Simulations Of Globular Clusters Research Articles

Simulations of globular clusters within their parent galaxies: Metallicity spreads and anomalous precursor populations

ABSTRACT Recent observations of globular clusters (GCs) suggest that elemental abundance variations may exist between first-generation (1G) stars. We propose that metal abundance (‘metallicity’) spreads within GC forming giant molecular clouds (GMCs) can influence the iron abundances of future cluster members. To investigate this, we use original hydrodynamical simulations to model GMC formation in a high redshift dwarf galaxy. Our simulations self-consistently model physical processes such as stellar feedback, dust formation and destruction, and molecular gas formation on dust grains, making them well suited to the study of GMC formation. We conclude that iron abundance variations in GMCs are due to the merging of gas clumps and self-enrichment processes. The metallicity dispersions of GC forming clumps is ∼0.1 dex, reflecting a growing number of studies that claim a non-zero dispersion within GCs. The galactic gas fraction is a key parameter for the formation of clumps and the metallicity ‘floor’ observed for both Galactic and extragalactic GCs are associated with the parent galaxy’s capacity to form massive GMCs. Finally, we argue that GMCs have the potential to trap surrounding metal-poor galactic disc stars, which we interpret as a precursor population (0G). These low metallicity stars are representative of the [Fe/H] value of the host dwarf and thus the chemistry of this 0G may be a fossilized record of the parent galaxy. These results depend on the initial metallicity and radial gradient of the galaxy, the threshold gas density for star formation, and the star formation prescription.

Simulations of globular clusters within their parent galaxies: multiple stellar populations and internal kinematics

ABSTRACT Using three-dimensional smoothed particle hydrodynamics simulations, we investigate the formation of multiple stellar populations (MSPs) in globular clusters (GCs) within the context of their parent galaxies. In our scenario, the second generation (2G) of stars originate from both asymptotic giant branch (AGB) polluters and pristine gas accreted from the host galaxy. Previous theoretical and numerical studies have demonstrated that this ‘AGB with dilution’ model has the potential to alleviate several problems faced by the classical AGB scenario. However, the accretion of pristine gas on to the GC has yet to be investigated within the context of the parent galaxy. This paper presents the preliminary results from our original simulation code which models GC formation from giant molecular clouds in a host galaxy, and subsequent gas accretion on to the GC. By simulating the genesis of the 2G over a 370 Myr time frame, we demonstrate that the fraction of 2G stars are inextricably linked to the GC’s environment. Our simulations rationalize the wide variety of abundance patterns, kinematics, and 2G concentrations by altering the initial conditions of both the GC progenitor and the host galaxy itself. Most notably, we reproduce a positive correlation between the fraction of 2G stars and the initial mass of the cluster. We discuss the physical implications of our scenario and compare our simulations with observations of the Galactic GC 47 Tucanae (47 Tuc). Finally, we present scaling relations that encompass the wider GC population and serve as a reference for future observations.

Black Hole Genealogy: Identifying Hierarchical Mergers with Gravitational Waves

Abstract In dense stellar environments, the merger products of binary black hole mergers may undergo additional mergers. These hierarchical mergers are naturally expected to have higher masses than the first generation of black holes made from stars. The components of hierarchical mergers are expected to have significant characteristic spins, imprinted by the orbital angular momentum of the previous mergers. However, since the population properties of first-generation black holes are uncertain, it is difficult to know if any given merger is first-generation or hierarchical. We use observations of gravitational waves to reconstruct the binary black hole mass and spin spectrum of a population including the possibility of hierarchical mergers. We employ a phenomenological model that captures the properties of merging binary black holes from simulations of globular clusters. Inspired by recent work on the formation of low-spin black holes, we include a zero-spin subpopulation. We analyze binary black holes from LIGO and Virgo’s first two observing runs, and find that this catalog is consistent with having no hierarchical mergers. We find that the most massive system in this catalog, GW170729, is mostly likely a first-generation merger, having a 4% probability of being a hierarchical merger assuming a 5 × 105 M ⊙ globular cluster mass. Using our model, we find that 99% of first-generation black holes in coalescing binaries have masses below M ⊙, and the fraction of binaries with near-zero component spins is less than (90% probability). Upcoming observations will determine if hierarchical mergers are a common source of gravitational waves.

A simple two-component description of energy equipartition and mass segregation for anisotropic globular clusters

In weakly-collisional stellar systems such as some globular clusters, partial energy equipartition and mass segregation are expected to develop as a result of the cumulative effect of stellar encounters, even in systems initially characterized by star-mass independent density and energy distributions. In parallel, numerical simulations have demonstrated that radially-biased pressure anisotropy slowly builds up in realistic models of globular clusters from initial isotropic conditions, leading to anisotropy profiles that, to some extent, mimic those resulting from incomplete violent relaxation known to be relevant to elliptical galaxies. In this paper, we consider a set of realistic simulations realized by means of Monte Carlo methods and analyze them by means of self-consistent, two-component models. For this purpose, we refer to an underlying distribution function originally conceived to describe elliptical galaxies, which has recently been truncated and adapted to the context of globular clusters. The two components are supposed to represent light stars (combining all main sequence stars) and heavy stars (giants, dark remnants, and binaries). We show that this conceptually simple family of two-component truncated models provides a reasonable description of simulated density, velocity dispersion, and anisotropy profiles, especially for the most relaxed systems, with the ability to quantitatively express the attained levels of energy equipartition and mass segregation. In contrast, two-component isotropic models based on the King distribution function do not offer a comparably satisfactory representation of the simulated globular clusters. With this work, we provide a new reliable diagnostic tool applicable to nonrotating globular clusters that are characterized by significant gradients in the local value of the mass-to-light ratio, beyond the commonly used one-component dynamical models. In particular, these models are supposed to be an optimal tool for the clusters that underfill the volume associated with the boundary surface determined by the tidal interaction with the host galaxy.

Realistic models of Globular Clusters with white dwarfs, neutron stars and black holes using GPU supercomputer

AbstractWe present some results from the DRAGON simulations, a set of four direct N-body simulations of globular clusters (GCs) with a million stars and five percent initial (primordial) binaries. These simulations were undertaken with the NBODY6++GPU code, which allowed us to follow dynamical and stellar evolution of individual stars and binaries, formation and evolution of white dwarfs, neutron stars, and black holes, and the effect of a galactic tidal field. The simulations are the largest existing models of a realistic globular cluster over its full lifetime of 12 billion years. In particular we will show here an investigation of the population of binaries including compact objects (such as white dwarfs - cataclysmic variables and merging black hole binaries in the model as counterparts of LIGO/Virgo sources); their distribution in the cluster and evolution with time.

MOCCA survey database I: Preliminary mock Extra Galactic Globular Cluster observations

AbstractThe photometric properties that we could observe for Extra-Galactic Globular Clusters (EGGCs) are the integrated light of the system and for nearby EGGCs it also is possible to measure both half-light radii and the color spatial distribution, e.g. for areas smaller and larger than the half-light radius. No information about the internal dynamical state of the system could be directly obtained from observations. On the other hand, simulations of Globular Clusters (GCs) can provide detailed information about the dynamical evolution of the system.We present a preliminary study of EGGCs’ photometric properties for different dynamical evolutionary stages. We apply this study to 12Gyr old GCs simulated as part of the MOCCA Survey Database. We determine the magnitudes in different bands from their projected snapshots using the Flexible Stellar Population Synthesis (FSPS) code and we measure the half-light radii from the surface brightness.

A new model for the multiple stellar populations within Terzan 5

Recent observational studies have demonstrated that the complex stellar system Terzan 5 (Ter 5) harbours multiple populations of stars. Several models have attempted to interpret the large age difference of several Gyrs between the dominant populations, but none have been universally accepted. We propose a new scenario whereby a collision between a metal-poor Ter 5 and a giant molecular cloud (GMC) serves as a catalyst for the generation of a super-solar population of stars. Using numerical simulations of this new "GC-GMC" collision scenario we demonstrate that, within a time frame of several Gyrs, our synthetic Ter 5 was capable of interacting with a metal-rich GMC in the central region of the Galaxy. As a consequence of this, our simulated globular cluster (GC) is able to capture enough gas from the colliding GMC to form a new population of metal-rich stars. Furthermore, the younger population created from the high-density regions of the captured gas is shown to have a stronger central mass concentration than the older metal-poor one, which is consistent with observations. A chemical link between Ter 5 and the bulge population of the Milky Way has long been observed and these simulations finally provide evidence for their similarities. Our model rationalises the 5 Gyrs of quiescence observed between the two dominant populations of Ter 5 and justifies the existence of the young generation. We discuss the advantages and disadvantages of the new scenario in the context of the observed physical properties of Ter 5.

Globular clusters with Gaia

The treatment of crowded fields in Gaia data will only be a reality in a few years from now. In particular, for globular clusters, only the end-of-mission data (public in 2022-2023) will have the necessary full crowding treatment and will reach sufficient quality for the faintest stars. As a consequence, the work on the deblending and decontamination pipelines is still ongoing. We describe the present status of the pipelines for different Gaia instruments, and we model the end-of-mission crowding errors on the basis of available information. We then apply the nominal post-launch Gaia performances, appropriately worsened by the estimated crowding errors, to a set of 18 simulated globular clusters with different concentration, distance, and field contamination. We conclude that there will be 103-104 stars with astrometric performances virtually untouched by crowding (contaminated by <1 mmag) in the majority of clusters. The most limiting factor will be field crowding, not cluster crowding: the most contaminated clusters will only contain 10-100 clean stars. We also conclude that: (i) the systemic proper motions and parallaxes will be determined to 1% or better up to 15 kpc, and the nearby clusters will have radial velocities to a few km/s ; (ii) internal kinematics will be of unprecendented quality, cluster masses will be determined to 10% up to 15 kpc and beyond, and it will be possible to identify differences of a few km/s or less in the kinematics (if any) of cluster sub-populations up to 10 kpc and beyond; (iii) the brightest stars (V<17 mag) will have space-quality, wide-field photometry (mmag errors), and all Gaia photometry will have 1-3% errors on the absolute photometric calibration.

A class of spherical, truncated, anisotropic models for application to globular clusters

Recently, a class of non-truncated radially-anisotropic models (the so-called $f^{(\nu)}$-models), originally constructed in the context of violent relaxation and modeling of elliptical galaxies, has been found to possess interesting qualities in relation to observed and simulated globular clusters. In view of new applications to globular clusters, we improve this class of models along two directions. To make them more suitable for the description of small stellar systems hosted by galaxies, we introduce a 'tidal' truncation (by means of a procedure that guarantees full continuity of the distribution function). The new $f_T^{(\nu)}$-models are shown to provide a better fit to the observed photometric and spectroscopic profiles for a sample of 13 globular clusters studied earlier by means of non-truncated models; interestingly, the best-fit models also perform better with respect to the radial-orbit instability. Then we design a flexible but simple two-component family of truncated models, to study the separate issues of mass segregation and of multiple populations. We do not aim at a fully realistic description of globular clusters, to compete with the description currently obtained by means of dedicated simulations. The goal here is to try to identify the simplest models, that is, those with the smallest number of free parameters, but still able to provide a reasonable description for clusters that are evidently beyond the reach of one-component models: with this tool we aim at identifying the key factors that characterize mass segregation or the presence of multiple populations. To reduce the relevant parameter space, we formulate a few physical arguments (based on recent observations and simulations). A first application to two well-studied globular clusters is briefly described and discussed.

Resolving stellar populations with crowded field 3D spectroscopy

(Abridged) We describe a new method to extract spectra of stars from observations of crowded stellar fields with integral field spectroscopy (IFS). Our approach extends the well-established concept of crowded field photometry in images into the domain of 3-dimensional spectroscopic datacubes. The main features of our algorithm are: (1) We assume that a high-fidelity input source catalogue already exists and that it is not needed to perform sophisticated source detection in the IFS data. (2) Source positions and properties of the point spread function (PSF) vary smoothly between spectral layers of the datacube, and these variations can be described by simple fitting functions. (3) The shape of the PSF can be adequately described by an analytical function. Even without isolated PSF calibrator stars we can therefore estimate the PSF by a model fit to the full ensemble of stars visible within the field of view. (4) By using sparse matrices to describe the sources, the problem of extracting the spectra of many stars simultaneously becomes computationally tractable. We present extensive performance and validation tests of our algorithm using realistic simulated datacubes that closely reproduce actual IFS observations of the central regions of Galactic globular clusters. We investigate the quality of the extracted spectra under the effects of crowding. The main effect of blending between two nearby stars is a decrease in the S/N in their spectra. The effect increases with the crowding in the field in a way that the maximum number of stars with useful spectra is always ~0.2 per spatial resolution element. This balance breaks down when exceeding a total source density of ~1 significantly detected star per resolution element. We close with an outlook by applying our method to a simulated globular cluster observation with the upcoming MUSE instrument at the ESO-VLT.

THE SIZE DIFFERENCE BETWEEN RED AND BLUE GLOBULAR CLUSTERS IS NOT DUE TO PROJECTION EFFECTS

Metal-rich (red) globular clusters in massive galaxies are, on average, smaller than metal-poor (blue) globular clusters. One of the possible explanations for this phenomenon is that the two populations of clusters have different spatial distributions. We test this idea by comparing clusters observed in unusually deep, high signal-to-noise images of M87 with a simulated globular cluster population in which the red and blue clusters have different spatial distributions, matching the observations. We compare the overall distribution of cluster effective radii as well as the relationship between effective radius and galactocentric distance for both the observed and simulated red and blue subpopulations. We find that the different spatial distributions does not produce a significant size difference between the red and blue subpopulations as a whole, or at a given galactocentric distance. These results suggest that the size difference between red and blue globular clusters is likely due to differences during formation or later evolution

Resolving Stellar Populations in Extragalactic Globular Cluster Systems

Photometric studies on globular cluster systems in early-type galaxies are widely used to resolve stellar populations in these galaxies. The knowledge of the age and metalicity structure within the globular cluster systems allows to set constraints on the major star formation episodes in the galaxy. Here we present our method of detecting age sub-populations in globular cluster systems based on optical/near-infrared observations and Monte-Carlo simulations. It is based on the determination of the cumulative age distribution and its comparison to simulated globular cluster systems. On various galaxies we will demonstrate the ability of our method to detect age sub-populations and show how we use the derived age structure to find correlations between various galaxy parameters and the formation/evolution of a given galaxy.

Extragalactic globular clusters in the near-infrared

We present the results of combined optical and near-infrared photometry for the globular cluster systems of the giant ellipticals IC 4051 and NGC 3311. We use the reduced age-metallicity degeneracy in (V - I) vs. (V - H) color-color diagrams to derive the cumulative age distribution within the red sub-population of globular clusters and to search for age sub-populations. The age distribution is then compared to the one determined for simulated globular cluster systems in order to set constraints on the relative age and size of these globular cluster sub-populations. In both galaxies we find a significant fraction of globular clusters with ages between 2-5 Gyr. We also investigate the metallicity distribution in both systems. Small number statistics prevent us from making any definite statements concerning NGC 3311, but we find that the derived metallicity distribution of the IC 4051 clusters strongly depends on the assumed age distribution. Based on our most likely result that finds a large number of young/intermediate age clusters (∼2 Gyr) within the selected globular cluster sample, we find metallicity peaks at ∼-0.2 for the old clusters and +0.8 for the young clusters. Only few very metal poor clusters are found. However, the metallicity distribution within the young/intermediate globular cluster population is significantly affected by our choice of the applied Single Stellar Population model. The mean metallicity of the second generation of globular clusters changes from the above mentioned and extremely high +0.8 dex to +0.2 dex. Note that the model dependency becomes less severe with an increasing age of the cluster population.

Intermediate-age globular clusters in early-type galaxies: Better age determinations by addingU-band observations to theV,I,Kdatasets

This paper represents an extension to a series of publications on combined optical and near-infrared photometry of globular cluster systems in early-type galaxies. Based on color-color diagrams the cumulative age distributions of their globular cluster systems have been derived and revealed intermediate age clusters in two galaxies, namely NGC 4365 and NGC 5846. The extension of this observations towards the blue wavelength range was performed in order to increase the age resolution of photometric studies. In this paper we present the results of U-band observations of NGC 4365 and NGC 5846 and their combination with previously obtained V, I and Ks-band photometry. (U − I )v s. (V − Ks) color-color diagrams are used to derive the cumulative age distribution. The later is compared to simulated globular cluster systems of known age and size composition in order to set constrains on relative ages and size of the sub-populations.

Deep HST V- and I-Band Observations of Two Globular Clusters in the Halo of M31.

We present deep (V ~= 27) V- and I-band stellar photometry of G302 and G312, two globular star clusters in the halo of M31. These data were obtained using the Hubble Space Telescope's Wide Field/Planetary Camera 2. We find iron abundances of [Fe/H] = -1.85 +/- 0.12 for G302 and [Fe/H] = -0.56 +/- 0.03 for G312, consistent with spectroscopic measurements. The color-magnitude diagrams for each cluster show no evidence for an intermediate-aged population of stars, or a second parameter effect in the morphology of the horizontal branch. G302 shows no evidence for a color gradient but the inner regions of G312 are bluer than the outer regions. G312 shows no evidence of ellipticity or an extended halo of unbound stars. G302 has a projected ellipticity of 0.195 +/- 0.012 with the projected major axis oriented towards the center of M31. G302 also shows evidence of an extended asymmetric stellar halo extending to at least twice the fitted Michie-King tidal radius. The amount of mass beyond the tidal radius of G302 is consistent with the stellar escape rates which have been predicted by N-body simulations of globular clusters in the Galactic tidal field.

Stellar Photometry by a Perfect CCD

We have developed algorithms for the construction of a simulated globular cluster, as it would appear on a frame obtained with a perfect CCD. This has allowed us to compare the absolute errors in the photometry of two different programs, DAOPHOT II (Stetson 1991, 1994) and SPS (Janes and Heasley 1993), with a special emphasis on criteria for selecting stars with the best photometry.