Mass Function Of Globular Clusters Research Articles

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.

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 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.

Testing feedback from star clusters in simulations of the Milky Way formation

ABSTRACT We present a suite of galaxy formation simulations that directly model star cluster formation and disruption. Starting from a model previously developed by our group, here we introduce several improvements to the prescriptions for cluster formation and feedback, then test these updates using a large suite of cosmological simulations of Milky Way mass galaxies. We perform a differential analysis with the goal of understanding how each of the updates affects star cluster populations. Two key parameters are the momentum boost of supernova feedback fboost and star formation efficiency per free-fall time ϵff. We find that fboost has a strong influence on the galactic star formation rate, with higher values leading to less star formation. The efficiency ϵff does not have a significant impact on the global star formation rate, but dramatically changes cluster properties, with increasing ϵff leading to a higher maximum cluster mass, shorter age spread of stars within clusters, and higher integrated star formation efficiencies. We also explore the redshift evolution of the observable cluster mass function, finding that most massive clusters have formed at high redshift z > 4. Extrapolation of cluster disruption to z = 0 produces good agreement with both the Galactic globular cluster mass function and age–metallicity relation. Our results emphasize the importance of using small-scale properties of galaxies to calibrate subgrid models of star cluster formation and feedback.

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.

New insight into the stellar mass function of Galactic globular clusters

ABSTRACT We present the results of the analysis of deep photometric data of 32 Galactic globular clusters. We analysed 69 parallel field images observed with the Wide Field Channel of the Advanced Camera for Surveys of the Hubble Space Telescope which complemented the already available photometry from the globular cluster treasury project covering the central regions of these clusters. This unprecedented data set has been used to calculate the relative fraction of stars at different masses (i.e. the present-day mass function) in these clusters by comparing the observed distribution of stars along the cluster main sequence and across the analysed field of view with the prediction of multimass dynamical models. For a subsample of 31 clusters, we were able to obtain also the half-mass radii, mass-to-light ratios, and the mass fraction of dark remnants using available radial velocity information. We found that the majority of globular clusters have single power-law mass functions F(m) ∝ mα with slopes α > −1 in the mass range 0.2 < m/M⊙ < 0.8. By exploring the correlations between the structural/dynamical and orbital parameters, we confirm the tight anticorrelation between the mass function slopes and the half-mass relaxation times already reported in previous works, and possible second-order dependence on the cluster metallicity. This might indicate the relative importance of both initial conditions and evolutionary effects on the present-day shape of the mass function.

The Optical Afterglow of GW170817: An Off-axis Structured Jet and Deep Constraints on a Globular Cluster Origin

Abstract We present a revised and complete optical afterglow light curve of the binary neutron star merger GW170817, enabled by deep Hubble Space Telescope (HST) F606W observations at ≈584 days post-merger, which provide a robust optical template. The light curve spans ≈110–362 days, and is fully consistent with emission from a relativistic structured jet viewed off-axis, as previously indicated by radio and X-ray data. Combined with contemporaneous radio and X-ray observations, we find no spectral evolution, with a weighted average spectral index of 〈 β 〉 = − 0.583 ± 0.013 , demonstrating that no synchrotron break frequencies evolve between the radio and X-ray bands over these timescales. We find that an extrapolation of the post-peak temporal slope of GW170817 to the luminosities of cosmological short gamma-ray bursts matches their observed jet break times, suggesting that their explosion properties are similar, and that the primary difference in GW170817 is viewing angle. Additionally, we place a deep limit on the luminosity and mass of an underlying globular cluster (GC) of L ≲ 6.7 × 103 L ⊙, or M ≲ 1.3 × 104 M ⊙, at least 4 standard deviations below the peak of the GC mass function of the host galaxy, NGC 4993. This limit provides a direct and strong constraint that GW170817 did not form and merge in a GC. As highlighted here, HST (and soon the James Webb Space Telescope) enables critical observations of the optical emission from neutron star merger jets and outflows.

Dynamical effects on the stellar mass function of multiple stellar populations in globular clusters

AbstractWe present a brief summary of the results of a study of the effects of dynamical evolution on the stellar mass function of multiple-population globular clusters. Theoretical studies have predicted that the process of multiple-population cluster formation results in a system in which second-generation (2G) stars are initially more centrally concentrated than first-generation (1G) stars. In the study presented here, we have explored the implications of the initial differences between the 2G and 1G structural properties for the evolution of the local (measured at different distances from a cluster center) and global mass function. We have studied both systems in which 1G and 2G stars start with the same initial mass function (IMF) and systems in which 1G and 2G stars have different IMFs. Finally we have explored the evolution of the spatial mixing and found that the multiscale nature of the clusters studied leads to a dependence of the mixing rate on the stellar mass.

A catalogue of masses, structural parameters, and velocity dispersion profiles of 112 Milky Way globular clusters

We have determined masses, stellar mass functions and structural parameters of 112 Milky Way globular clusters by fitting a large set of N-body simulations to their velocity dispersion and surface density profiles. The velocity dispersion profiles were calculated based on a combination of more than 15,000 high-precision radial velocities which we derived from archival ESO/VLT and Keck spectra together with ~20,000 published radial velocities from the literature. Our fits also include the stellar mass functions of the globular clusters, which are available for 47 clusters in our sample, allowing us to self-consistently take the effects of mass segregation and ongoing cluster dissolution into account. We confirm the strong correlation between the global mass functions of globular clusters and their relaxation times recently found by Sollima & Baumgardt (2017). We also find a correlation of the escape velocity from the centre of a globular cluster and the fraction of first generation stars (FG) in the cluster recently derived for 57 globular clusters by Milone et al. (2017), but no correlation between the FG star fraction and the global mass function of a globular cluster. This could indicate that the ability of a globular cluster to keep the wind ejecta from the polluting star(s) is the crucial parameter determining the presence and fraction of second generation stars and not its later dynamical mass loss.

Globular cluster formation and evolution in the context of cosmological galaxy assembly: open questions.

We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state of the art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages greater than or equal to 12.5 Gyr and formed around the time of reionization. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z∼6 with the James Webb Space Telescope (JWST) promise further insight. GCs are known to host multiple populations of stars with variations in their chemical abundances. Recently, such multiple populations have been detected in ∼2 Gyr old compact, massive star clusters. This suggests a common, single pathway for the formation of GCs at high and low redshift. The shape of the initial mass function for GCs remains unknown; however, for massive galaxies a power-law mass function is favoured. Significant progress has been made recently modelling GC formation in the context of galaxy formation, with success in reproducing many of the observed GC-galaxy scaling relations.

The global mass functions of 35 Galactic globular clusters – II. Clues on the initial mass function and black hole retention fraction

In this paper we compare the mass function slopes of Galactic globular clusters recently determined by Sollima & Baumgardt (2017) with a set of dedicated N-body simulations of star clusters containing between 65,000 to 200,000 stars. We study clusters starting with a range of initial mass functions (IMFs), black hole retention fractions and orbital parameters in the parent galaxy. We find that the present-day mass functions of globular clusters agree well with those expected for star clusters starting with Kroupa or Chabrier IMFs, and are incompatible with clusters starting with single power-law mass functions for the low-mass stars. The amount of mass segregation seen in the globular clusters studied by Sollima & Baumgardt (2017) can be fully explained by two-body relaxation driven mass segregation from initially unsegregated star clusters. Based on the present-day global mass functions, we expect that a typical globular cluster in our sample has lost about 75% of its mass since formation, while the most evolved clusters have already lost more than 90% of their initial mass and should dissolve within the next 1 to 2 Gyr. Most clusters studied by Sollima & Baumgardt also show a large difference between their central and global MF slopes, implying that the majority of Galactic globular clusters is either near or already past core collapse. The strong mass segregation seen in most clusters also implies that only a small fraction of all black holes formed in globular clusters still reside in them.

Evolution of Star Clusters in Time-variable Tidal Fields

Abstract Strong tidal forces can dominate star cluster evolution in merging galaxies, determining their mass-loss rates and lifetimes. In order to model this evolution, we have developed a second-order accurate numerical method for integrating a star cluster in an arbitrary time-variable tidal field. We extend the Kira N-body integrator to handle these external fields. We obtain realistic tidal histories from a galaxy merger simulation including sink particles, which we interpret as young star clusters. Coupling these tidal accelerations to N-body models of isolated clusters, we perform detailed dynamical studies. This generalizes the formalism previously used to explore the dynamical effects of the galactic tidal field on clusters in circular orbits. We find that, in contrast to previous studies that considered only stellar and dark matter dynamics, tidal interactions between clusters and dense gas in the galactic disk can significantly influence cluster mass loss and lifetimes. Using our models, we develop an effective semianalytic model that can be used for fast estimation of cluster mass loss in a galactic tidal field and to study the evolution of the globular cluster mass function in isolated and merging galaxies.

EVOLUTION OF THE MASS AND LUMINOSITY FUNCTIONS OF GLOBULAR STAR CLUSTERS

ABSTRACT We reexamine the dynamical evolution of the mass and luminosity functions of globular star clusters (GCMF and GCLF). Fall & Zhang (2001, FZ01) showed that a power-law MF, as commonly seen among young cluster systems, would evolve by dynamical processes over a Hubble time into a peaked MF with a shape very similar to the observed GCMF in the Milky Way and other galaxies. To simplify the calculations, the semi-analytical FZ01 model adopted the “classical” theory of stellar escape from clusters, and neglected variations in the /L ratios of clusters. Kruijssen & Portegies Zwart (2009, KPZ09) modified the FZ01 model to include “retarded” and mass-dependent stellar escape, the latter causing significant /L variations. KPZ09 asserted that their model was compatible with observations, whereas the FZ01 model was not. We show here that this claim is not correct; the FZ01 and KPZ09 models fit the observed Galactic GCLF equally well. We also show that there is no detectable correlation between /L and L for GCs in the Milky Way and Andromeda galaxies, in contradiction with the KPZ09 model. Our comparisons of the FZ01 and KPZ09 models with observations can be explained most simply if stars escape at rates approaching the classical limit for high-mass clusters, as expected on theoretical grounds.

If it does not kill them, it makes them stronger: collisional evolution of star clusters with tidal shocks

Abstract The radii of young (≲100 Myr) star clusters correlate only weakly with their masses. This shallow relation has been used to argue that impulsive tidal perturbations, or ‘shocks’, by passing giant molecular clouds (GMCs) preferentially disrupt low-mass clusters. We show that this mass–radius relation is in fact the result of the combined effect of two-body relaxation and repeated tidal shocks. Clusters in a broad range of environments including those like the solar neighbourhood evolve towards a typical radius of a few parsecs, as observed, independent of the initial radius. This equilibrium mass–radius relation is the result of a competition between expansion by relaxation and shrinking due to shocks. Interactions with GMCs are more disruptive for low-mass clusters, which helps to evolve the globular cluster mass function (GCMF). However, the properties of the interstellar medium in high-redshift galaxies required to establish a universal GCMF shape are more extreme than previously derived, challenging the idea that all GCs formed with the same power-law mass function.

Effects of cosmic string velocities and the origin of globular clusters

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

Stellar population properties of the most massive globular clusters and ultra-compact dwarf galaxies of the Fornax cluster

AbstractMost ultra-compact dwarf galaxies (UCDs) and very massive globular clusters reside in nearby galaxy clusters or around nearby giant galaxies. Due to their distance (> 4 Mpc) and compactness (reff < 100 pc) they are barely resolved, and thus it is difficult to obtain their internal properties. Here I present our most recent attempts to constrain the mass function, stellar content and dynamical state of UCDs in the Fornax cluster. Thanks to radial velocity membership assignment of ~ 950 globular clusters (GCs) and UCDs in the core of Fornax, the shape of their mass function is well constrained. It is consistent with the ‘standard’ Gaussian mass function of GCs. Our recent simulations on the disruption process of nucleated dwarf galaxies in cluster environments showed that ~ 40% of the most massive UCDs should originate from nuclear star clusters. Some Fornax UCDs actually show evidence for this scenario, as revealed by extended low surface brightness disks around them and onsets of tidal tails. Multi-band UV to optical imaging as well as low to medium resolution spectroscopy revealed that there exist UCDs with youngish ages, (sub-)solar [α/Fe] abundances, and probably He-enriched populations.

Cosmic strings and the origin of globular clusters

We hypothesize that cosmic string loops are the seeds about which globular clusters accrete. Fixing the cosmic string tension by demanding that the peak in the distribution of masses of objects accreting onto string loops agrees with the peak in the observed mass distribution of globular clusters in our Milky Way galaxy, we then compute the expected number density and mass function of globular clusters, and compare with observations. Our hypothesis naturally explains why globular clusters are the oldest and most dense objects in a galaxy, and why they are found in the halo of the galaxy.

Contribution of stripped nuclear clusters to globular cluster and ultracompact dwarf galaxy populations

We use the Millennium II cosmological simulation combined with the semi-analytic galaxy formation model of Guo et al. (2011) to predict the contribution of galactic nuclei formed by the tidal stripping of nucleated dwarf galaxies to globular cluster (GC) and ultra-compact dwarf galaxy (UCD) populations of galaxies. We follow the merger trees of galaxies in clusters back in time and determine the absolute number and stellar masses of disrupted galaxies. We assume that at all times nuclei have a distribution in nucleus-to-galaxy mass and nucleation fraction of galaxies similar to that observed in the present day universe. Our results show stripped nuclei follow a mass function $N(M) \sim M^{-1.5}$ in the mass range $10^6 < M/M_\odot < 10^8$, significantly flatter than found for globular clusters. The contribution of stripped nuclei will therefore be most important among high-mass GCs and UCDs. For the Milky Way we predict between 1 and 3 star clusters more massive than $10^5 M_\odot$ come from tidally disrupted dwarf galaxies, with the most massive cluster formed having a typical mass of a few times $10^6 M_\odot$, like omega Centauri. For a galaxy cluster with a mass $7 \times 10^{13} M_\odot$, similar to Fornax, we predict $\sim$19 UCDs more massive than $2\times10^6 M_\odot$ and $\sim$9 UCDs more massive than $10^7 M_\odot$ within a projected distance of 300 kpc come from tidally stripped dwarf galaxies. The observed number of UCDs are $\sim$200 and 23, respectively. We conclude that most UCDs in galaxy clusters are probably simply the high mass end of the GC mass function.

Clues on the missing sources of reionization from self-consistent modelling of Milky Way and dwarf galaxy globular clusters

Globular clusters are unique tracers of ancient star formation. We determine the formation efficiencies of globular clusters across cosmic time by modelling the formation and dynamical evolution of the globular cluster population of a Milky Way type galaxy in hierarchical cosmology, using the merger tree from the Via Lactea II simulation. All of the models are constrained to reproduce the observed specific frequency and initial mass function of globular clusters in isolated dwarfs. Globular cluster orbits are then computed in a time varying gravitational potential after they are either accreted from a satellite halo or formed in situ, within the Milky Way halo. We find that the Galactocentric distances and metallicity distribution of globular clusters are very sensitive to the formation efficiencies of globular clusters as a function of redshift and halo mass. Our most accurate models reveal two distinct peaks in the globular cluster formation efficiency at z ∼ 2 and 7–12 and prefer a formation efficiency that is mildly increasing with decreasing halo mass, the opposite of what expected for feedback-regulated star formation. This model accurately reproduces the positions, velocities, mass function, metallicity distribution, and age distribution of globular clusters in the Milky Way and predicts that ∼40 per cent formed in situ, within the Milky Way halo, while the other ∼60 per cent were accreted from about 20 satellite dwarf galaxies with vcir > 30 km s−1, and about 29 per cent of all globular clusters formed at redshifts z > 7. These results further strengthen the notion that globular cluster formation was an important mode of star formation in high-redshift galaxies and likely played a significant role in the reionization of the intergalactic medium.

SIZES, HALF-MASS DENSITIES, AND MASS FUNCTIONS OF STAR CLUSTERS IN THE MERGER REMNANT NGC 1316: CLUES TO THE FATE OF SECOND-GENERATION GLOBULAR CLUSTERS

We study mass functions of globular clusters derived from HST/ACS images of the early-type merger remnant galaxy NGC 1316 which hosts a significant population of metal-rich globular clusters of intermediate age (~3 Gyr). For the old, metal-poor (`blue') clusters, the peak mass of the mass function M_p increases with internal half-mass density rho_h as (M_p proportional to rho_h^0.44) whereas it stays approximately constant with galactocentric distance R_gal. The mass functions of these clusters are consistent with a simple scenario in which they formed with a Schechter initial mass function and evolved subsequently by internal two-body relaxation. For the intermediate-age population of metal-rich ("red") clusters, the faint end of the previously reported power-law luminosity function of the clusters with R_gal > 9 kpc is due to many of those clusters having radii larger than the theoretical maximum value imposed by the tidal field of NGC 1316 at their R_gal. This renders disruption by two-body relaxation ineffective. Only a few such diffuse clusters are found in the inner regions of NGC 1316. Completeness tests indicate that this is a physical effect. Using comparisons with star clusters in other galaxies and cluster disruption calculations using published models, we hypothesize that most red clusters in the low-rho_h tail of the initial distribution have already been destroyed in the inner regions of NGC 1316 by tidal shocking, and that several remaining low-rho_h clusters will evolve dynamically to become similar to "faint fuzzies" that exist in several lenticular galaxies. Finally, we discuss the nature of diffuse red clusters in early-type galaxies.