Ratios of star cluster core and half-mass radii: a cautionary note on intermediate-mass black holes in star clusters

There is currently much interest in the possible presence of intermediate-mass black holes (IMBHs) in the cores of globular clusters (GCs). Based on theoretical arguments and simulation results it has previously been suggested that a large core radius – or particularly a large ratio of the core radius to half-mass radius – is a promising indicator for finding such a black hole (BH) in a star cluster. In this study N -body models of 100 000 stars with and without primordial binaries are used to investigate the long-term structural evolution of star clusters. Importantly, the simulation data are analysed using the same processes by which structural parameters are extracted from observed star clusters. This gives a ratio of the core and half-mass (or half-light) radii that are directly comparable to the Galactic GC sample. As a result, it is shown that the ratios observed for the bulk of this sample can be explained without the need for an IMBH. Furthermore, it is possible that clusters with large core to half-light radius ratios harbour a BH binary (comprising stellar mass BHs) rather than a single massive BH. This work does not rule out the existence of IMBHs in the cores of at least some star clusters.     

Star clusters around recoiled black holes in the Milky Way halo

Gravitational wave emission by coalescing black holes (BHs) kicks the remnant BH with a typical velocity of hundreds of  km s⁻¹  . This velocity is sufficiently large to remove the remnant BH from a low-mass galaxy but is below the escape velocity from the Milky Way (MW) galaxy. If central BHs were common in the galactic building blocks that merged to make the MW, then numerous BHs that were kicked out of low-mass galaxies should be freely floating in the MW halo today. We use a large statistical sample of possible merger tree histories for the MW to estimate the expected number of recoiled BH remnants present in the MW halo today. We find that hundreds of BHs should remain bound to the MW halo after leaving their parent low-mass galaxies. Each BH carries a compact cluster of old stars that populated the core of its original host galaxy. Using the time-dependent Fokker–Planck equation, we find that the present-day clusters are  ≲1 pc  in size, and their central bright regions should be unresolved in most existing sky surveys. These compact systems are distinguishable from globular clusters by their internal (Keplerian) velocity dispersion greater than 100 km s⁻¹ and their high mass-to-light ratio owing to the central BH. An observational discovery of this relic population of star clusters in the MW halo would constrain the formation history of the MW and the dynamics of BH mergers in the early Universe. A similar population should exist around other galaxies and may potentially be detectable in M31 and M33.     

Evolution of globular cluster systems in three galaxies of the Fornax cluster

We studied and compared the radial profiles of globular clusters and of the stellar bulge component in three galaxies of the Fornax cluster observed with the WFPC2 of the Hubble Space Telescope ( HST ). The stars are more concentrated toward the galactic centres than globular clusters, in agreement with what has already been observed in many other galaxies: if the observed difference is the result of evolution of the globular cluster systems starting from initial profiles similar to those of the halo–bulge stellar components, a relevant fraction of their initial mass (74, 47 and 52 per cent for NGC 1379, 1399 and 1404, respectively) should have disappeared in the inner regions. This mass has probably contributed to the nuclear field population, local dynamics and high-energy phenomena in the primeval life of the galaxy. An indication in favour of the evolutionary interpretation of the difference between the globular cluster system and stellar bulge radial profiles is given by the positive correlation we found between the value of the mass lost from the globular cluster system and the central galactic black hole mass in the set of seven galaxies for which these data are available.     

Extrapolating SMBH correlations down the mass scale: the case for IMBHs in globular clusters

Empirical evidence for both stellar mass black holes (M _•<10²  M _⊙) and supermassive black holes (SMBHs, M _•>10⁵  M _⊙) is well established. Moreover, every galaxy with a bulge appears to host a SMBH, whose mass is correlated with the bulge mass, and even more strongly with the central stellar velocity dispersion σ _c , the M _•–σ relation. On the other hand, evidence for “intermediate-mass” black holes (IMBHs, with masses in the range 100–10⁵ M _⊙) is relatively sparse, with only a few mass measurements reported in globular clusters (GCs), dwarf galaxies and low-mass AGNs. We explore the question of whether globular clusters extend the M _•–σ relationship for galaxies to lower black hole masses and find that available data for globular clusters are consistent with the extrapolation of this relationship. We use this extrapolated M _•–σ relationship to predict the putative black hole masses of those globular clusters where existence of central IMBH was proposed. We discuss how globular clusters can be used as a constraint on theories making specific predictions for the low-mass end of the M _•–σ relation.     

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 10⁴ yr) occur in faint ( L ≲10¹⁰ L_⊙) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 10⁵ yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of the order of 10⁶ M_⊙, independent of galaxy luminosity; thus, disrupted stars may contribute significantly to the present BH mass in galaxies fainter than ∼10⁹ L_⊙.     

Bursts of gravitational radiation from active galactic nuclei and globular clusters

The characteristics of gravitational bursts from active galactic nuclei, and globular clusters are obtained for three astrophysical situations:(i) scattering of stars by massive black holes residued at the centers of galaxies and globular clusters; (ii) the close encounters of stars in the nuclear regions of these objects; (iii) scattering of stars by black holes of stellar mass containing in the stellar population of galactic nuclei and clusters. The most effective source of gravitational bursts appears to be a scattering of stars by the massive central black holes which produces the bursts with dimensionless amplitudeh10^–19–10^–21 and frequencies from 10^–1 to 10^–5 Hz. The characteristics obtained correspond to the possiblities of a future gravitational-wave experiment with use of laser Doppler tracking of interplanetary spacecrafts.     

The evolution of massive black hole seeds

We investigate the evolution of high-redshift seed black hole masses at late times and their observational signatures. The massive black hole seeds studied here form at extremely high redshifts from the direct collapse of pre-galactic gas discs. Populating dark matter haloes with seeds formed in this way, we follow the mass assembly of these black holes to the present time using a Monte Carlo merger tree. Using this machinery, we predict the black hole mass function at high redshifts and at the present time, the integrated mass density of black holes and the luminosity function of accreting black holes as a function of redshift. These predictions are made for a set of three seed models with varying black hole formation efficiency. Given the accuracy of present observational constraints, all three models can be adequately fitted. Discrimination between the models appears predominantly at the low-mass end of the present-day black hole mass function which is not observationally well constrained. However, all our models predict that low surface brightness, bulgeless galaxies with large discs are least likely to be sites for the formation of massive seed black holes at high redshifts. The efficiency of seed formation at high redshifts has a direct influence on the black hole occupation fraction in galaxies at   z = 0  . This effect is more pronounced for low-mass galaxies. This is the key discriminant between the models studied here and the Population III remnant seed model. We find that there exist a population of low-mass galaxies that do not host nuclear black holes. Our prediction of the shape of the M _BH–σ relation at the low-mass end is in agreement with the recent observational determination from the census of low-mass galaxies in the Virgo cluster.     

Radio observations of NGC 2808 and other globular clusters: constraints on intermediate-mass black holes

We present the results of a deep radio observation of the globular cluster NGC 2808. We show that there are no sources detected within the core of the cluster, placing constraints on both the pulsar population of the cluster and the mass of a possible intermediate-mass black hole in NGC 2808. We compare the results for this cluster with other constraints on intermediate-mass black holes derived from accretion measures. With the exception of G1 in M 31 which has previously shown radio emission, even with considerably more conservative assumptions, only the clusters with the poorest of observational constraints are consistent with falling on the   M _BH–σ  relation. This result is interpreted in terms of the fundamental differences between galaxies and globular clusters.     

Galaxies and Star Clusters – From the Computer to the Real World

G01 New evidence for a connection between massive black holes and ULX G02 Long‐Term Evolution of Massive Black Hole Binaries G03 NBODY Meets Stellar Population Synthesis G04 N‐body modelling of real globular star clusters G05 Fokker‐Planck rotating models of globular clusters with black hole G06 Observational Manifestation of chaos in spiral galaxies: quantitative analysis and qualitative explanation G07 GRAPE Clusters: Beyond the Million‐Body Problem G08 Orbital decay of star clusters and Massive Black Holes in cuspy galactic nuclei G09 An Edge‐on Disk Galaxy Catalog G10 Complexes of open clusters in the Solar neighborhood G11 Search for and investigation of new stellar clusters using the data from huge stellar catalogues G12 Computing 2D images of 3D galactic disk models G13 Outer Pseudoring in the Galaxy G14 Where are tidal‐dwarf galaxies? G15 Ultra compact dwarf galaxies in nearby clusters G16 Impact of an Accretion Disk on the Structure of a stellar cluster in active galactic nuclei G17 Order and Chaos in the edge‐on profiles of disk galaxies G18 On the stability of OB‐star configurations in the Orion Nebula cluster G19 Older stars captured in young star clusters by cloud collapse G20 General features of the population of open clusters within 1 kpc from the Sun G21 Unstable modes in thin stellar disks G22 From Newton to Einstein – Dynamics of N‐body systems G23 On the relation between the maximum stellar mass and the star cluster mass     

The connection between globular cluster systems and the host galaxies

A large number of early-type galaxies are now known to possess blue and red subpopulations of globular clusters. We have compiled a data base of 28 such galaxies exhibiting bimodal globular cluster colour distributions. After converting to a common V – I colour system, we investigate correlations between the mean colour of the blue and red subpopulations with galaxy velocity dispersion. We support previous claims that the mean colours of the blue globular clusters are unrelated to their host galaxy. They must have formed rather independently of the galaxy potential they now inhabit. The mean blue colour is similar to that for halo globular clusters in our Galaxy and M31. The red globular clusters, on the other hand, reveal a strong correlation with galaxy velocity dispersion. Furthermore, in well-studied galaxies the red subpopulation has similar, and possibly identical, colours to the galaxy halo stars. Our results indicate an intimate link between the red globular clusters and the host galaxy; they share a common formation history. A natural explanation for these trends would be the formation of the red globular clusters during galaxy collapse.     

Quasars lensed by globular clusters of spiral and elliptical galaxies

Based on the SDSS catalog, we have found new close quasar—galaxy pairs. We analyze the radial distribution of quasars from pairs around galaxies of different types. We show that the quasars from pairs follow the density profile of halo globular clusters. This is new observational evidence that the quasars projected onto the halos of galaxies are magnified by gravitational lensing by halo globular clusters.     

Keck imaging of the globular cluster systems in the early-type galaxies NGC 1052 and 7332

The presence of two globular cluster subpopulations in early-type galaxies is now the norm rather than the exception. Here we present two more examples for which the host galaxy appears to have undergone a recent merger. Using multi-colour Keck imaging of NGC 1052 and 7332 we find evidence for a bimodal globular cluster colour distribution in both galaxies, with roughly equal numbers of blue and red globular clusters. The blue ones have similar colours to those in the Milky Way halo and are thus probably very old and metal-poor. If the red globular cluster subpopulations are at least of solar metallicity, then stellar population models indicate young ages. We discuss the origin of globular clusters within the framework of formation models. We conclude that recent merger events in these two galaxies have had little effect on their overall globular cluster systems. We also derive globular cluster density profiles, global specific frequencies and, in the case of NGC 1052, radial colour gradients and azimuthal distribution. In general these globular cluster properties are normal for early-type galaxies.     

Gravitational microlensing: A parallel,large-data implementation

Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as individual lenses. The magnification from such microlensing results in rapid brightness fluctuations which reveal not only the properties of the lensing masses, but also the surface brightness distribution in the source. However, while the combination of deflections due to individual stars is linear, the resulting magnifications are highly non-linear, leading to significant computational challenges which currently limit the range of problems which can be tackled. This paper presents a new and novel implementation of a numerical approach to gravitational microlensing, increasing the scale of the problems that can be tackled by more than two orders of magnitude, opening up a new regime of astrophysically interesting problems.     

Warped discs and the directional stability of jets in active galactic nuclei

The radial distribution of globular clusters in galaxies is always less peaked to the centre than that of the halo stars. Extending previous work to a sample of Hubble Space Telescope globular cluster systems in ellipticals, we evaluate the number of clusters potentially lost to the galactic centre as the integrals of the difference between the observed globular cluster system distribution and the underlying halo light profile. In the sample of galaxies examined it is found that the initial populations of globular clusters may have been ∼30 per cent to 50 per cent richer than now. If these 'missing' globular clusters have decayed and have been partly destroyed in the very central galactic zones, they have carried there a significant quantity of mass that, plausibly, contributed to the formation and feeding of a massive object therein. It is relevant to note that the observed correlation between the core radius of the globular cluster system and the parent galaxy luminosity can be interpreted as a result of evolution.     

Globular cluster systems in nearby dwarf galaxies – I. HST/ACS observations and dynamical properties of globular clusters at low environmental density

We investigate the old globular cluster (GC) population of 68 faint  ( M _V > −16 mag)  dwarf galaxies located in the halo regions of nearby (≲12 Mpc) loose galaxy groups and in the field environment based on archival Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS) images in F606W and F814W filters. The combined colour distribution of 175 GC candidates peaks at  ( V − I ) = 0.96 ± 0.07 mag  and the GC luminosity function turnover for the entire sample is found at   M _{V ,TO}=−7.6 ± 0.11 mag  , similar to the old metal-poor Large Magellanic Cloud (LMC) GC population. Our data reveal a tentative trend of   M _{V ,TO}  becoming fainter from late- to early-type galaxies. The luminosity and colour distributions of GCs in dIrrs show a lack of faint blue GCs (bGCs). Our analysis reveals that this might reflect a relatively younger GC system than typically found in luminous early-type galaxies. If verified by spectroscopy, this would suggest a later formation epoch of the first metal-poor star clusters in dwarf galaxies. We find several bright (massive) GCs which reside in the nuclear regions of their host galaxies. These nuclear clusters have similar luminosities and structural parameters as the peculiar Galactic clusters suspected of being the remnant nuclei of accreted dwarf galaxies, such as M54 and ωCen. Except for these nuclear clusters, the distribution of GCs in dIrrs in the half-light radius versus cluster mass plane is very similar to that of Galactic young halo clusters, which suggests comparable formation and dynamical evolution histories. A comparison with theoretical models of cluster disruption indicates that GCs in low-mass galaxies evolve dynamically as self-gravitating systems in a benign tidal environment.     

Compact massive objects in Virgo galaxies: the black hole population

We investigate the distribution of massive black holes (MBHs) in the Virgo cluster. Observations suggest that active galactic nuclei activity is widespread in massive galaxies ( M _*≳ 10¹⁰ M_⊙), while at lower galaxy masses star clusters are more abundant, which might imply a limited presence of central black holes in these galaxy-mass regimes. We explore if this possible threshold in MBH hosting is linked to nature , nurture or a mixture of both. The nature scenario arises naturally in hierarchical cosmologies, as MBH formation mechanisms typically are efficient in biased systems, which would later evolve into massive galaxies. Nurture , in the guise of MBH ejections following MBH mergers, provides an additional mechanism that is more effective for low mass, satellite galaxies. The combination of inefficient formation, and lower retention of MBHs, leads to the natural explanation of the distribution of compact massive objects in Virgo galaxies. If MBHs arrive to the correlation with the host mass and velocity dispersion during merger-triggered accretion episodes, sustained tidal stripping of the host galaxies creates a population of MBHs which lie above the expected scaling between the holes and their host mass, suggesting a possible environmental dependence.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (10²–10⁴ M _⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.     

MEDEA: a real time imaging pipeline for pixel lensing

Pixel lensing is a technique used to search for baryonic components of dark matter (MACHOs) and allows detection of microlensing events even when the target galaxies are not resolved into individual stars. Potentially, it has the advantage of providing higher statistics than other methods but, unfortunately, traditional approaches to pixel lensing are very demanding in terms of computing time. We present the new, user friendly, tool MEDEA (Microlensing Experiment Data-Analysis Software for Events with Amplification). The package can be used either in a fully automatic or semi-automatic mode and can perform an on-line identification of events by means of a two level trigger and a quasi-on-line data analysis. The package will find application in the exploration of large databases as well as in the exploitation of specifically tailored future surveys.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.