (∼50%–60%). The disk fraction for S127B is higher than those of previously studied low-metallicity clusters (<30%), probably due to S127B’s age. This suggests that a large fraction of very young stars in low-metallicity environments have disks, but the disks are lost on a very short timescale. These results are consistent with our previous studies of low-metallicity star-forming regions, suggesting that a solar neighborhood IMF and low disk fraction are typical characteristics for low-metallicity regions, regardless of cluster scales.

Merger rate of black hole binaries from globular clusters: Theoretical error bars and comparison to gravitational wave data from GWTC-2

Black hole binaries formed dynamically in globular clusters are believed to be one of the main sources of gravitational waves in the Universe. Here, we use our new population synthesis code, cBHBd, to determine the redshift evolution of the merger rate density and masses of black hole binaries formed in globular clusters. We simulate $\sim 2$ million models to explore the parameter space that is relevant to real clusters and over all mass scales. We show that when uncertainties on the initial cluster mass function and density are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Other model parameters (e.g., natal kicks, black hole masses, metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modelling the merger rate density as a function of redshift as $R(z)=R_0(1+z)^\kappa$ at $z<2$, and marginalizing over uncertainties, we find: $R_0=7.2^{+21.5}_{-5.5}{\rm Gpc^{-3}yr^{-1}}$ and $\kappa=1.6^{+0.4}_{-0.6}$ ($90\%$ credibility). The rate parameters for binaries that merge inside the clusters are ${R}_{\rm 0,in}=1.6^{+1.9}_{-1.0}{\rm Gpc^{-3}yr^{-1}}$ and $\kappa_{\rm in}=2.3^{+1.3}_{-1.0}$; $\sim 20\%$ of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute $\lesssim 0.4 \rm Gpc^{-3}yr^{-1}$ to the local rate. A comparison to the merger rate reported by LIGO-Virgo shows that a scenario in which most of the detected black hole mergers are formed in globular clusters is consistent with current constraints, and requires initial cluster half-mass densities $\gtrsim 10^4 M_\odot \rm pc^{-3}$. Such models also reproduce the inferred primary black hole mass distribution for masses $13-30 M_\odot$, but under-predict the data outside this range.

The future of IMF studies with the ELT and MICADO

Context. Young stellar cluster cores in the local Universe provide the most pristine information available on the stellar initial mass function (IMF), but their stellar densities are too high to be resolved by present-day instrumentation. With a resolving power 100 times better than the Hubble Space Telescope, the Multi-Adaptive Optics Imaging CameraA for Deep Observations (MICADO), which is the near-infrared camera on the Extremely Large Telescope (ELT), will for the first time provide access to a significant number of dense young stellar clusters that are critical for direct studies on the universality and shape of the IMF. Aims. In this work we aim to estimate the lowest stellar mass that MICADO will be able to reliably detect given a stellar density and distance. We also show that instrumental effects that will play a critical role, and report the number of young clusters that will be accessible for IMF studies in the local Universe with the ELT. Methods. We used SimCADO*, the instrument simulator package for the MICADO camera, to generate observations of 56 dense stellar regions with densities similar to the cores of young stellar clusters. We placed the cluster fields at distances between 8 kpc and 5 Mpc from the Earth, implying core densities from 102 to 105 stars arcsec−2, and determined the lowest reliably observable mass for each stellar field through point-spread function fitting photometry. Results. Our results show that stellar densities of &lt;103 stars arcsec−2 will be easily resolvable by MICADO. The lowest reliably observable mass in the Large Magellanic Cloud will be around 0.1 M⊙ for clusters with densities &lt;103 stars arcsec−2. MICADO will be able to access the stellar content of the cores of all dense young stellar clusters in the Magellanic Clouds, allowing the peak and shape of the IMF to be studied in great detail outside the Milky Way. At a distance of 2 Mpc, all stars with M &gt; 2 M⊙ will be resolved in fields of &lt;104 stars arcsec−2, allowing the high-mass end of the IMF to be studied in all galaxies out to and including NGC 300. Conclusions. We show that MICADO on the ELT will be able to probe the IMF of star clusters that are ten times denser than what the James Webb Space Telescope will be able to access, and over one hundred times denser than the clusters that the Hubble Space Telescope can successfully resolve. While the sensitivity of MICADO will not allow us to study the brown dwarf regime outside the Milky Way, it will enable access to all stellar members of over 1000 young clusters in the Milky Way and the Magellanic Clouds. Furthermore, direct measurements of the Salpeter slope of the IMF will be possible in over 1500 young clusters out to a distance of 5 Mpc. MICADO on the ELT will be able to measure resolved IMFs for a large ensemble of young clusters under starkly different environments and test the universality of the IMF in the local Universe.

The impact of star formation sampling effects on the spectra of lensed z &amp;gt; 6 galaxies detectable with JWST

ABSTRACT The upcoming James Webb Space Telescope (JWST) will allow observations of high-redshift galaxies at fainter detection levels than ever before, and JWST surveys targeting gravitationally lensed fields are expected to bring z ≳ 6 objects with very low star formation rate (SFR) within reach of spectroscopic studies. As galaxies at lower and lower star formation activity are brought into view, many of the standard methods used in the analysis of integrated galaxy spectra are at some point bound to break down, due to violation of the assumptions of a well-sampled stellar initial mass function (IMF) and a slowly varying SFR. We argue that galaxies with SFR ∼ 0.1 M⊙ yr−1 are likely to turn up at the spectroscopic detection limit of JWST in lensed fields, and investigate to what extent star formation sampling may affect the spectral analysis of such objects. We use the slug spectral synthesis code to demonstrate that such effects are likely to have significant impacts on spectral diagnostics of, for example, the Balmer emission lines. These effects are found to stem primarily from SFRs varying rapidly on short (∼Myr) time-scales due to star formation in finite units (star clusters), whereas the effects of an undersampled IMF is deemed insignificant in comparison. In contrast, the ratio between the He ii- and H i-ionizing flux is found to be sensitive to IMF-sampling as well as ICMF-sampling (sampling of the initial cluster mass function), which may affect interpretations of galaxies containing Population III stars or other sources of hard ionizing radiation.

Young star cluster populations in the E-MOSAICS simulations

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

A model for the minimum mass of bound stellar clusters and its dependence on the galactic environment

ABSTRACT We present a simple physical model for the minimum mass of bound stellar clusters as a function of the galactic environment. The model evaluates which parts of a hierarchically clustered star-forming region remain bound given the time-scales for gravitational collapse, star formation, and stellar feedback. We predict the initial cluster mass functions (ICMFs) for a variety of galaxies and we show that these predictions are consistent with observations of the solar neighbourhood and nearby galaxies, including the Large Magellanic Cloud and M31. In these galaxies, the low minimum cluster mass of ∼102 M⊙ is caused by sampling statistics, representing the lowest mass at which massive (feedback-generating) stars are expected to form. At the high gas density and shear found in the Milky Way’s Central Molecular Zone and the nucleus of M82, the model predicts that a mass &gt;102 M⊙ must collapse into a single cluster prior to feedback-driven dispersal, resulting in narrow ICMFs with elevated characteristic masses. We find that the minimum cluster mass is a sensitive probe of star formation physics due to its steep dependence on the star formation efficiency per free-fall time. Finally, we provide predictions for globular cluster (GC) populations, finding a narrow ICMF for dwarf galaxy progenitors at high redshift, which can explain the high specific frequency of GCs at low metallicities observed in Local Group dwarfs like Fornax and WLM. The predicted ICMFs in high-redshift galaxies constitute a critical test of the model, ideally suited for the upcoming generation of telescopes.

Unexpectedly high formation rate of merging binary black holes in open clusters

AbstractGravitational wave direct detections suggest that 30 M⊙ binary black holes (BBHs) commonly exist in the universe. One possible formation scenario of such BBHs is dynamical three-body encounters in dense star clusters. We performed a series of direct N-body simulations with a mass of 2500 and 10000 M⊙ and found a new channel for the formation of BBHs which is dominant in open clusters. In open clusters, the core-collapse time is shorter than in globular clusters, and therefore massive main-sequence (MS) binaries can form before they evolve to BHs. These MS binaries experience common envelope evolution and evolve to hard BBHs, which can merge within the Hubble time. The number of BBH mergers per unit mass obtained from our simulations reached 20–50 % of that for globular clusters, assuming an initial cluster mass function. Thus, open clusters can be a dominant formation site of hard BBHs.

Formation of globular cluster systems – II. Impact of the cut-off of the cluster initial mass function

Observations of young star clusters reveal that the high-mass end of the cluster initial mass function (CIMF) deviates from a pure power-law and instead truncates exponentially. We investigate the effects of this truncation on the formation of globular cluster (GC) systems by updating our analytic model for cluster formation and evolution, which is based on dark matter halo merger trees coupled to empirical galactic scaling relations, and has been shown in previous work to match a wide array of observational data. The cutoff masses of $M_c=10^{6.5} M_{\odot}$ or $10^{7}M_{\odot}$ match many scaling relations: between the GC system mass and host halo mass, between the average metallicity of the GC system and host halo mass, and the distribution of cluster masses. This range of $M_c$ agrees with indirect measurements from extragalactic GC systems. Models with $M_c<10^{6.5}M_{\odot}$ cannot reproduce the observed GC metallicity and mass distributions in massive galaxies. The slope of the mass-metallicity relation for metal-poor clusters (blue tilt) for all $M_c$ models is consistent with observations within their errors, when measured using the same method. We introduce an alternative, more robust fitting method, which reveals a trend of increasing tilt slope for lower $M_c$. In our model the blue tilt arises because the metal-poor clusters form in relatively low-mass galaxies which lack sufficient cold gas to sample the CIMF at highest masses. Massive blue clusters form in progressively more massive galaxies and inherit their higher metallicity. The metal-rich clusters do not exhibit such a tilt because they form in significantly more massive galaxies, which have enough cold gas to fully sample the CIMF.

The Arches cluster revisited

The Arches is one of the youngest, densest and most massive clusters in the Galaxy. As such it provides a unique insight into the lifecycle of the most massive stars known and the formation and survival of such stellar aggregates in the extreme conditions of the Galactic Centre. In a previous study we presented an initial stellar census for the Arches and in this work we expand upon this, providing new and revised classifications for ∼30% of the 105 spectroscopically identified cluster members as well as distinguishing potential massive runaways. The results of this survey emphasise the homogeneity and co-evality of the Arches and confirm the absence of H-free Wolf-Rayets of WC sub-type and predicted luminosities. The increased depth of our complete dataset also provides significantly better constraints on the main sequence population; with the identification of O9.5 V stars for the first time we now spectroscopically sample stars with initial masses ranging from ∼16 M⊙ to ≥120 M⊙. Indeed, following from our expanded stellar census we might expect ≳50 stars within the Arches to have been born with masses ≳60 M⊙, while all 105 spectroscopically confirmed cluster members are massive enough to leave relativistic remnants upon their demise. Moreover the well defined observational properties of the main sequence cohort will be critical to the construction of an extinction law appropriate for the Galactic Centre and consequently the quantitative analysis of the Arches population and subsequent determination of the cluster initial mass function.

Redshift Evolution of the Black Hole Merger Rate from Globular Clusters

Abstract As the sensitivity of current and future gravitational-wave detectors improves, it will become possible to measure the evolution of the binary black hole merger rate with redshift. Here, we combine detailed fits to state-of-the-art dynamical models of binary black hole formation in dense star clusters with a cosmological model of cluster formation across cosmic time. We find a typical merger rate of 14 Gpc−3 yr−1 in the local universe, with a reasonable range of 4–18 Gpc−3 yr−1, depending on the rate of cluster disruption and the cluster initial mass function. This rate increases by a factor of 6 to redshift z = 2.7 before declining at higher redshifts. We compare the merger rate from binaries produced in clusters to similar estimates from isolated binaries and triples in galactic fields, and discuss various ways that these different formation channels could add up to the current merger rate observed by the Laser Interferometer Gravitational-Wave Observatory/Virgo.