arXiv subjects

Holger Baumgardt

Publications and source records attributed to Holger Baumgardt.

At least 73 records · Page 4Linked to original sources

arXiv2017

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.

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arXiv2017

The global mass functions of 35 Galactic globular clusters: I. Observational data and correlations with cluster parameters

We have derived the global mass functions of a sample of 35 Galactic globular clusters by comparing deep Hubble Space Telescope photometry with suitable multimass dynamical models. For a subset of 29 clusters with available radial velocity information we were also able to determine dynamical parameters, mass-to-light ratios and the mass fraction of dark remnants. The derived global mass functions are well described by single power-laws in the mass range $0.2 < m/M_\odot < 0.8$ with mass function slopes $α>-1$. Less evolved clusters show deviations from a single-power law, indicating that the original shape of their mass distribution was not a power-law. We find a tight anticorrelation between the present-day mass function slopes and the half-mass relaxation times, which can be understood if clusters started from the same universal IMF and internal dynamical evolution is the main driver in shaping the present-day mass functions. Alternatively, IMF differences correlated with the present-day half-mass relaxation time are needed to explain the observed correlation. The large range of mass function slopes seen for our clusters implies that most globular clusters are dynamically highly evolved, a fact that seems difficult to reconcile with standard estimates for the dynamical evolution of clusters. The mass function slopes also correlate with the dark remnant fractions indicating a preferential retention of massive remnants in clusters subject to high mass-loss rates.

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arXiv2017

Diffuse Galactic antimatter from faint thermonuclear supernovae in old stellar populations

Our Galaxy hosts the annihilation of a few $\times 10^{43}$ low-energy positrons every second. Radioactive isotopes capable of supplying such positrons are synthesised in stars, stellar remnants, and supernovae. For decades, however, there has been no positive identification of a main stellar positron source leading to suggestions that many positrons originate from exotic sources like the Galaxy's central super-massive black hole or dark matter annihilation. %, but such sources would not explain the recently-detected positron signal from the extended Galactic disk. Here we show that a single type of transient source, deriving from stellar populations of age 3-6 Gyr and yielding ~0.03 $M_\odot$ of the positron emitter $^{44}$Ti, can simultaneously explain the strength and morphology of the Galactic positron annihilation signal and the solar system abundance of the $^{44}$Ti decay product $^{44}$Ca. This transient is likely the merger of two low-mass white dwarfs, observed in external galaxies as the sub-luminous, thermonuclear supernova known as SN1991bg-like.

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arXiv2017

An intermediate-mass black hole in the centre of the globular cluster 47 Tucanae

Intermediate mass black holes play a critical role in understanding the evolutionary connection between stellar mass and super-massive black holes. However, to date the existence of these species of black holes remains ambiguous and their formation process is therefore unknown. It has been long suspected that black holes with masses $10^{2}-10^{4}M_{\odot}$ should form and reside in dense stellar systems. Therefore, dedicated observational campaigns have targeted globular cluster for many decades searching for signatures of these elusive objects. All candidates found in these targeted searches appear radio dim and do not have the X-ray to radio flux ratio predicted by the fundamental plane for accreting black holes. Based on the lack of an electromagnetic counterpart upper limits of $2060 M_{\odot}$ and $470 M_{\odot}$ have been placed on the mass of a putative black hole in 47 Tucanae (NGC 104) from radio and X-ray observations respectively. Here we show there is evidence for a central black hole in 47 Tuc with a mass of M$_{\bullet}\sim2300 M_{\odot}$$_{-850}^{+1500}$ when the dynamical state of the globular cluster is probed with pulsars. The existence of an intermediate mass black hole in the centre of one of the densest clusters with no detectable electromagnetic counterpart suggests that the black hole is not accreting at a sufficient rate and therefore contrary to expectations is gas starved. This intermediate mass black hole might be a member of electromagnetically invisible population of black holes that are the elusive seeds leading to the formation of supermassive black holes in galaxies.

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arXiv2017

Detection of Supermassive Black Holes in Two Virgo Ultracompact Dwarf Galaxies

We present the detection of supermassive black holes (BHs) in two Virgo ultracompact dwarf galaxies (UCDs), VUCD3 and M59cO. We use adaptive optics assisted data from the Gemini/NIFS instrument to derive radial velocity dispersion profiles for both objects. Mass models for the two UCDs are created using multi-band Hubble Space Telescope (HST) imaging, including the modeling of mild color gradients seen in both objects. We then find a best-fit stellar mass-to-light ratio ($M/L$) and BH mass by combining the kinematic data and the deprojected stellar mass profile using Jeans Anisotropic Models (JAM). Assuming axisymmetric isotropic Jeans models, we detect BHs in both objects with masses of $4.4^{+2.5}_{-3.0} \times 10^6$ $M_{\odot}$ in VUCD3 and $5.8^{+2.5}_{-2.8} \times 10^6$ $M_{\odot}$ in M59cO (3$σ$ uncertainties). The BH mass is degenerate with the anisotropy parameter, $β_z$; for the data to be consistent with no BH requires $β_z = 0.4$ and $β_z = 0.6$ for VUCD3 and M59cO, respectively. Comparing these values with nuclear star clusters shows that while it is possible that these UCDs are highly radially anisotropic, it seems unlikely. These detections constitute the second and third UCDs known to host supermassive BHs. They both have a high fraction of their total mass in their BH; $\sim$13% for VUCD3 and $\sim$18% for M59cO. They also have low best-fit stellar $M/L$s, supporting the proposed scenario that most massive UCDs host high mass fraction BHs. The properties of the BHs and UCDs are consistent with both objects being the tidally stripped remnants of $\sim$10$^9$ M$_\odot$ galaxies.

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arXiv2017

Direct N-body simulations of globular clusters -- III. Palomar\,4 on an eccentric orbit

Palomar 4 is a low-density globular cluster with a current mass $\approx30000 M_{\odot}$ in the outer halo of the Milky Way with a two-body relaxation time of the order of a Hubble time. Yet, it is strongly mass segregated and contains a stellar mass function depleted of low-mass stars. Pal 4 was either born this way or it is a result of extraordinary dynamical evolution. Since two-body relaxation cannot explain these signatures alone, enhanced mass loss through tidal shocking may have had a strong influence on Pal 4. Here, we compute a grid of direct N-body simulations to model Pal 4 on various eccentric orbits within the Milky Way potential to find likely initial conditions that reproduce its observed mass, half-light radius, stellar MF-slope and line-of-sight velocity dispersion. We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of $e\approx 0.9$ and pericentric distance of $R_p\approx5$ kpc. In this scenario, the required 3D half-mass radius at birth is similar to the average sizes of typical GCs ($R_h\approx4-5$ pc), while its birth mass is about $M_0\approx10^5 M_{\odot}$. We also find a high degree of primordial mass segregation among the cluster stars, which seems to be necessary in every scenario we considered. Thus, using the tidal effect to constrain the perigalactic distance of the orbit of Pal 4, we predict that the proper motion of Pal 4 should be in the range $-0.52\leqμ_δ\leq-0.38$ mas\,yr$^{-1}$ and $-0.30\leqμ_{α\cosδ}\leq-0.15$ mas\,yr$^{-1}$.

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arXiv2016

The velocity dispersion and mass function of the outer halo globular cluster Palomar 4

We obtained precise line-of-sight radial velocities of 23 member stars of the remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution Echelle Spectrograph (HIRES) at the Keck I telescope. We also measured the mass function of the cluster down to a limiting magnitude of V~28 mag using archival HST/WFPC2 imaging. We derived the cluster's surface brightness profile based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We find a mean cluster velocity of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is shallower than a Kroupa mass function and the cluster is significantly depleted in low-mass stars in its center compared to its outskirts. Since the relaxation time of Pal 4 is of the order of a Hubble time, this points to primordial mass segregation in this cluster. Extrapolating the measured mass function towards lower-mass stars and including the contribution of compact remnants, we derive a total cluster mass of 29800 M_solar. For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of Modified Newtonian Dynamics (MOND). Pal 4 adds to the growing body of evidence that the dynamics of star clusters in the outer Galactic halo can hardly be explained by MOND.

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arXiv2016

N-body modeling of globular clusters: Masses, mass-to-light ratios and intermediate-mass black holes

We have determined the masses and mass-to-light ratios of 50 Galactic globular clusters by comparing their velocity dispersion and surface brightness profiles against a large grid of 900 N-body simulations of star clusters of varying initial concentration, size and central black hole mass fraction. Our models follow the evolution of the clusters under the combined effects of stellar evolution and two-body relaxation allowing us to take the effects of mass segregation and energy equipartition between stars self-consistently into account. For a subset of 16 well observed clusters we also derive their kinematic distances. We find an average mass-to-light ratio of Galactic globular clusters of $ =1.98 \pm 0.03$, which agrees very well with the expected M/L ratio if the initial mass function of the clusters was a standard Kroupa or Chabrier mass function. We do not find evidence for a decrease of the average mass-to-light ratio with metallicity. The surface brightness and velocity dispersion profiles of most globular clusters are incompatible with the presence of intermediate-mass black holes (IMBHs) with more than a few thousand $M_\odot$ in them. The only clear exception is $ω$ Cen, where the velocity dispersion profile provides strong evidence for the presence of a $\sim$40,000 $M_\odot$ IMBH in the centre of the cluster.

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arXiv2016

Probing the boundary between star clusters and dwarf galaxies: A MUSE view on the dynamics of Crater/Laevens I

We present MUSE observations of the debated ultra faint stellar system Crater. We spectroscopically confirm 26 member stars of this system via radial velocity measurements. We derive the systematic instrumental velocity uncertainty of MUSE spectra to be 2.27$\rm \,km\,s^{-1}$. This new dataset increases the confirmed member stars of Crater by a factor of 3. One out of three bright blue stars and a fainter blue star just above the main-sequence-turn-off are also found to be likely members of the system. The observations reveal that Crater has a systemic radial velocity of $v_{\rm sys}=148.18^{\rm +1.08}_{\rm -1.15}\rm \,km\,s^{-1}$, whereas the most likely velocity dispersion of this system is $σ_{\rm v}=2.04^{\rm +2.19}_{\rm -1.06} \rm \,km\,s^{-1}$. The total dynamical mass of the system, assuming dynamical equilibrium is then $M_{\rm tot}=1.50^{+4.9}_{-1.2}\cdot 10^{\rm 5}M_{\odot}$ implying a mass-to-light ratio of M/L$_{\rm V}$=8.52$^{+28.0}_{-6.5}\, M_{\odot}/L_{\odot}$, which is consistent with a purely baryonic stellar population within its errors and no significant evidence for the presence dark matter was found. We also find evidence for a velocity gradient in the radial velocity distribution. We conclude that our findings strongly support that Crater is a faint intermediate-age outer halo globular cluster and not a dwarf galaxy.

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arXiv2016

Constraining ultra-compact dwarf galaxy formation with galaxy clusters in the local universe

We compare the predictions of a semi-analytic model for ultra-compact dwarf galaxy (UCD) formation by tidal stripping to the observed properties of globular clusters (GCs) and UCDs in the Fornax and Virgo clusters. For Fornax we find the predicted number of stripped nuclei agrees very well with the excess number of GCs$+$UCDs above the GC luminosity function. GCs$+$UCDs with masses $>10^{7.3}$ M$_\odot$ are consistent with being entirely formed by tidal stripping. Stripped nuclei can also account for Virgo UCDs with masses $>10^{7.3}$ M$_\odot$ where numbers are complete by mass. For both Fornax and Virgo, the predicted velocity dispersions and radial distributions of stripped nuclei are consistent with that of UCDs within $\sim$50-100 kpc but disagree at larger distances where dispersions are too high and radial distributions too extended. Stripped nuclei are predicted to have radially biased anisotropies at all radii, agreeing with Virgo UCDs at clustercentric distances larger than 50 kpc. However, ongoing disruption is not included in our model which would cause orbits to become tangentially biased at small radii. We find the predicted metallicities and central black hole masses of stripped nuclei agree well with the metallicities and implied black hole masses of UCDs for masses $>10^{6.5}$ M$_\odot$. The predicted black hole masses also agree well with that of M60-UCD1, the first UCD with a confirmed central black hole. These results suggest that observed GC$+$UCD populations are a combination of genuine GCs and stripped nuclei, with the contribution of stripped nuclei increasing toward the high-mass end.

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arXiv2016

Limits on the significant mass-loss scenario based on the globular clusters of the Fornax dwarf spheroidal galaxy

Many of the scenarios proposed to explain the origin of chemically peculiar stars in globular clusters (GCs) require significant mass-loss ($\ge95\%$) to explain the observed fraction of such stars. In the GCs of the Fornax dwarf galaxy significant mass-loss could be a problem. Larsen et al. (2012) showed that there is a large ratio of GCs to metal-poor field stars in Fornax and about $20-25\%$ of all the stars with ${\rm [Fe/H]}<-2$ belong to the four metal-poor GCs. This imposes an upper limit of $\sim80\%$ mass-loss that could have happened in Fornax GCs. In this paper, we propose a solution to this problem by suggesting that stars can leave the Fornax galaxy. We use a series of $N$-body simulations, to determine the limit of mass-loss from Fornax as a function of the initial orbital radii of GCs and the speed with which stars leave Fornax GCs. We consider a set of cored and cuspy density profiles for Fornax. Our results show that with a cuspy model for Fornax, the fraction of stars which leave the galaxy, can be as high as $\sim90\%$, when the initial orbital radii of GCs are $R=2-3\,\rm{kpc}$ and the initial speed of stars is $v>20\,\rm{km\,s^{-1}}$. We show that such large velocities can be achieved by gas expulsion induced mass-loss but not stellar evolution induced mass-loss. Our results imply that one cannot interpret the metallicity distribution of Fornax field stars as evidence against significant mass-loss in Fornax GCs, if mass-loss is due to gas expulsion.

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arXiv2016

The Binary Fraction and Mass Segregation in Alpha Persei Open Cluster

We have obtained membership probabilities of stars within a field of radius $\sim3^\circ$ around the centre of the open cluster Alpha Persei using proper motions and photometry from the PPMXL and WISE catalogues. We have identified 810 possible stellar members of Alpha Persei. We derived the global and radial present-day mass function (MF) of the cluster and found that they are well matched by two-stage power-law relations with different slopes at different radii. The global MF of Alpha Persei shows a turnover at $m=0.62\,\mathrm{M}_{\odot}$ with low and high-mass slopes of $α_\mathrm{low}=0.50\pm0.09$ ($0.1<m/\mathrm{M}_{\odot}<0.62$) and $α_\mathrm{high}=2.32\pm0.14$ ($0.62\leq m/\mathrm{M}_{\odot}<4.68$) respectively. The high-mass slope of the cluster increases from $2.01$ inside $1\hbox{$.\!\!^\circ$}10$ to $2.63$ outside $2\hbox{$.\!\!^\circ$}2$, whereas the mean stellar mass decreases from $0.95$ to $0.57\,\mathrm{M}_{\odot}$ in the same regions, signifying clear evidence of mass segregation in the cluster. From an examination of the high-quality colour-magnitude data of the cluster and performing a series of Monte Carlo simulations we obtained a binary fraction of $f_{\rm bin}=34\pm12$ percent for stars with $0.70<m/\mathrm{M}_{\odot}<4.68$. This is significantly larger than the observed binary fraction, indicating that this open cluster contains a large population of unresolved binaries. Finally, we corrected the mass-function slopes for the effect of unresolved binaries and found low- and high-mass slopes of $α_\mathrm{low}=0.89\pm0.11$ and $α_\mathrm{high}=2.37\pm0.09$ and a total cluster mass of $352\,\mathrm{M}_{\odot}$.

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arXiv2015

Dynamical Evolution of Outer-Halo Globular Clusters

Outer-halo globular clusters show large half-light radii and flat stellar mass functions, depleted in low-mass stars. Using N-body simulations of globular clusters on eccentric orbits within a Milky Way-like potential, we show how a cluster's half-mass radius and its mass function develop over time. The slope of the central mass function flattens proportionally to the amount of mass a cluster has lost, and the half-mass radius grows to a size proportional to the average strength of the tidal field. The main driver of these processes is mass segregation of dark remnants. We conclude that the extended, depleted clusters observed in the Milky Way must have had small half-mass radii in the past, and that they expanded due to the weak tidal field they spend most of their lifetime in. Moreover, their mass functions must have been steeper in the past but flattened significantly as a cause of mass segregation and tidal mass loss.

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arXiv2015

Kinematics of dwarf galaxies in gas-rich groups, and the survival and detectability of tidal dwarf galaxies

We present DEIMOS multi-object spectroscopy (MOS) of 22 star-forming dwarf galaxies located in four gas-rich groups, including six newly-discovered dwarfs. Two of the galaxies are strong tidal dwarf galaxy (TDG) candidates based on our luminosity-metallicity relation definition. We model the rotation curves of these galaxies. Our sample shows low mass-to-light ratios (M/L=0.73$\pm0.39M_\odot/L_\odot$) as expected for young, star-forming dwarfs. One of the galaxies in our sample has an apparently strongly-falling rotation curve, reaching zero rotational velocity outside the turnover radius of $r_{turn}=1.2r_e$. This may be 1) a polar ring galaxy, with a tilted bar within a face-on disk; 2) a kinematic warp. These scenarios are indistinguishable with our current data due to limitations of slit alignment inherent to MOS-mode observations. We consider whether TDGs can be detected based on their tidal radius, beyond which tidal stripping removes kinematic tracers such as H$α$ emission. When the tidal radius is less than about twice the turnover radius, the expected falling rotation curve cannot be reliably measured. This is problematic for as much as half of our sample, and indeed more generally, galaxies in groups like these. Further to this, the H$α$ light that remains must be sufficiently bright to be detected; this is only the case for three (14%) galaxies in our sample. We conclude that the falling rotation curves expected of tidal dwarf galaxies are intrinsically difficult to detect.

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arXiv2015

Possible smoking-gun evidence for initial mass segregation in re-virialized post-gas expulsion globular clusters

We perform a series of direct $N$-body calculations to investigate the effect of residual gas expulsion from the gas-embedded progenitors of present-day globular clusters (GCs) on the stellar mass function (MF). Our models start either tidally filling or underfilling, and either with or without primordial mass segregation. We cover 100 Myr of the evolution of modeled clusters and show that the expulsion of residual gas from initially mass-segregated clusters leads to a significantly shallower slope of the stellar MF in the low- ($m\leq 0.50 M_\odot$) and intermediate-mass ($\simeq 0.50-0.85 M_\odot$) regime. Therefore, the imprint of residual gas expulsion and primordial mass segregation might be visible in the present-day MF. We find that the strength of the external tidal field, as an essential parameter, influences the degree of flattening, such that a primordially mass-segregated tidally-filling cluster with $r_h/r_t\geq 0.1$ shows a strongly depleted MF in the intermediate stellar mass range. Therefore, the shape of the present-day stellar MF in this mass range probes the birth place of clusters in the Galactic environment. We furthermore find that this flattening agrees with the observed correlation between the concentration of a cluster and its MF slope, as found by de Marchi et al.. We show that if the expansion through the residual gas expulsion in primordial mass segregated clusters is the reason for this correlation then GCs most probably formed in strongly fluctuating local tidal fields in the early proto-Milky Way potential, supporting the recent conclusion by Marks \& Kroupa.

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arXiv2015

Unveiling Gargantua: A new search strategy for the most massive central cluster black holes

We aim to unveil the most massive central cluster black holes in the universe. We present a new search strategy which is based on a black hole mass gain sensitive 'calorimeter' and which links the innermost stellar density profile of a galaxy to the adiabatic growth of its central SMBH. In a first step we convert observationally inferred feedback powers into SMBH growth rates by using reasonable energy conversion efficiency parameters, $ε$. In the main part of this paper we use these black hole growth rates, sorted in logarithmically increasing steps encompassing our whole parameter space, to conduct $N$-Body computations of brightest cluster galaxies with the newly developed MUESLI software. For the initial setup of galaxies we use core-Sersic models in order to account for SMBH scouring. We find that adiabatically driven core re-growth is significant at the highest accretion rates. As a result, the most massive black holes should be located in BCGs with less pronounced cores when compared to the predictions of empirical scaling relations which are usually calibrated in less extreme environments. For efficiency parameters $ε<0.1$, BCGs in the most massive, relaxed and X-ray luminous galaxy clusters might even develop steeply rising density cusps. Finally, we discuss several promising candidates for follow up investigations, among them the nuclear black hole in the Phoenix cluster. Based on our results, it might have a mass of the order of $10^{11} M_\odot$.

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arXiv2015

Dynamical Constraints on the Origin of Multiple Stellar Populations in Globular Clusters

We have carried out a large grid of N-body simulations in order to investigate if mass-loss as a result of primordial gas expulsion can be responsible for the large fraction of second generation stars in globular clusters (GCs) with multiple stellar populations (MSPs). Our clusters start with two stellar populations in which $10\%$ of all stars are second generation stars. We simulate clusters with different initial masses, different ratios of the half-mass radius of first to second generation stars, different primordial gas fractions and Galactic tidal fields with varying strength. We then let our clusters undergo primordial gas-loss and obtain their final properties such as mass, half-mass radius and the fraction of second generation stars. Using our N-body grid we then perform a Monte Carlo analysis to constrain the initial masses, radii and required gas expulsion time-scales of GCs with MSPs. Our results can explain the present-day properties of GCs only if (1) a substantial amount of gas was present in the clusters after the formation of second generation stars and (2) gas expulsion time-scales were extremely short ($\lesssim 10^5$ yr). Such short gas expulsion time-scales are in agreement with recent predictions that dark remnants have ejected the primordial gas from globular clusters, and pose a potential problem for the AGB scenario. In addition, our results predict a strong anti-correlation between the number ratio of second-generation stars in GCs and the present-day mass of GCs. So far, the observational data show only a significantly weaker anti-correlation, if any at all.

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arXiv2015

A re-evaluation of the central velocity-dispersion profile in NGC 6388

Recently, two independent groups found very different results when measuring the central velocity dispersion of the galactic globular cluster NGC 6388 with different methods. While Lützgendorf et al. (2011) found a rising profile and a high central velocity dispersion (23.3 km/s), measurements obtained by Lanzoni et al. (2013) showed a value 40% lower. The value of the central velocity dispersion has a serious impact on the mass and possible presence of an intermediate-mass black hole at the center of NGC 6388. We use a photometric catalog of NGC 6388 to create a simulated SINFONI and ARGUS dataset. The construction of the IFU data cube is done with different observing conditions reproducing the conditions reported for the original observations as closely as possible. In addition, we produce an N-body realization of a 10^6 M_SUN stellar cluster with the same photometric properties as NGC 6388 to account for unresolved stars. We find that the individual radial velocities, i.e. the measurements from the simulated SINFONI data, are systematically biased towards lower velocity dispersions. The reason is that due to the wings in the point spread function the velocities get biased towards the mean cluster velocity. This study shows that even with AO supported observations, individual radial velocities in crowded fields are likely to be biased. The ARGUS observations do not show this kind of bias but were found to have larger uncertainties than previously obtained. We find a bias towards higher velocity dispersions in the ARGUS pointing when fixing the extreme velocities of the three brightest stars but find those variations are within the determined uncertainties. We rerun Jeans models and fit the kinematic profile with the new uncertainties. This yields a BH mass of M_BH = (2.8 +- 0.4) x 10^4 M_SUN and M/L ratio M/L = (1.6 +- 0.1) M_SUN/L_SUN, consistent with our previous results.

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