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  • 1
    Publication Date: 2015-09-06
    Description: We use N -body simulations to model the 12 Gyr evolution of a suite of star clusters with identical initial stellar mass functions over a range of initial cluster masses, sizes, and orbits. Our models reproduce the distribution of present-day global stellar mass functions that is observed in the Milky Way globular cluster population. We find that the slope of a star cluster's stellar mass function is strongly correlated with the fraction of mass that the cluster has lost, independent of the cluster's initial mass, and nearly independent of its orbit and initial size. Thus, the mass function–initial mass relation can be used to determine a Galactic cluster's initial total stellar mass, if the initial stellarmass function is known. We apply the mass function–initial mass relation presented here to determine the initial stellar masses of 33 Galactic globular clusters, assuming an universal Kroupa initial mass function. Our study suggests that globular clusters had initial masses that were on average a factor of 4.5 times larger than their present-day mass, with three clusters showing evidence for being 10 times more massive at birth.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
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  • 2
    Publication Date: 2016-10-08
    Description: A number of recent observational studies of Galactic globular clusters have measured the variation in the slope of a cluster's stellar mass function α with clustercentric distance r . In order to gather a deeper understanding of the information contained in such observations, we have explored the evolution of α( r ) for star clusters with a variety of initial conditions using a large suite of N -body simulations. We have specifically studied how the time evolution of α( r ) is affected by initial size, mass, binary fraction, primordial mass segregation, black hole retention, an external tidal field, and the initial mass function itself. Previous studies have shown that the evolution of α G is closely related to the amount of mass-loss suffered by a cluster. Hence, for each simulation, we have also followed the evolution of the slope of the cluster's global stellar mass function, α G , and have shown that clusters follow a well-defined track in the α G –dα( r )/d(ln( r / r m )) plane. The location of a cluster on the α G –dα( r )/d(ln( r / r m )) plane can therefore constrain its dynamical history and, in particular, constrain possible variations in the stellar initial mass function. The α G –dα( r )/d(ln( r / r m )) plane thus serves as a key tool for fully exploiting the information contained in wide-field studies of cluster stellar mass functions.
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  • 3
    Publication Date: 2016-10-30
    Description: We make use of N -body simulations to determine the relationship between two observable parameters that are used to quantify mass segregation and energy equipartition in star clusters. Mass segregation can be quantified by measuring how the slope of a cluster's stellar mass function α changes with clustercentric distance r , and then calculating $\delta _\alpha = \frac{{\rm d} \alpha (r)}{{\rm d} ln(r/r_{\rm m})}$ , where r m is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by , which is a measure of how stellar velocity dispersion depends on stellar mass m via ( m ) m – . Through a suite of N -body star cluster simulations with a range of initial sizes, binary fractions, orbits, black hole retention fractions, and initial mass functions, we present the co-evolution of α and . We find that measurements of the global are strongly affected by the radial dependence of and mean stellar mass and the relationship between and α depends mainly on the cluster's initial conditions and the tidal field. Within r m , where these effects are minimized, we find that and α initially share a linear relationship. However, once the degree of mass segregation increases such that the radial dependence of and mean stellar mass become a factor within r m , or the cluster undergoes core collapse, the relationship breaks down. We propose a method for determining within r m from an observational measurement of α . In cases where and α can be measured independently, this new method offers a way of measuring the cluster's dynamical state.
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  • 4
    Publication Date: 2016-06-10
    Description: We investigate the shallow increase in globular cluster half-light radii with projected galactocentric distance R gc observed in the giant galaxies M87, NGC 1399, and NGC 5128. To model the trend in each galaxy, we explore the effects of orbital anisotropy and tidally underfilling clusters. While a strong degeneracy exists between the two parameters, we use kinematic studies to help constrain the distance R β beyond which cluster orbits become anisotropic, as well as the distance R fα beyond which clusters are tidally underfilling. For M87 we find R β  〉 27 kpc and 20 〈  R fα  〈 40 kpc and for NGC 1399 R β  〉 13 kpc and 10 〈  R fα  〈 30 kpc. The connection of R fα with each galaxy's mass profile indicates the relationship between size and R gc may be imposed at formation, with only inner clusters being tidally affected. The best-fitting models suggest the dynamical histories of brightest cluster galaxies yield similar present-day distributions of cluster properties. For NGC 5128, the central giant in a small galaxy group, we find R β  〉 5 kpc and R fα  〉 30 kpc. While we cannot rule out a dependence on R gc , NGC 5128 is well fitted by a tidally filling cluster population with an isotropic distribution of orbits, suggesting it may have formed via an initial fast accretion phase. Perturbations from the surrounding environment may also affect a galaxy's orbital anisotropy profile, as outer clusters in M87 and NGC 1399 have primarily radial orbits while outer NGC 5128 clusters remain isotropic.
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  • 5
    Publication Date: 2015-10-15
    Description: We investigate how the Milky Way tidal field can affect the spatial mixing of multiple stellar populations in the globular cluster NGC 6362. We use N -body simulations of multiple-population clusters on the orbit of this cluster around the Milky Way. Models of the formation of multiple populations in globular clusters predict that the second population should initially be more centrally concentrated than the first. However, NGC 6362 is comprised of two chemically distinct stellar populations having the same radial distribution. We show that the high mass-loss rate experienced on this cluster's orbit significantly accelerates the spatial mixing of the two populations expected from two-body relaxation. We also find that for a range of initial second-population concentrations, cluster masses, tidal filling factors and fraction of first-population stars, a cluster with two populations should be mixed when it has lost 70–80 per cent of its initial mass. These results fully account for the complete spatial mixing of NGC 6362, since, based on its shallow present-day mass function, independent studies estimate that the cluster has lost 85 per cent of its initial mass.
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  • 6
    Publication Date: 2015-12-16
    Description: We perform N -body simulations of star clusters in time-dependant galactic potentials. Since the Milky Way was built up through mergers with dwarf galaxies, its globular cluster population is made up of clusters formed both during the initial collapse of the Galaxy and in dwarf galaxies that were later accreted. Throughout a dwarf Milky Way merger, dwarf galaxy clusters are subject to a changing galactic potential. Building on our previous work, we investigate how this changing galactic potential affects the evolution of a cluster's half-mass radius. In particular, we simulate clusters on circular orbits around a dwarf galaxy that either falls into the Milky Way or evaporates as it orbits the Milky Way. We find that the dynamical evolution of a star cluster is determined by whichever galaxy has the strongest tidal field at the position of the cluster. Thus, clusters entering the Milky Way undergo changes in size as the Milky Way tidal field becomes stronger and that of the dwarf diminishes. We find that ultimately accreted clusters quickly become the same size as a cluster born in the Milky Way on the same orbit. Assuming their initial sizes are similar, clusters born in the Galaxy and those that are accreted cannot be separated based on their current size alone.
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  • 7
    Publication Date: 2014-11-13
    Description: In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters. Using the mocca Monte Carlo code for cluster evolution, our simulations cover three decades in present-day total cluster mass. Our results are compared to the observations of Milone et al. using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with a universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa. With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (10 4 –10 6  M  pc –3 ), or low initial binary fractions (~5–10 per cent) with a dominant hard binary component combined with moderate initial densities near their present-day values (10 2 –10 3  M  pc –3 ). This apparent degeneracy can potentially be broken using the binary fractions outside the half-mass radius – only high initial binary fractions with a significant soft component combined with high initial densities can reproduce the observed anticorrelation between the binary fractions outside the half-mass radius and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique first introduced in Leigh et al. that the relative fractions of hard and soft binaries can be used to further constrain both the initial cluster density and the initial mass–density relation. Our results favour an initial mass–density relation of the form $r_{\rm h} \propto M_{\rm clus}^{\alpha }$ with α 〈 1/3, corresponding to an initial correlation between cluster mass and density.
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  • 8
    Publication Date: 2014-10-23
    Description: We perform N -body simulations of a cluster that forms in a dwarf galaxy and is then accreted by the Milky Way to investigate how a cluster's structure is affected by a galaxy merger. We find that the cluster's half-mass radius will respond quickly to this change in potential. When the cluster is placed on an orbit in the Milky Way with a stronger tidal field the cluster experiences a sharp decrease in size in response to increased tidal forces. Conversely, when placed on an orbit with a weaker tidal field, the cluster expands since tidal forces decrease and no longer limit the expansion due to internal effects. In all cases, we find that the cluster's half-mass radius will eventually be indistinguishable from a cluster that has always lived in the Milky Way on that orbit. These adjustments occur within 1–2 half-mass relaxation times of the cluster in the dwarf galaxy. We also find this effect to be qualitatively independent of the time that the cluster is taken from the dwarf galaxy. In contrast to the half-mass radius, we show the core radius of the cluster is not affected by the potential the cluster lives in. Our work suggests that structural properties of accreted clusters are not distinct from clusters born in the Milky Way. Other cluster properties, such as metallicity and horizontal branch morphology, may be the only way to identify accreted star clusters in the Milky Way.
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  • 9
    Publication Date: 2014-10-24
    Description: We perform N -body simulations of a cluster that forms in a dwarf galaxy and is then accreted by the Milky Way to investigate how a cluster's structure is affected by a galaxy merger. We find that the cluster's half-mass radius will respond quickly to this change in potential. When the cluster is placed on an orbit in the Milky Way with a stronger tidal field the cluster experiences a sharp decrease in size in response to increased tidal forces. Conversely, when placed on an orbit with a weaker tidal field, the cluster expands since tidal forces decrease and no longer limit the expansion due to internal effects. In all cases, we find that the cluster's half-mass radius will eventually be indistinguishable from a cluster that has always lived in the Milky Way on that orbit. These adjustments occur within 1–2 half-mass relaxation times of the cluster in the dwarf galaxy. We also find this effect to be qualitatively independent of the time that the cluster is taken from the dwarf galaxy. In contrast to the half-mass radius, we show the core radius of the cluster is not affected by the potential the cluster lives in. Our work suggests that structural properties of accreted clusters are not distinct from clusters born in the Milky Way. Other cluster properties, such as metallicity and horizontal branch morphology, may be the only way to identify accreted star clusters in the Milky Way.
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  • 10
    Publication Date: 2014-10-10
    Description: We have performed N -body simulations of tidally filling star clusters with a range of orbits in a Milky Way-like potential to study the effects of orbital inclination and eccentricity on their structure and evolution. At small galactocentric distances R gc , a non-zero inclination results in increased mass-loss rates. Tidal heating and disc shocking, the latter sometimes consisting of two shocking events as the cluster moves towards and away from the disc, help remove stars from the cluster. Clusters with inclined orbits at large R gc have decreased mass-loss rates than the non-inclined case, since the strength of the disc potential decreases with R gc . Clusters with inclined and eccentric orbits experience increased tidal heating due to a constantly changing potential, weaker disc shocks since passages occur at higher R gc , and an additional tidal shock at perigalacticon. The effects of orbital inclination decrease with orbital eccentricity, as a highly eccentric cluster spends the majority of its lifetime at a large R gc . The limiting radii of clusters with inclined orbits are best represented by the r t of the cluster when at its maximum height above the disc, where the cluster spends the majority of its lifetime and the rate of change in r t is a minimum. Conversely, the effective radius is independent of inclination in all cases.
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