Evaporative evolution of stellar clusters is shown to be relaxation limited when the number of stars satisfies $N>>N_c$, where $N_c\simeq 1600$. For a Maxwell velocity distribution that extends beyond the escape velocity, this process is {\em bright} in that the Kelvin-Helmholtz time scale, $f_H^{-1}t_{relax}$, is shorter than the Ambartsumian-Spitzer time scale, $f_N^{-1}t_{relax}$, where $f_H>f_N$ denote the fractional changes in total energy and number of stars per relaxation time, $t_{relax}$. The resulting evaporative lifetime $t_{ev}\simeq 20.5 t_{relax}$ for isolated clusters is consistent with Fokker-Planck and N-body simulations, where $t_{relax}$ is expressed in terms of the half-mass radius. We calculate the grey body factor by averaging over the anisotropic perturbation of the potential barrier across the tidal sphere, and derive the tidal sensitivity ${d\ln t_{ev}}/{dy}\simeq -1.9$ to -0.7 as a function of the ratio $y$ of the virial-to-tidal radius. Relaxation limited evaporation applies to the majority of globular clusters of the Milky Way with $N=10^4-10^6$ that are in a pre-collapse phase. It drives streams of stars into the tidal field with a mean kinetic energy of 0.71 relative to temperature of the cluster. Their $S$ shape morphology leads in sub-orbital and a trails in super-orbital streams separated by $3.4σ/Ω$ in the radial direction of the orbit, where $Ω$ denotes the orbital angular velocity and $σ$ the stellar velocity dispersion in the cluster. These correlations may be tested by advanced wide field photometry and spectroscopy.
The mass evaporation rate of globular clusters evolving in a strong Galactic tidal field is derived through the analysis of large, multi-mass $N$-body simulations. For comparison, we also study the same evaporation rates using MOCCA Monte Carlo models for globular cluster evolution. Our results show that the mass evaporation rate is a dynamical value; that is, far from a constant single number found in earlier analytical work and commonly used in the literature. Moreover, the evaporation rate derived with these simulations is higher than values previously published. These models also show that…
Resonant relaxation has been discussed as an efficient process that changes the angular momenta of stars orbiting around a central supermassive black hole due to the fluctuating gravitational field of the stellar cluster. Other spherical stellar systems, such as globular clusters, exhibit a restricted form of this effect where enhanced relaxation rate only occurs in the directions of the angular momentum vectors, but not in their magnitudes; this is called vector resonant relaxation (VRR). To explore this effect, we performed a large set of direct N-body simulations, with up to 512k particles …
Globular clusters contain a finite number of stars. As a result, they inevitably undergo secular evolution (`relaxation') causing their mean distribution function (DF) to evolve on long timescales. On one hand, this long-term evolution may be interpreted as driven by the accumulation of local deflections along each star's mean field trajectory -- so-called `non-resonant relaxation'. On the other hand, it can be thought of as driven by non-local, collectively dressed and resonant couplings between stellar orbits, a process termed `resonant relaxation'. In this paper we consider a model globular…
We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^(ν) models, originally designed to represent stellar systems produced by a violent relaxati…
Thin halo star streams originate from the evaporation of globular clusters and therefore provide information about the early epoch globular cluster population. The observed tidal tails from halo globular clusters in the Milky Way are much more shorter than expected from a star cluster orbiting for 10~Gyr. The discrepancy is likely the result of the assumption that the clusters have been orbiting in a non-evolving galactic halo for a Hubble time. As a first step towards more realistic stream histories, a toy model that combines an idealized merger model with a simplified model of the internal c…
Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar's "non-resonant" (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each sta…
The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the cluster's self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity an…
We have determined the amount of stellar mass segregation in over 50 globular clusters and ultra-faint dwarf galaxy candidates based on deep HST and ground-based photometry. We find that the amount of mass segregation in globular clusters is strongly correlated with their relaxation time and that all clusters with relaxation times of the order of their ages or longer have little to no mass segregation. For each cluster, the amount of mass segregation seen is fully compatible with the amount expected by dynamical evolution from initially unsegregated clusters, showing that globular clusters for…
Collisional relaxation describes the stochastic process with which a self-gravitating system near equilibrium evolves in phase space due to the fluctuating gravitational field of the system. The characteristic timescale of this process is called the relaxation time. In this paper, we highlight the difference between two measures of the relaxation time in globular clusters: (i) the diffusion time with which the isolating integrals of motion (i.e. energy E and angular momentum magnitude L) of individual stars change stochastically and (ii) the asymptotic timescale required for a family of orbits…
The internal dynamics of globular clusters (GCs) is strongly affected by two-body interactions that bring the systems to a state of partial energy equipartition. Using a set of Monte Carlo clusters simulations, we investigate the role of the onset of energy equipartition in shaping the mass-to-light ratio (M/L) in GCs. Our simulations show that the M/L profiles cannot be considered constant and their specific shape strongly depends on the dynamical age of the clusters. Dynamically younger clusters display a central peak up to M/L $\simeq25$ $M_\odot/L_\odot$ caused by the retention of dark rem…
Using the Optimal Filter Technique applied to Sloan Digital Sky Survey photometry, we have found extended tails stretching about 1 degree (or several tens of half-light radii) from either side of the ultra-faint globular cluster Palomar 1. The tails contain roughly as many stars as does the cluster itself. Using deeper Hubble Space Telescope data, we see that the isophotes twist in a chacteristic S-shape on moving outwards from the cluster centre to the tails. We argue that the main mechanism forming the tails may be relaxation driven evaporation and that Pal 1 may have been accreted from a no…
We summarise some of the recent progress in understanding the formation and evolution of globular clusters (GCs) in the context of galaxy formation and evolution. It is discussed that an end-to-end model for GC formation and evolution should capture four different phases: (1) star and cluster formation in the high-pressure interstellar medium of high-redshift galaxies, (2) cluster disruption by tidal shocks in the gas-rich host galaxy disc, (3) cluster migration into the galaxy halo, and (4) the final evaporation-dominated evolution of GCs until the present day. Previous models have mainly foc…
Using imaging that shows four magnitudes of main sequence stars, we have discovered that the Galactic globular cluster NGC 1851 is surrounded by a halo that is visible from the tidal radius of 700 arcsec (41 pc) to more than 4500 arcsec (>250 pc). This halo is symmetric and falls in density as a power law of $r^{-1.24}$. It contains approximately 0.1% of the dynamical mass of NGC 1851. There is no evidence for tidal tails. Current models of globular cluster evolution do not explain this feature, although simulations of tidal influences on dwarf spheroidal galaxies qualitatively mimic these res…
We study the dynamical evolution of globular clusters using our Hénon-type Monte Carlo code for stellar dynamics including all relevant physics such as two-body relaxation, single and binary stellar evolution, Galactic tidal stripping, and strong interactions such as physical collisions and binary mediated scattering. We compute a large database of several hundred models starting from broad ranges of initial conditions guided by observations of young and massive star clusters. We show that these initial conditions very naturally lead to present day clusters with properties including the centra…
The log-normal shape of the mass function for metal-poor halo globular clusters is proposed to result from an initial M^{-2} power law modified rapidly by evaporation, collisions with clouds, and mutual cluster interactions in the dense environment of a redshift z~5-15 disk galaxy. Galaxy interactions subsequently spray these clusters into the galaxy group environment, where they fall into other growing galaxies and populate their halos. Clusters forming later in z~2-5 galaxies, and those formed during major mergers, produce metal-rich globulars. Monte Carlo models of evolving cluster populati…
By adopting empirical estimates of the Helium enhancement (Delta Y) between consecutive stellar generations for a sample of Galactic globular clusters (GGC), we uniquely constraint the star formation efficiency of each stellar generation in these stellar systems. In our approach, the star formation efficiency is the central factor that links stellar generations as it defines both their stellar mass and the remaining mass available for further star formation, fixing also the amount of matter required to contaminate the next stellar generation. In this way, the star formation efficiency is here …
We present a cosmological zoom-in simulation of a Milky Way-like galaxy used to explore the formation and evolution of star clusters. We investigate in particular the origin of the bimodality observed in the colour and metallicity of globular clusters, and the environmental evolution through cosmic times in the form of tidal tensors. Our results self-consistently confirm previous findings that the blue, metal-poor clusters form in satellite galaxies which are accreted onto the Milky Way, while the red, metal-rich clusters form mostly in situ or, to a lower extent in massive, self-enriched gala…
The Galactic halo has a complex assembly history, which can be seen in its wealth of kinematic and chemical substructure. Globular clusters lose stars through tidal interactions with the Galaxy and cluster evaporation processes, meaning that they are inevitably a source of halo stars. These "migrants" from globular clusters can be recognized in the halo field by the characteristic light element abundance anticorrelations that are commonly observed only in globular cluster stars, and the number of halo stars that can be chemically tagged to globular clusters can be used to place limits on the f…
As a result of the slow action of two-body encounters, globular clusters develop mass segregation and attain a condition of only partial energy equipartition even in their central, most relaxed regions. Realistic numerical simulations show that, during the process, a radially-biased anisotropy profile slowly builds up, mimicking that resulting from incomplete violent relaxation. Commonly used dynamical models, such as the one-component King models, cannot describe these properties. Here we show that simple two-component models based on a distribution function originally conceived to describe e…
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 o…
Two-body interactions play a major role in shaping the structural and dynamical properties of globular clusters (GCs) over their long-term evolution. In particular, GCs evolve toward a state of partial energy equipartition that induces a mass-dependence in their kinematics. By using a set of Monte Carlo cluster simulations evolved in quasi-isolation, we show that the stellar mass dependence of the velocity dispersion $σ(m)$ can be described by an exponential function $σ^2\propto \exp(-m/m_\mathrm{eq})$, with the parameter $m_\mathrm{eq}$ quantifying the degree of partial energy equipartition o…
We present an analysis of the radial dependence of the stellar mass function in the diffuse outer-halo globular cluster Palomar 14. Using archival HST/WFPC2 data of the cluster's central 39 pc (corresponding to ~0.85*r_h) we find that the mass function in the mass range of 0.55 to 0.85 solar masses is well approximated by a power-law at all radii. The mass function steepens with increasing radius, from a shallow power-law slope of 0.66+/-0.32 in the cluster's centre to a slope of 1.61+/-0.33 beyond the core radius, showing that the cluster is mass-segregated. This is seemingly in conflict with…
There is an increasing number of recent observational results which show that some globular clusters exhibit internal rotation while they travel along their orbital trajectories around the Milky Way center. Based on these findings, we looked for any relationship between the inclination angles of the globular clusters' orbits with respect to the Milky Way plane and those of their rotation. We discovered that the relative inclination, in the sense rotation axis inclination - orbit axis inclination, is a function of the globular cluster's orbit inclination. Rotation and orbit axes are aligned for…
By adopting the empirical constraints related to the estimates of Helium enhancement ($ΔY$), present mass ratio between first and second stellar generations ($M_{1G}/M_{2G}$) and the actual mass of Galactic globular clusters ($M_{GC}$), we envisage a possible scenario for the formation of these stellar systems. Our approach allows for the possible loss of stars through evaporation or tidal interactions and different star formation efficiencies. In our approach the star formation efficiency of the first generation ($ε_{1G}$) is the central factor that links the stellar generations as it not onl…
Internal rotation is considered to play a major role in the dynamics of some globular clusters. However, in only few cases it has been studied by quantitative application of realistic and physically justified global models. Here we present a dynamical analysis of the photometry and three-dimensional kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of…
Star clusters have hierarchical patterns in space and time, suggesting formation processes in the densest regions of a turbulent interstellar medium. Clusters also have hierarchical substructure when they are young, which makes them all look like the inner mixed parts of a pervasive stellar hierarchy. Young field stars share this distribution, presumably because some of them came from dissolved clusters and others formed in a dispersed fashion in the same gas. The fraction of star formation that ends up in clusters is apparently not constant, but may increase with interstellar pressure. Hierar…
We have determined masses, stellar mass functions and structural parameters of 112 Milky Way globular clusters by fitting a large set of N-body simulations to their velocity dispersion and surface density profiles. The velocity dispersion profiles were calculated based on a combination of more than 15,000 high-precision radial velocities which we derived from archival ESO/VLT and Keck spectra together with ~20,000 published radial velocities from the literature. Our fits also include the stellar mass functions of the globular clusters, which are available for 47 clusters in our sample, allowin…
Using a Monte Carlo code, we construct a dynamic evolutionary model of the Galactic globular cluster M22 (NGC6656). The initial conditions are chosen so that, after about 12Gyr of stellar and dynamical evolution, the model is an approximate fit to the surface brightness and velocity dispersion profiles of the cluster, to its mass function, and to the current binary fraction. Depending on the distribution of black hole natal kicks, we predict that the present-day population of stellar-mass black holes ranges from about 40 (no kicks) down to essentially zero (kicks distributed like those of neut…
This is the first of a series of papers presenting the results from our survey of 25 Galactic globular clusters with the MUSE integral-field spectrograph. In combination with our dedicated algorithm for source deblending, MUSE provides unique multiplex capabilities in crowded stellar fields and allows us to acquire samples of up to 20 000 stars within the half-light radius of each cluster. The present paper focuses on the analysis of the internal dynamics of 22 out of the 25 clusters, using about 500 000 spectra of 200 000 individual stars. Thanks to the large stellar samples per cluster, we a…
We describe Monte Carlo models for the dynamical evolution of the nearby globular cluster NGC 6397. The code includes treatments of two-body relaxation, most kinds of three- and four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide, and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12Gyr of evolution, gives a model with a fairly satisfactory match to the surface brightness profile, the velocity dispersion profile, and the luminosity function in two fields. We describe …
Massive globular clusters lose stars via internal and external processes. Internal processes include mainly two-body relaxation, while external processes include interactions with the Galactic tidal field. We perform a suite of N-body simulations of such massive clusters using three different direct-summation N-body codes, exploring different Galactic orbits and particle numbers. By inspecting the rate at which a star's energy changes as it becomes energetically unbound from the cluster, we can neatly identify two populations we call kicks and sweeps, that escape through two-body encounters in…
Galactic globular clusters (GCs) are believed to have formed in-situ in the Galaxy as well as in dwarf galaxies later accreted onto the Milky Way. However, to date, there is no unambiguous signature to distinguish accreted GCs. Using specifically designed $N$-body simulations of GCs evolving in a variety of time-dependent tidal fields (describing the potential of a dwarf galaxy-Milky Way merger), we analyze the effects imprinted to the internal kinematics of an accreted GC. In particular, we look at the evolution of the velocity anisotropy. Our simulations show that at early phases, the veloci…
The Fermi satellite has recently detected gamma ray emission from the central regions of our Galaxy. This may be evidence for dark matter particles, a major component of the standard cosmological model, annihilating to produce high-energy photons. We show that the observed signal may instead be generated by millisecond pulsars that formed in dense star clusters in the Galactic halo. Most of these clusters were ultimately disrupted by evaporation and gravitational tides, contributing to a spherical bulge of stars and stellar remnants. The gamma ray amplitude, angular distribution, and spectral …
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-l…
Sizeable number of stellar-mass black holes (BHs) in globular clusters (GCs) can strongly influence the dynamical evolution and observational properties of their host cluster. Using results from a large set of numerical simulations, we identify the key ingredients needed to sustain a sizeable population of BHs in GCs up to a Hubble time. We find that while BH natal kick prescriptions are essential in determining the initial retention fraction of BHs in GCs, the long-term survival of BHs is determined by the size, initial central density and half-mass relaxation time of the GC. Simulated GC mod…
We investigate how the Milky Way tidal field can affect the spatial mixing of multiple stellar populations in the globular cluster NGC 6362. We use $N$-body simulations of multiple population clusters on the orbit of this cluster around the Milky Way. Models of the formation of multiple populations in globular clusters predict that the second population should initially be more centrally concentrated than the first. However, NGC 6362 is comprised of two chemically distinct stellar populations having the same radial distribution. We show that the high mass loss rate experienced on this cluster'…
We incorporate a semi-analytic formula for the main sequence lifetime of helium-rich stars in N-body simulations of multiple population globular clusters to investigate how the enriched helium stars impact the dynamics of globular clusters. We show that a globular cluster with a helium-rich concentrated population will be slightly smaller than a globular cluster with a normal-helium second generation, with the largest difference seen in the extended normal-helium population. This effect is shown both for a cluster in isolation and one in a realistic Milky Way tidal field. We show that this eff…
We present a simple theory for the evolution of initially compact clusters in a tidal field. The fundamental ingredient of the model is that a cluster conducts a constant fraction of its own energy through the half-mass radius by two-body interactions every half-mass relaxation time. This energy is produced in a self-regulative way in the core by an (unspecified) energy source. We find that the half-mass radius increases during the first part (roughly half) of the evolution and decreases in the second half, while the escape rate is constant and set by the tidal field. We present evolutionary t…
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 vario…
Binary Stars as Dynamical Tracers in Globular Clusters .I. First Observations of Bimodal Spatial Distributions
University of Bologna（博洛尼亚大学）；INAF – Astrophysics and Space Science Observatory of Bologna（意大利国家天体物理研究所波洛尼亚天文与空间科学观测站）；Indiana University（印第安纳大学）；European Southern Observatory（欧洲南方天文台）
Scaling relations for globular clusters (GC) differ from scaling relations for pressure supported (elliptical) galaxies. We show that two-body relaxation is the dominant mechanism in shaping the bivariate dependence of density on mass and Galactocentric distance for Milky Way GCs with masses <10^6 Msun, and it is possible, but not required, that GCs formed with similar scaling relations as ultra-compact dwarf galaxies. We use a fast cluster evolution model to fit a parameterised model for the initial properties of Milky Way GCs to the observed present-day properties. The best-fit cluster initi…
We present an end-to-end, two-phase model for the origin of globular clusters (GCs). In the model, populations of stellar clusters form in the high-pressure discs of high-redshift ($z>2$) galaxies (a rapid-disruption phase due to tidal perturbations from the dense interstellar medium), after which the galaxy mergers associated with hierarchical galaxy formation redistribute the surviving, massive clusters into the galaxy haloes, where they remain until the present day (a slow-disruption phase due to tidal evaporation). The high galaxy merger rates of $z>2$ galaxies allow these clusters to be `…
We investigate the ratio between the half-mass radii r_h of Galactic globular clusters and their Jacobi radii r_J given by the potential of the Milky Way and show that clusters with galactocentric distances R_{GC}>8 kpc fall into two distinct groups: one group of compact, tidally-underfilling clusters with r_h/r_J<0.05 and another group of tidally filling clusters which have 0.1 < r_h/r_J<0.3. We find no correlation between the membership of a particular cluster to one of these groups and its membership in the old or younger halo population. Based on the relaxation times and orbits of the clus…
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 …
We report on the extent of the effects of the Milky Way's gravitational field in shaping the structural parameters and internal dynamics of its globular cluster population. We make use of a homogeneous, up-to-date data set with kinematics, structural properties, current and initial masses of 156 globular clusters. In general, cluster radii increase as the Milky Way potential weakens; with the core and Jacobi radii being those which increase at the slowest and fastest rate respectively. We interpret this result as the innermost regions of globular clusters being less sensitive to changes in the…
We present core radii for 54 Milky Way globular clusters determined by fitting King-Michie models to cumulative projected star count distributions. We find that fitting star counts rather than surface brightness profiles produces results that differ significantly due to the presence of mass segregation. The sample in each cluster is further broken down into various mass groups, each of which is fit independently, allowing us to determine how the concentration of each cluster varies with mass. The majority of the clusters in our sample show general agreement with the standard picture that more …
The evolution of globular clusters due to 2-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Henon provided the insight that we do not need to know the details of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homo…
Henon sought the most general spherical potential in which the radial periods of orbits depended only on energy. He named this potential the isochrone, and discovered that it provided a good representation of data for globular clusters. He sought an explanation in terms of resonant relaxation. The role that resonant relaxation might play in globular clusters is still an open question, but the isochrone potential is guaranteed a role in dynamical astronomy because it is the most general potential in which closed-form expressions for angle-action coordinates are available. I explain how this pro…
This is the third paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation. The first paper provided an accurate spectral solution of the equation for isotropic pre-collapse star clusters and the second detailed the physical feature of the model. Based on the works, the present work applies the solution to the observed structural profiles of Galactic globular clusters. For fitting to the profiles, the most fundamental (quasi-)stationary model, the King model, and the variants have shown successful results while they can not apply to core-collapsing and co…
In weakly collisional stellar systems such as some globular clusters, partial energy equipartition and mass segregation are expected to develop as a result of the cumulative effect of stellar encounters even in systems initially characterized by star-mass independent density and energy distributions. In parallel, numerical simulations have demonstrated that radially-biased pressure anisotropy slowly builds up in realistic models of globular clusters from initial isotropic conditions, leading to anisotropy profiles that, to some extent, mimic those resulting from incomplete violent relaxation k…
Recently, a class of non-truncated radially-anisotropic models (the so-called $f^{(ν)}$-models), originally constructed in the context of violent relaxation and modeling of elliptical galaxies, has been found to possess interesting qualities in relation to observed and simulated globular clusters. In view of new applications to globular clusters, we improve this class of models along two directions. To make them more suitable for the description of small stellar systems hosted by galaxies, we introduce a 'tidal' truncation (by means of a procedure that guarantees full continuity of the distrib…
We present kinematical analyses of 22 Galactic globular clusters using the Hubble Space Telescope proper motion (HSTPROMO) catalogues recently presented in Bellini et al. (2014). For most clusters, this is the first proper-motion study ever performed, and, for many, this is the most detailed kinematic study of any kind. We use cleaned samples of bright stars to determine binned velocity-dispersion and velocity-anisotropy radial profiles and two-dimensional velocity-dispersion spatial maps. Using these profiles, we search for correlations between cluster kinematics and structural properties. We…
The relaxation time at the half-mass radius of Galactic globular clusters (GGCs) is typically within a few Gyr. Hence, the majority of GGCs are expected to be well relaxed systems, given their age is around 12-13 Gyr. So any initial radial segregation between stars of the same initial mass on the main sequence (MS), in particular, the progenitors of the present day sub-giant and red-giant branch (SGB, RGB) stars should already have dissipated. However, a body of evidence contradicting to these expectations has been accumulated to date. The paradox could be solved by taking into account the eff…
We consider the formation of binary intermediate black holes (BIMBH) in globular clusters (GC), which could happen either in situ or due to the mergers between clusters. We simulate the evolution of the BIMBH orbit (and its subsequent merger) due to stellar ejections. We also take into account the evaporation of GCs due to the tidal field of the host galaxy and two-body relaxation. Our results show that if at least $10^{-3}$ of all GCs become BIMBH hosts and the BIMBH masses are $\sim1\%$ of the GC mass, at least one of the inspiralling (or merging) BIMBHs will be detected by LISA during its 4…
As part of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters, we present a detailed investigation of the internal kinematics of NGC 5986. The analysis is based on about 300 individual radial velocities of stars located at various distances from the cluster center, up to 300 arcseconds (about 4 half-mass radii). Our analysis reveals the presence of a solid-body rotation extending from the cluster center to the outermost regions probed by the data, and a velocity dispersion profile initially declining with the distance from the cluster's center, but flattening a…
We present result from DECam SDSS i PSF photometry of the radial stellar density profiles of the Large Magellanic Cloud (LMC) old globular clusters (GCs) NGC1841, 2210, Hodge11 and Reticulum, which extent out of ~ 380 pc from their centres. We found that the studied LMC GCs would not seem to exhibit extended stellar structures like those frequently seen in Galactic globular clusters (GGCs), which could suggest that the LMC gravitational field has not been efficient in stripping stars off its GCs. The concentration parameter $c$ of the studied LMC GCs would seem to depend on both the internal d…
