arXiv subjects

William E. Harris

Publications and source records attributed to William E. Harris.

At least 55 records · Page 3Linked to original sources

arXiv2018

Estimating the Milky Way's Mass via Hierarchical Bayes: A Blind Test on MUGS2 Simulated Galaxies

In a series of three papers, Eadie et al. developed a hierarchical Bayesian method to estimate the Milky Way Galaxy's mass given a physical model for the potential, a measurement model, and kinematic data of test particles such as globular clusters (GCs) or halo stars in the Galaxy's halo. The Galaxy's virial mass was found to have a 95\% Bayesian credible region (c.r.) of $(0.67, 1.09) \times 10^{12} M_{\odot}$. In the present study, we test the hierarchical Bayesian method against simulated galaxies created in the McMaster Unbiased Galaxy Simulations 2 (MUGS2), for which the true mass is known. We estimate the masses of MUGS2 galaxies using GC analogs from the simulations as tracers. The analysis, completed as a blind test, recovers the true $M_{200}$ of the MUGS2 galaxies within 95\% Bayesian c.r. in 8 out of 18 cases. Of the 10 galaxy masses that were not recovered within the 95\% c.r., a large subset have posterior distributions that occupy extreme ends of the parameter space allowed by the priors. A few incorrect mass estimates are explained by the exceptional evolution history of the galaxies. We also find evidence that the model cannot describe both the galaxies' inner and outer structure simultaneously in some cases. After removing the GC analogs associated with the galactic disks, the true masses were found more reliably (13 out of 18 were predicted within the c.r.). Finally, we discuss how representative the GC analogs are of the real GC population in the Milky Way.

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arXiv2018

A universal route for the formation of massive star clusters in giant molecular clouds

Young massive star clusters (YMCs, with M $\geq$10$^4$ M$_{\odot}$) are proposed modern-day analogues of the globular clusters (GCs) that were products of extreme star formation in the early universe. The exact conditions and mechanisms under which YMCs form remain unknown -- a fact further complicated by the extreme radiation fields produced by their numerous massive young stars. Here we show that GC-sized clusters are naturally produced in radiation-hydrodynamic simulations of isolated 10$^7$ M$_{\odot}$ Giant Molecular Clouds (GMCs) with properties typical of the local universe, even under the influence of radiative feedback. In all cases, these massive clusters grow to GC-level masses within 5 Myr via a roughly equal combination of filamentary gas accretion and mergers with several less massive clusters. Lowering the heavy-element abundance of the GMC by a factor of 10 reduces the opacity of the gas to radiation and better represents the high-redshift formation conditions of GCs. This results in higher gas accretion leading to a mass increase of the largest cluster by a factor of ~4. When combined with simulations of less massive GMCs (10$^{4-6}$ M$_{\odot}$), a clear relation emerges between the maximum YMC mass and the mass of the host GMC. Our results demonstrate that YMCs, and potentially GCs, are a simple extension of local cluster formation to more massive clouds and do not require suggested exotic formation scenarios.

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arXiv2017

Detection of the Stellar Intracluster Medium in Perseus (Abell 426)

Hubble Space Telescope photometry from the ACS/WFC and WFPC2 cameras is used to detect and measure globular clusters (GCs) in the central region of the rich Perseus cluster of galaxies. A detectable population of Intragalactic GCs is found extending out to at least 500 kpc from the cluster center. These objects display luminosity and color (metallicity) distributions that are entirely normal for GC populations. Extrapolating from the limited spatial coverage of the HST fields, we estimate very roughly that the entire Perseus cluster should contain ~50000 or more IGCs, but a targetted wide-field survey will be needed for a more definitive answer. Separate brief results are presented for the rich GC systems in NGC 1272 and NGC 1275, the two largest Perseus ellipticals. For NGC 1272 we find a specific frequency S_N = 8, while for the central giant NGC 1275, S_N ~ 12. In both these giant galaxies, the GC colors are well matched by bimodal distributions, with the majority in the blue (metal-poor) component. This preliminary study suggests that Perseus is a prime target for a more comprehensive deep imaging survey of Intragalactic GCs.

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arXiv2017

Galactic Dark Matter Halos and Globular Cluster Populations. III: Extension to Extreme Environments

The total mass M_GCS in the globular cluster (GC) system of a galaxy is empirically a near-constant fraction of the total mass M_h = M_bary + M_dark of the galaxy, across a range of 10^5 in galaxy mass. This trend is radically unlike the strongly nonlinear behavior of total stellar mass M_star versus M_h. We discuss extensions of this trend to two more extreme situations: (a) entire clusters of galaxies, and (b) the Ultra-Diffuse Galaxies (UDGs) recently discovered in Coma and elsewhere. Our calibration of the ratio η_M = M_GCS / M_h from normal galaxies, accounting for new revisions in the adopted mass-to-light ratio for GCs, now gives η_M = 2.9 \times 10^{-5} as the mean absolute mass fraction. We find that the same ratio appears valid for galaxy clusters and UDGs. Estimates of η_M in the four clusters we examine tend to be slightly higher than for individual galaxies, butmore data and better constraints on the mean GC mass in such systems are needed to determine if this difference is significant. We use the constancy of η_M to estimate total masses for several individual cases; for example, the total mass of the Milky Way is calculated to be M_h = 1.1 \times 10^{12} M_sun. Physical explanations for the uniformity of η_M are still descriptive, but point to a picture in which massive, dense star clusters in their formation stages were relatively immune to the feedback that more strongly influenced lower-density regions where most stars form.

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arXiv2016

Globular Clusters As Tracers of Fine Structure in the Dramatic Shell Galaxy NGC 474

Globular clusters (GCs) are some of the most visible tracers of the merging and accretion history of galaxy halos. Metal-poor GCs, in particular, are thought to arrive in massive galaxies largely through dry, minor merging events, but it is rare to see a direct connection between GCs and visible stellar streams. NGC 474 is a post-merger early-type galaxy with dramatic fine structures made of concentric shells and radial streams that have been more clearly revealed by deep imaging. We present a study of GCs in NGC 474 to better establish the relationship between merger-induced fine structure and the GC system. We find that many GCs are superimposed on visible streams and shells, and about 35% of GCs outside $3R_{\rm e,galaxy}$ are located in regions of fine structure. The spatial correlation between the GCs and fine structure is significant at the 99.9% level, showing that this correlation is not coincidental. The colors of the GCs on the fine structures are mostly blue, and we also find an intermediate-color population that is dominant in the central region, and which will likely passively evolve to have colors consistent with a traditional metal-rich GC population. The association of the blue GCs with fine structures is direct confirmation that many metal-poor GCs are accreted onto massive galaxy halos through merging events, and that progenitors of these mergers are sub-L* galaxies.

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arXiv2016

Globular Cluster Scale Sizes in Giant Galaxies: Orbital Anisotropy and Tidally Under-filling Clusters in M87, NGC 1399, and NGC 5128

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 under-filling 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 under-filling. 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 fitted 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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arXiv2016

Where Are Most of the Globular Clusters in Today's Universe?

The total number of globular clusters (GCs) in a galaxy rises continuously with the galaxy luminosity L, while the relative number of galaxies decreases with L following the Schechter function. The product of these two very nonlinear functions gives the relative number of GCs contained by all galaxies at a given L. It is shown that GCs, in this universal sense, are most commonly found in galaxies within a narrow range around $L_{\star}$. In addition, blue (metal-poor) GCs outnumber the red (metal-richer) ones globally by 4 to 1 when all galaxies are added, pointing to the conclusion that the earliest stages of galaxy formation were especially favorable to forming massive, dense star clusters.

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arXiv2015

Globular Cluster Systems in Brightest Cluster Galaxies. II: NGC 6166

We present new deep photometry of the globular cluster system (GCS) around NGC 6166, the central supergiant galaxy in Abell 2199. HST data from the ACS and WFC3 cameras in F475W, F814W are used to determine the spatial distribution of the GCS, its metallicity distribution function (MDF), and the dependence of the MDF on galactocentric radius and on GC luminosity. The MDF is extremely broad, with the classic red and blue subpopulations heavily overlapped, but a double-Gaussian model can still formally match the MDF closely. The spatial distribution follows a Sersic-like profile detectably to a projected radius of at least $R_{gc} = 250$ kpc. To that radius, the total number of clusters in the system is N_{GC} = 39000 +- 2000, the global specific frequency is S_N = 11.2 +- 0.6, and 57\% of the total are blue, metal-poor clusters. The GCS may fade smoothly into the Intra-Cluster Medium of A2199; we see no clear transition from the core of the galaxy to the cD halo or the ICM. The radial distribution, projected ellipticity, and mean metallicity of the red (metal-richer) clusters match the halo light extremely well for R > 15 kpc, both of them varying as σ_{MRGC} ~ σ_{light} ~ R^-1.8. By comparison, the blue (metal-poor) GC component has a much shallower falloff σ_{MPGC} ~ R^-1.0 and a more nearly spherical distribution. This strong difference in their density distributions produces a net metallicity gradient in the GCS as a whole that is primarily generated by the population gradient. With NGC 6166 we appear to be penetrating into a regime of high enough galaxy mass and rich enough environment that the bimodal two-phase description of GC formation is no longer as clear or effective as it has been in smaller galaxies.

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arXiv2015

Estimating the Galactic Mass Profile in the Presence of Incomplete Data

A powerful method to measure the mass profile of a galaxy is through the velocities of tracer particles distributed through its halo. Transforming this kind of data accurately to a mass profile M(r), however, is not a trivial problem. In particular, limited or incomplete data may substantially affect the analysis. In this paper we develop a Bayesian method to deal with incomplete data effectively; we have a hybrid-Gibbs sampler that treats the unknown velocity components of tracers as parameters in the model. We explore the effectiveness of our model using simulated data, and then apply our method to the Milky Way using velocity and position data from globular clusters and dwarf galaxies. We find that in general, missing velocity components have little effect on the total mass estimate. However, the results are quite sensitive to the outer globular cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile M(r) of the Milky Way, and provide estimates for the model parameters with 95 percent Bayesian credible intervals. The mass contained within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1) kpc, where the uncertainties span the 95 percent credible intervals. The code we developed for this work, Galactic Mass Estimator (GME), will be available as an open source package in the R Project for Statistical Computing.

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arXiv2014

Red giants in the outer halo of the elliptical galaxy NGC 5128 / Centaurus A

We used VIMOS on VLT to perform $V$ and $I$ band imaging of the outermost halo of NGC 5128 / Centaurus A ($(m-M)_0=27.91\pm0.08$), 65 kpc from the galaxy's center and along the major axis. The stellar population has been resolved to $I_0 \approx 27$ with a $50\%$ completeness limit of $I_0 = 24.7$, well below the tip of the red-giant branch (TRGB), which is seen at $I_0 \approx 23.9$. The surface density of NGC 5128 halo stars in our fields was sufficiently low that dim, unresolved background galaxies were a major contaminant in the source counts. We isolated a clean sample of red-giant-branch (RGB) stars extending to $\approx 0.8$ mag below the TRGB through conservative magnitude and color cuts, to remove the (predominantly blue) unresolved background galaxies. We derived stellar metallicities from colors of the stars via isochrones and measured the density falloff of the halo as a function of metallicity by combining our observations with HST imaging taken of NGC 5128 halo fields closer to the galaxy center. We found both metal-rich and metal-poor stellar populations and found that the falloff of the two follows the same de Vaucouleurs' law profiles from $\approx 8$ kpc out to $\approx$ 70 kpc. The metallicity distribution function (MDF) and the density falloff agree with the results of two recent studies of similar outermost halo fields in NGC 5128. We found no evidence of a "transition" in the radial profile of the halo, in which the metal-rich halo density would drop rapidly, leaving the underlying metal-poor halo to dominate by default out to greater radial extent, as has been seen in the outer halo of two other large galaxies. If NGC 5128 has such a transition, it must lie at larger galactocentric distances.

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arXiv2014

Globular Cluster Systems in Brightest Cluster Galaxies: A Near-Universal Luminosity Function?

We present the first results from our HST Brightest Cluster Galaxy (BCG) survey of seven central supergiant cluster galaxies and their globular cluster (GC) systems. We measure a total of 48000 GCs in all seven galaxies, representing the largest single GC database. We find that a log-normal shape accurately matches the observed luminosity function (LF) of the GCs down to the GCLF turnover point, which is near our photometric limit. In addition, the LF has a virtually identical shape in all seven galaxies. Our data underscore the similarity in the formation mechanism of massive star clusters in diverse galactic environments. At the highest luminosities (log L > 10^7 L_Sun) we find small numbers of "superluminous" objects in five of the galaxies; their luminosity and color ranges are at least partly consistent with those of UCDs (Ultra-Compact Dwarfs). Lastly, we find preliminary evidence that in the outer halo (R > 20 kpc), the LF turnover point shows a weak dependence on projected distance, scaling as L_0 ~ R^-0.2, while the LF dispersion remains nearly constant.

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arXiv2014

The Effects of Orbital Inclination on the Scale Size and Evolution of Tidally Filling Star Clusters

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 Rgc, a non-zero inclination results in increased mass loss rates. Tidal heating and disk shocking, the latter sometimes consisting of two shocking events as the cluster moves towards and away from the disk, help remove stars from the cluster. Clusters with inclined orbits at large Rgc have decreased mass loss rates than the non-inclined case, since the strength the disk potential decreases with Rgc. Clusters with inclined and eccentric orbits experience increased tidal heating due to a constantly changing potential, weaker disk shocks since passages occur at higher Rgc, 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 Rgc. The limiting radii of clusters with inclined orbits are best represented by the rt of the cluster when at its maximum height above the disk, where the cluster spends the majority of its lifetime and the rate of change in rt is a minimum. Conversely, the effective radius is independent of inclination in all cases.

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arXiv2014

The Effect of Orbital Eccentricity on the Dynamical Evolution of Star Clusters

We use N-body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters on circular and eccentric orbits. For a given perigalactic distance, increasing orbital eccentricity slows the dynamical evolution of a cluster due to a weaker mean tidal field. However, we find that perigalactic passes and tidal heating due to an eccentric orbit can partially compensate for the decreased mean tidal field by energizing stars to higher velocities and stripping additional stars from the cluster, accelerating the relaxation process. We find that the corresponding circular orbit which best describes the evolution of a cluster on an eccentric orbit is much less than its semi-major axis or time averaged galactocentric distance. Since clusters spend the majority of their lifetimes near apogalacticon, the properties of clusters which appear very dynamically evolved for a given galactocentric distance can be explained by an eccentric orbit. Additionally we find that the evolution of the slope of the mass function within the core radius is roughly orbit-independent, so it could place additional constraints on the initial mass and initial size of globular clusters with solved orbits. We use our results to demonstrate how the orbit of Milky Way globular clusters can be constrained given standard observable parameters like galactocentric distance and the slope of the mass function. We then place constraints on the unsolved orbits of NGC 1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass functions.

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arXiv2014

The pre-processing of subhaloes in SDSS groups and clusters

We investigate pre-processing using the observed quenched fraction of group and cluster galaxies in the Yang et al. (2007) SDSS-DR7 group catalogue in the redshift range of 0.01 < z < 0.045. We categorize group galaxies as virialized, infall or backsplash and we apply a combination of the Dressler-Shectman statistic and group member velocities to identify subhaloes. On average the fraction of galaxies that reside in subhaloes is a function of host halo mass, where more massive systems have a higher fraction of subhalo galaxies both in the overall galaxy and infall populations. Additionally, we find that between 2 < r_200 < 3 the quiescent fraction is higher in the subhalo population with respect to both the field and non-subhalo populations. At these large radii (2 < r_200 < 3), the majority of galaxies (~ 80 %) belong to the infall population and therefore, we attribute the enhanced quenching to infalling subhalo galaxies, indicating that pre-processing has occurred in the subhalo population. We conclude that pre-processing plays a significant role in the observed quiescent fraction, but only for the most massive (M_halo > 10^14.5 M_sun) systems in our sample.

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arXiv2014

Dark Matter Halos in Galaxies and Globular Cluster Populations

We combine a new, comprehensive database for globular cluster populations in all types of galaxies with a new calibration of galaxy halo masses based entirely on weak lensing. Correlating these two sets of data, we find that the mass ratio $η\equiv M_{GCS}/M_{h}$ (total mass in globular clusters, divided by halo mass) is essentially constant at $\langle η\rangle \sim 4 \times 10^{-5}$, strongly confirming earlier suggestions in the literature. Globular clusters are the only known stellar population that formed in essentially direct proportion to host galaxy halo mass. The intrinsic scatter in $η$ appears to be at most 0.2 dex; we argue that some of this scatter is due to differing degrees of tidal stripping of the globular cluster systems between central and satellite galaxies. We suggest that this correlation can be understood if most globular clusters form at very early stages in galaxy evolution, largely avoiding the feedback processes that inhibited the bulk of field-star formation in their host galaxies. The actual mean value of $η$ also suggests that about $1/4$ of the \emph{initial} gas mass present in protogalaxies collected into GMCs large enough to form massive, dense star clusters. Finally, our calibration of $\langle η\rangle$ indicates that the halo masses of the Milky Way and M31 are $(1.2\pm0.5)\times 10^{12} M_{\odot}$ and $(3.9\pm1.8)\times 10^{12} M_{\odot}$ respectively.

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arXiv2013

Globular clusters and supermassive black holes in galaxies: further analysis and a larger sample

We explore several correlations between various large-scale galaxy properties, particularly total globular cluster population (N_GCS), the central black hole mass (M_BH), velocity dispersion (nominally sigma_e), and bulge mass (M_dyn). Our data sample of 49 galaxies, for which both N_GC and M_BH are known, is larger than used in previous discussions of these two parameters and we employ the same sample to explore all pairs of correlations. Further, within this galaxy sample we investigate the scatter in each quantity, with emphasis on the range of published values for sigma_e and effective radius (R_e). We find that these two quantities in particular are difficult to measure consistently and caution that precise intercomparison of galaxy properties involving R_e and sigma_e is particularly difficult. Using both chi^2 and Monte Carlo Markov Chain (MCMC) fitting techniques, we show that quoted observational uncertainties for all parameters are too small to represent the true scatter in the data. We find that the correlation between M_dyn and N_GC is stronger than either the M_BH-sigma_e or M_BH-N_GC relations. We suggest that this is because both the galaxy bulge population ans N_GC were fundamentally established at an early epoch during the same series of star-forming events. By contrast, although the seed for M_BH was likely formed at a similar epoch, its growth over time is less similar from galaxy to galaxy and thus less predictable.

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arXiv2013

Cluster formation in molecular clouds: I. stellar populations, star formation rates, and ionizing radiation

We present a model for the radiative output of star clusters in the process of star formation suitable for use in hydrodynamical simulations of radiative feedback. Gas in a clump, defined as a region whose density exceeds 10^4 cm^-3, is converted to stars via the random sampling of the Chabrier IMF. A star formation efficiency controls the rate of star formation. We have completed a suite of simulations which follow the evolution of accretion-fed clumps with initial masses ranging from 0 to 10^5 M_sol and accretion rates ranging from 10^-5 to 10^-1 M_sol yr^-1. The stellar content is tracked over time which allows the aggregate luminosity, ionizing photon rate, number of stars, and star formation rate (SFR) to be determined. For a fiducial clump of 10^4 M_sol, the luminosity is ~4x10^6 L_sol with a SFR of roughly 3x10^-3 M_sol yr^-1. We identify two regimes in our model. The accretion-dominated regime obtains the majority of its gas through accretion and is characterized by an increasing SFR while the reservoir-dominated regime has the majority of its mass present in the initial clump with a decreasing SFR. We show that our model can reproduce the expected number of O stars, which dominate the radiative output of the cluster. We find a nearly linear relationship between SFR and mass as seen in observations. We conclude that our model is an accurate and straightforward way to represent the output of clusters in hydrodynamical simulations with radiative feedback.

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arXiv2013

Globular Cluster Scale Sizes in Giant Galaxies: The Case of M87 and the Role of Orbital Anisotropy and Tidal Filling

We present new Hubble Space Telescope imaging of the outer regions of M87 in order to study its globular cluster (GC) population out to large galactocentric distances. We discuss particularly the relationship between GC effective radii $r_h$ and projected galactocentric distance $R_{gc}$. The observations suggest a shallow trend $r_h \propto R_{gc}^{0.14}$ out to $R_{gc} \sim 100$ kpc, in agreement with studies of other giant elliptical galaxies. To theoretically reproduce this relationship we simulate GC populations with various distributions of orbits. For an isotropic distribution of cluster orbits we find a steeper trend of $r_h \propto R_{gc}^{0.4}$. Instead we suggest that (a) if the cluster system has an orbital anisotropy profile, where orbits become preferentially radial with increasing galactocentric distance, AND (b) if clusters become more tidally under-filling with galactocentric distance, the observed relationship can be recovered. We also apply this approach to the red and blue GC populations separately and predict that red clusters are preferentially under-filling at large $R_{gc}$ and have a more isotropic distribution of orbits than blue clusters.

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