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 star's orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with $N$-body realisations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropisation, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster's anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters' long-term evolution.
We investigate the internal dynamics of anisotropic, rotating globular clusters with a multimass stellar population by performing new direct N-body simulations. In addition to the well-known radial mass segregation effect, where heavy stars and stellar remnants sink toward the center of the cluster, we find a mass segregation in the distribution of orbital inclinations as well. This newly discovered anisotropic mass segregation leads to the formation of a disk-like structure of massive objects near the equatorial plane of a rotating cluster. This result has important implications on the expect…
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…
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 …
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 present a preliminary analysis of the effect of dynamical friction on the orbits of part of the globular clusters in our Galaxy. Our study considers an anisotropic velocity dispersion field approximated using the results of studies in the literature. An axisymmetric Galactic model with mass components consisting of a disc, a bulge, and a dark halo is employed in the computations. We provide a method to compute the dynamical friction acceleration in ellipsoidal, oblate, and prolate velocity distribution functions with similar density in velocity space. Orbital properties, such as mean time-v…
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…
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…
We investigate the globular cluster system of the isolated elliptical NGC 7796, present new photometry of the galaxy, and use published kinematical data to constrain the dark matter content. Deep images in B and R, obtained with the VIsible MultiObject Spectrograph (VIMOS) at the VLT, form the data base. We present isotropic and anisotropic Jeans-models and give a morphological description of the companion dwarf galaxy. The globular cluster system has about 2000 members, so it is not as rich as those of giant ellipticals in galaxy clusters with a comparable stellar mass, but richer than many c…
We discuss the existence of elliptical polarisation in rotational spectral lines of CO and other molecules within the context of the Anisotropic Resonant Scattering (ARS) model. We show that the effect of ARS on the radiation field can lead to not only the previously predicted transformation of background linear polarisation into circular polarisation (i.e., Faraday conversion), but also the occurrence of Faraday rotation and the generation of elliptically polarised signals in an otherwise initially unpolarised radiation field. This is due to a collective behaviour between the large number of …
Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense tha…
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 Milky Way's satellite galaxies and Globular Clusters (GCs) are known to exhibit an anisotropic spatial distribution. We examine in detail this anisotropy by the means of the inertia tensor. We estimate the statistical significance of the results by repeating this analysis for random catalogues which use the radial distribution of the real sample. Our method reproduces the well-known planar structure in the distribution of the satellite galaxies. We show that for GCs several anisotropic structures are observed. The GCs at small distances, $2<R<10$ kpc, show a structure coplanar with the Gal…
We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the system evolves forward in time via a gravitational $N$-body code until the model cluster is able to reproduce select properties of an observed cluster. The method is first applied to observations of mock isotropic and anisotropic clusters while fitting against the cluster's three dimensional or projected density profile, density weighted mean-squared velocity p…
External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the Strong Equivalence Principle (SEP) and change the dynamics of self-bound stellar systems moving in space-varying background gravitational fields. We study two kinds of re-virialisation of the stellar systems: the violent phase transition and the adiabatic phase transition for systems moving on radial orbits, where the external field evolves from strong to weak and whose corresponding dynamics changes from Newtonian to Milgromian. We find that the time scale for the phase tranformation from Newtonian to Milgromian gravit…
Finding an intermediate-mass black hole (IMBH) in a globular cluster (GC), or proving its absence, is a crucial ingredient in our understanding of galaxy formation and evolution. The challenge is to identify a unique signature of an IMBH that cannot be accounted for by other processes. Observational claims of IMBH detection are often based on analyses of the kinematics of stars, such as a rise in the velocity dispersion profile towards the centre. In this contribution we discuss the degeneracy between this IMBH signal and pressure anisotropy in the GC. We show that that by considering anisotro…
Globular clusters (GCs) and many nuclear clusters (NCs) show evidence for hosting multiple generations of stellar populations. Younger stellar populations in NCs appear to reside in disk like structures, including the nuclear cluster in our own Galactic center as well as in M31. Kinematic studies of the anomalous globular cluster Omega Centauri, thought to possibly be a former dwarf galaxy (or a galactic nucleus), show evidence for its hosting of a central, kinematically cold disk component. These observations suggest that formation of second (or multiple) generation stars may occur in flatten…
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…
We use Gaia Data Release 2 to determine the mean proper motions for 150 Milky Way globular clusters (almost the entire known population), with a typical uncertainty of 0.05 mas/yr limited mainly by systematic errors. Combining them with distance and line-of-sight velocity measurements from the literature, we analyze the distribution of globular clusters in the 6d phase space, using both position/velocity and action/angle coordinates. The population of clusters in the central 10 kpc has a mean rotational velocity reaching 50-80 km/s, and a nearly isotropic velocity dispersion 100-120 km/s, whil…
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…
Gaia Data Release 2 provides a wealth of data to study the internal structure of nearby globular clusters. We use this data to investigate the internal kinematics of 11 nearby globular clusters, with a particular focus on their poorly-studied outer regions. We apply a strict set of selection criteria to remove contaminating sources and create pure cluster-member samples over a significant fraction of the radial range of each cluster. We confirm previous measurements of rotation (or a lack thereof) in the inner regions of several clusters, while extending the detection of rotation well beyond w…
We explore the possibility of the formation of globular clusters under ultraviolet (UV) background radiation. One-dimensional spherical symmetric radiation hydrodynamics (RHD) simulations by Hasegawa et al. have demonstrated that the collapse of low-mass (10^6-10^7 solar masses) gas clouds exposed to intense UV radiation can lead to the formation of compact star clusters like globular clusters (GCs) if gas clouds contract with supersonic infall velocities. However, three-dimensional effects, such as the anisotropy of background radiation and the inhomogeneity in gas clouds, have not been studi…
This paper is the third in a series investigating, by means of $N$-body simulations, the implications of an initial radially anisotropic velocity distribution on the dynamics of star clusters. Such a velocity distribution may be imprinted during a cluster's early evolutionary stages and several observational studies have found examples of old globular clusters in which radial anisotropy is still present in the current velocity distribution. Here we focus on its influence on mass segregation and the dynamics of primordial binary stars (disruptions, ejections, and component exchanges). The large…
We have studied the system of globular clusters (GCs) that formed in other galaxies and eventually accreted onto the Milky Way. Thus, the samples of GCs belonging to different tidal streams, obtained on the basis of the latest data from the Gaia observatory, were taken from the literature. We measured the anisotropy of the distribution of these GCs using the gyration tensor and found that the distribution of GCs in the streams is isotropic. Nevertheless, it can be seen that some of the accreted GCs included into existing samples actually belong to the disk of the Galaxy. To clarify the origin …
We apply the Tremaine-Weinberg theory of dynamical friction to compute the orbital decay of a globular cluster (GC), on an initially circular orbit inside a cored spherical galaxy with isotropic stellar velocities. The retarding torque on the GC, T(rp) < 0 , is a function of its orbital radius rp . The torque is exerted by stars whose orbits are resonant with the GC's orbit, and given as a sum over the infinitely many possible resonances by the Lynden-Bell Kalnajs (LBK) formula. We calculate the LBK torque T(rp) and determine rp(t), for a GC of mass Mp = 2 x 10^5 M_sun and an Isochrone galaxy …
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 consist…
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…
Dynamical models allow us to connect the motion of a set of tracers to the underlying gravitational potential, and thus to the total (luminous and dark) matter distribution. They are particularly useful for understanding the mass and spatial distribution of dark matter (DM) in a galaxy. Globular clusters (GCs) are an ideal tracer population in dynamical models, since they are bright and can be found far out into the halo of galaxies. We aim to test how well Jeans-Anisotropic-MGE (JAM) models using GCs (positions and line-of-sight velocities) as tracers can constrain the mass and radial distrib…
We quantify to what extent tidal erosion of globular clusters (GCs) has contributed to the observed u-shaped relation between GC specific frequencies S_N and host galaxy luminosity M_V. We used our MUESLI code to calculate GC survival rates for typical early-type galaxy potentials covering a wide range of observed galaxy properties. We do this for isotropic and radially anisotropic GC velocity distributions. We find that the calculated GC survival fraction, f_s, depends linearly on the logarithm of the 3D mass density, rho_3D, within the galaxy's half light radius, with f_s proportional to (rh…
We investigate the shallow increase in globular cluster half-light radii with projected galactocentric distance $R_{gc}$ observed in the giant galaxies M87, NGC 1399, and NGC 5128. To model the trend in each galaxy, we explore the effects of orbital anisotropy and tidally under-filling clusters. While a strong degeneracy exists between the two parameters, we use kinematic studies to help constrain the distance $R_β$ beyond which cluster orbits become anisotropic, as well as the distance $R_{fα}$ beyond which clusters are tidally under-filling. For M87 we find $R_β> 27$ kpc and $20 < R_{fα} < 4…
The origin of multiple stellar populations in Globular Clusters (GCs) is one of the greatest mysteries of modern stellar astrophysics. N-body simulations suggest that the present-day dynamics of GC stars can constrain the events that occurred at high redshift and led to the formation of multiple populations. Here, we combine multi-band photometry from the Hubble Space Telescope (HST) and ground-based facilities with HST and Gaia Data Release 2 proper motions to investigate the spatial distributions and the motions in the plane of the sky of multiple populations in the type II GCs NGC 5139 ($ω\…
This study constitutes part of a larger effort aimed at better characterizing the Galactic globular clusters (GGCs) located towards the inner Milky Way bulge and disk. Here, we focus on internal kinematics of nine GGCs, obtained from space-based imaging over time baselines of $>$9 years. We exploit multiple avenues to assess the dynamical state of the target GGCs, constructing radial profiles of projected stellar density, proper motion dispersion, and anisotropy. We posit that two-thirds (6/9) of our target GGCs are in an advanced dynamical state, and are close to (or have recently undergone) …
We study the azimuthal distribution of globular clusters (GCs) in early-type galaxies and compare them to their host galaxies using data from the ACS Virgo Cluster Survey. We find that in host galaxies with visible elongation (epsilon > 0.2) and intermediate to high luminosities (M_z<-19), the GCs are preferentially aligned along the major axis of the stellar light. The red (metal-rich) GC subpopulations show strong alignment with the major axis of the host galaxy, which supports the notion that these GCs are associated with metal-rich field stars. The metal-rich GCs in lenticular galaxies sho…
The Gaia Sausage is an elongated structure in velocity space discovered by Belokurov et al. (2018) using the kinematics of metal-rich halo stars. It was created by a massive dwarf galaxy ($\sim 5 \times 10^{10} M_\odot$) on a strongly radial orbit that merged with the Milky Way at a redshift $z\lesssim 3$. We search forthe associated Sausage Globular Clusters by analysing the structure of 91 Milky Way globular clusters (GCs) in action space using the Gaia Data Release 2 catalogue, complemented with Hubble Space Telescope proper motions. There is a characteristic energy $E_{\rm crit}$ which sep…
We examine the significance of a planar arrangement in the spatial distribution of the Milky Way's globular clusters (GCs). We find that, when separated on the basis of horizontal branch morphology and metallicity, the outer-most canonical young halo GC sample (at galactocentric radii in excess of 10 kpc) exhibit an anisotropic distribution that may be equated to a plane (24 +/- 4) kpc thick (rms) and inclined at 8 degrees +/- 5 degrees to the polar axis of the Milky Way disk. To quantify the significance of this plane we determine the fraction of times that an isotropic distribution replicate…
We use Monte Carlo $Λ$CDM assembly histories, minor-merger N-body simulations and empirical relations between halo mass and the globular cluster (GC) abundance to study the kinematical properties of halo GCs in massive galaxies, with $M_{vir}(z=0)=10^{13.5}M_\odot$. While the accreted stellar halo is dominated by the contributions of massive satellites, we show that satellites with low virial mass (i.e. low satellite-to-host virial mass ratio, VMRs) are important contributors to the population of accreted GCs. The relative contribution of accretion events with low VMRs is highest for the halo …
Our understanding of the kinematic properties of multiple stellar populations (mPOPs) in Galactic globular clusters (GCs) is still limited compared to what we know about their chemical and photometric characteristics. Such limitation arises from the lack of a comprehensive observational investigation of this topic. Here we present the first homogeneous kinematic analysis of mPOPs in 56 GCs based on high-precision proper motions computed with Hubble Space Telescope data. We focused on red-giant-branch stars, for which the mPOP tagging is clearer, and measured the velocity dispersion of stars be…
We use N-body simulations to study the tidal evolution of globular clusters (GCs) in dwarf spheroidal (dSph) galaxies. Our models adopt a cosmologically motivated scenario in which the dSph is approximated by a static NFW halo with a triaxial shape. We apply our models to five GCs spanning three orders of magnitude in stellar density and two in mass, chosen to represent the properties exhibited by the five GCs of the Fornax dSph. We show that only the object representing Fornax's least dense GC (F1) can be fully disrupted by Fornax's internal tidal field--the four denser clusters survive even …
Numerous observational studies have revealed the ubiquitous presence of multiple stellar populations in globular clusters and cast many hard challenges for the study of the formation and dynamical history of these stellar systems. In this Letter we present the results of a study of the kinematic properties of multiple populations in NGC 2808 based on high-precision Hubble Space Telescope proper-motion measurements. In a recent study, Milone et al. have identified five distinct populations (A, B, C, D, and E) in NGC 2808. Populations D and E coincide with the helium-enhanced populations in the …
