Context. Intermediate-mass black holes (IMBHs) may provide the missing link to understanding the growth of supermassive black holes in the early Universe. Some formation scenarios predict that IMBHs ...could have formed by runaway collisions in globular clusters (GCs). However, it is challenging to set observational constraints on the mass of a black hole in a largely gas-free (and hence accretion-free) stellar system such as a GC. Understanding the influence of an IMBH in the center of a GC on its environment might provide indirect detection methods. Aims. Our goal is to test the effects of different initial compositions of GCs on their evolution in a tidal field. We pin down the crucial observables that indicate the presence of an IMBH at the center of the cluster. In addition to central IMBHs, we also consider the effects of different stellar-mass black hole retention and stellar binary fractions. Methods. We performed a set of 22 N-body simulations and varied particle numbers, IMBH masses, stellar-mass black-hole retention fractions, and stellar binary fractions. These models are all run in an external tidal field to study the effect of black holes on the cluster mass loss, mass function, and life times. Finally, we compared our results with observational data. Results. We found that a central massive black hole increases the escape rate of high-mass stars from a star cluster, implying that the relative depletion of the mass function at the low-mass end proceeds less rapidly. Furthermore, we found a similar behavior for a cluster hosting a high number of stellar-mass black holes instead of one massive central IMBH. The presence of an IMBH also weakly affects the fraction of the cluster mass that is constituted by stellar remnants, as does the presence of primordial binaries. We compared our simulations with observational data from the literature and found good agreement between our models and observed mass functions and structural parameters of GCs. We exploited this agreement to identify GCs that could potentially host IMBHs.
We compare the predictions of a semi-analytic model for ultracompact 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 >107.3 M⊙ are consistent with being entirely formed by tidal stripping. Stripped nuclei can also account for Virgo UCDs with masses >107.3 M⊙ 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 ∼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 >106.5 M⊙. 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 towards the high-mass end.
ABSTRACT
Populations of stellar-mass black holes (BHs) in globular clusters (GCs) influence their dynamical evolution and have important implications on one of the main formation channels for ...gravitational wave sources. Inferring the size of these populations remains difficult, however. In this work, multimass models of 34 Milky Way GCs, first presented in Dickson et al., are used to explore the present-day BH populations. Direct constraints on both the total and visible mass components provided by several observables allow these models to accurately determine the distribution of the dark mass (including BHs) within clusters, as we demonstrate in a proof-of-concept fitting of the models to mock observations extracted from Monte Carlo cluster models. New constraints on the BH population retained to the present-day in each cluster are inferred from our models. We find that BH mass fractions ranging from 0 to 1 per cent of the total mass are typically required to explain the observations, except for ω Cen, for which we infer a mass fraction above 5 per cent, in agreement with previous works. Relationships between the dark remnant populations and other cluster parameters are examined, demonstrating a clear anticorrelation between the amount of BHs and mass segregation between visible stars, as well as a correlation between remnant mass fractions and the dynamical age of clusters. Our inferred BH populations are in good agreement overall with other recent studies using different methodologies, but with notable discrepancies for individual clusters.
The structural and dynamical properties of star clusters are generally derived by means of the comparison between steady-state analytic models and the available observables. With the aim of studying ...the biases of this approach, we fitted different analytic models to simulated observations obtained from a suite of direct N-body simulations of star clusters in different stages of their evolution and under different levels of tidal stress to derive mass, mass function and degree of anisotropy. We find that masses can be under/overestimated up to 50 per cent depending on the degree of relaxation reached by the cluster, the available range of observed masses and distances of radial velocity measures from the cluster centre and the strength of the tidal field. The mass function slope appears to be better constrainable and less sensitive to model inadequacies unless strongly dynamically evolved clusters and a non-optimal location of the measured luminosity function are considered. The degree and the characteristics of the anisotropy developed in the N-body simulations are not adequately reproduced by popular analytic models and can be detected only if accurate proper motions are available. We show how to reduce the uncertainties in the mass, mass function and anisotropy estimation and provide predictions for the improvements expected when Gaia proper motions will be available in the near future.
Context. Intermediate-mass black holes (IMBHs) are of interest in a wide range of astrophysical fields. In particular, the possibility of finding them at the centers of globular clusters has recently ...drawn attention. IMBHs became detectable since the quality of observational data sets, particularly those obtained with HST and with high resolution ground based spectrographs, advanced to the point where it is possible to measure velocity dispersions at a spatial resolution comparable to the size of the gravitational sphere of influence for plausible IMBH masses. Aims. We present results from ground based VLT/FLAMES spectroscopy in combination with HST data for the globular cluster NGC 6388. The aim of this work is to probe whether this massive cluster hosts an intermediate-mass black hole at its center and to compare the results with the expected value predicted by the M• − σ scaling relation. Methods. The spectroscopic data, containing integral field unit measurements, provide kinematic signatures in the center of the cluster while the photometric data give information of the stellar density. Together, these data sets are compared to dynamical models and present evidence of an additional compact dark mass at the center: a black hole. Results. Using analytical Jeans models in combination with various Monte Carlo simulations to estimate the errors, we derive (with 68% confidence limits) a best fit black-hole mass of (17 ± 9) × 103 M⊙ and a global mass-to-light ratio of M/LV = (1.6 ± 0.3) M⊙/L⊙.
Gravitationally bound group of stars which are identified as globular clusters are known to have a small amount of dark matter. Assuming that globular clusters are formed within dark matter halos, ...they must have lost significant amount of dark matter. Observations of globular clusters reported flattening velocity dispersion on the outskirt clusters. This could be a sign of existence of dark matter. Theoretically, dynamical processes such as dynamical friction and mass segregation and tidal stripping could be responsible for the depletion of dark matter from the cluster center. Numerical simulations are conducted to follow the evolution of the models of globular clusters composed out of stars and dark matter particles. The results show that the dark matter is depleted from the center of globular clusters due to dynamical friction and mass segregation of stars. An external tidal field from a Milky Way like galaxy effects to deplete the dark matter in the outer part of the clusters. However, within the Hubble time, about 80 % of dark matter's initial values still remain in the outer part of clusters. This might explain the existence of significant amount of dark matter in the outer part of observed clusters.
The disruption rate of stars by supermassive black holes (SMBHs) is calculated numerically with a modified version of Aarseth's nbody6 code. Equal-mass systems without primordial binaries are ...treated. The initial stellar distribution around the SMBH follows a Sérsic n= 4 profile representing bulges of late-type galaxies as well of early-type galaxies without central light deficits, i.e. without cores. In order to infer relaxation-driven effects and to increase the statistical significance, a very large set of N-body integrations with different particle numbers N, ranging from 103 to 0.5 × 106 particles, is performed. Three different black hole capture radii are taken into account, enabling us to scale these results to a broad range of astrophysical systems with relaxation times shorter than one Hubble time, i.e. for SMBHs up to M
*≈ 107 M⊙. The computed number of disrupted stars is driven by diffusion in angular momentum space into the loss cone of the black hole and the rate scales with the total number of particles as (dN/dt) ∝Nb
, where b is as large as 0.83. This is significantly steeper than the expected scaling (d N/dt) ∝ ln (N) derived from simplest energy relaxation arguments. Only a relatively modest dependence of the tidal disruption rate on the mass of the SMBH is found and we discuss our results in the context of the M
*-σ relation. The number of disrupted stars contributes a significant part to the mass growth of black holes in the lower mass range as long as a significant part of the stellar mass becomes swallowed by the SMBH. This also bears direct consequences for the search and existence of intermediate-mass black holes in globular clusters. For SMBHs similar to the galactic centre black hole Sgr A★, a tidal disruption rate of 55 ± 27 events Myr−1 is deduced. Finally relaxation-driven stellar feeding cannot account for the masses of massive black holes M
*≥ 107 M⊙ in complete agreement with conventional gas accretion and feedback models.
Context. The formation of supermassive black holes at high redshift still remains a puzzle to astronomers. No accretion mechanism can explain the fast growth from a stellar mass black hole to several ...billion solar masses in less than one Gyr. The growth of supermassive black holes becomes reasonable only when starting from a massive seed black hole with mass on the order of 102−105 M⊙. Intermediate-mass black holes are therefore an important field of research. Especially the possibility of finding them in the centers of globular clusters has recently drawn attention. Searching for kinematic signatures of a dark mass in the centers of globular clusters provides a unique test for the existence of intermediate-mass black holes and will shed light on the process of black-hole formation and cluster evolution. Aims. We are investigating six galactic globular clusters for the presence of an intermediate-mass black hole at their centers. Based on their kinematic and photometric properties, we selected the globular clusters NGC 1851, NGC 1904 (M 79), NGC 5694, NGC 5824, NGC 6093 (M 80), and NGC 6266 (M 62). Methods. We used integral field spectroscopy to obtain the central velocity-dispersion profile of each cluster. In addition we completed these profiles with outer kinematic points from previous measurements for the clusters NGC 1851, NGC 1094, NGC 5824, and NGC 6093. We also computed the cluster photometric center and the surface brightness profile using HST data. After combining these datasets we compared them to analytic Jeans models. We used varying M/LV profiles for clusters with enough data points in order to reproduce their kinematic profiles in an optimal way. Finally, we varried the mass of the central black hole and tested whether the cluster is better fitted with or without an intermediate-mass black hole. Results. We present the statistical significance, including upper limits, of the black-hole mass for each cluster. NGC 1904 and NGC 6266 provide the highest significance for a black hole. Jeans models in combination with a M/LV profile obtained from N-body simulations (in the case of NGC 6266) predict a central black hole of M• = (3 ± 1) × 103 M⊙ for NGC 1904 and M• = (2 ± 1) × 103 M⊙ for NGC 6266. Furthermore, we discuss the possible influence of dark remnants and mass segregation at the center of the cluster on the detection of an IMBH.
Ultra-compact dwarf galaxies (UCDs) are stellar systems with masses of around 107 to 108M⊙ and half-mass radii of 10–100 pc. They have some properties in common with massive globular clusters, ...however dynamical mass estimates have shown that UCDs have mass-to-light ratios which are on average about twice as large than those of globular clusters at comparable metallicity, and tend to be larger than what one would expect for old stellar systems composed out of stars with standard mass functions. One possible explanation for elevated high mass-to-light ratios in UCDs is the existence of a substantial amount of dark matter, which could have ended up in UCDs if they are the remnant nuclei of tidally stripped dwarf galaxies, and dark matter was dragged into these nuclei prior to tidal stripping through, for example, adiabatic gas infall. Tidal stripping of dwarf galaxies has also been suggested as the origin of several massive globular clusters like Omega Cen, in which case one should expect that globular clusters also form with substantial amounts of dark matter in them. In this paper, we present collisional N-body simulations which study the co-evolution of a system composed out of stars and dark matter. We find that the dark matter gets removed from the central regions of such systems due to dynamical friction and mass segregation of stars. The friction time-scale is significantly shorter than a Hubble time for typical globular clusters, while most UCDs have friction times much longer than a Hubble time. Therefore, a significant dark matter fraction remains within the half-mass radius of present-day UCDs, making dark matter a viable explanation for the elevated M/L ratios of UCDs. If at least some globular clusters formed in a way similar to UCDs, we predict a substantial amount of dark matter in their outer parts.
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