arXiv subjects

A. L. Varri

Publications and source records attributed to A. L. Varri.

16 recordsLinked to original sources

arXiv2026

Disruption of a Giant: Spectroscopic Identification of Members in the Periphery and Tidal Tails of $\omega$ Centauri

$\omega$ Centauri ($\omega$ Cen, NGC\,5139) is one of the most enigmatic globular clusters in the Milky Way, with the recent detection of tidal tails adding further to its complexity. We report the results of a spectroscopic study of stars in the outer regions of $\omega$ Cen, which provides an improved characterisation of the cluster periphery and confirms the existence of tidal tails. Our targets, which lie in six VLT/FLAMES fields sampling six degrees across the sky, are selected using a Bayesian inference technique. We confirm 157 members of $\omega$ Cen based on line-of-sight velocity and [Fe/H] measurements, indicating an overall success rate of 93 per cent. We trace stars along the tidal tails to a cluster-centric radius of 3.2~deg, identifying five members in the debris and additional lower-probability candidates. The analysis of the kinematics and metallicities of the new members provides evidence of continuity in these properties from the bound component of the progenitor cluster into its tidal debris. We find that the metallicities of stars in the peripheral regions and tidal tails of $\omega$ Cen are broadly consistent with those in the \textit{Fimbulthul} stream to which the cluster has been previously linked. Our study provides a glimpse of the promise of new and forthcoming wide-field multi-object spectrographs for advancing understanding of tidal structures around Milky Way globular clusters.

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arXiv2026

ROLLIN': Rotating globular cluster simulations. I. The kinematic evolution of realistic direct N-body models

Internal rotation has emerged as a fundamental feature of globular clusters (GCs), yet its origin and long-term evolution remain poorly understood. We explore the evolution of rotating GCs over a Hubble time under the combined influence of two-body relaxation, tidal field, and stellar evolution. We introduce the ROLLIN' simulations, a suite of 25 N-body models characterized by a realistic number of stars from 250k to 1.5M, ran with the direct N-body code NBODY6++GPU and evolved for 14 Gyr. With present-day masses of 5 x 10^4 - 5x10^5 M_sun, the models cover the parameter space of low-density MW GCs. Our analysis reveals that rapidly rotating GCs experience earlier and more pronounced core collapse, efficiently segregating massive objects and remnants in their centers within the first few 100 Myr. In the long-term, internal rotation declines and a correlation emerges between rotation and GC mass, in agreement with observations. The primary driver of this evolution is mass loss, capturing both internal (stellar evolution, evaporation) and external processes (tidal stripping). The velocity anisotropy also evolves in response to mass loss: GCs initially near isotropy develop radial anisotropy, peaking around 40% mass loss, before progressing toward isotropy or tangentiality. The GC orbital history also plays a role, as retrograde rotators retain rotation more effectively than prograde rotators. Finally, we quantify the long-term changes of GCs after 12 Gyr: (1) The surface density decreases by up to 2 orders of magnitude. (2) The half-mass radius increases by a factor of 3-5. (3) The rotation decreases by a factor >5 for GCs that have lost >50% of their mass. The ROLLIN' simulations demonstrate that angular momentum is crucial to understand the origin, evolution, and survival of GCs. These models provide a benchmark for interpreting GC observations in the local and high-z Universe.

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arXiv2023

Ongoing hierarchical massive cluster assembly: the LISCA II structure in the Perseus complex

We report on the identification of a massive ($\sim10^5$ M$_\odot$) sub-structured stellar system in the Galactic Perseus complex likely undergoing hierarchical cluster assembly. Such a system comprises nine star clusters (including the well-known clusters NGC 654 and NGC 663) and an extended and low-density stellar halo. Gaia-DR3 and available spectroscopic data show that all its components are physically consistent in the 6D phase-space (position, parallax, and 3D motion), homogeneous in age (14 $-$ 44 Myr), and chemical content (half-solar metallicity). In addition, the system's global stellar density distribution is that of typical star clusters and shows clear evidence of mass segregation. We find that the hierarchical structure is mostly contracting towards the center with a speed of up to $\simeq4-5$ km s$^{-1}$, while the innermost regions expand at a lower rate (about $\simeq1$ km s$^{-1}$) and are dominated by random motions. Interestingly, this pattern is dominated by the kinematics of massive stars, while low-mass stars ($M<2$ M$_\odot$) are characterized by contraction across the entire cluster. Finally, the nine star clusters in the system are all characterized by a relatively flat velocity dispersion profile possibly resulting from ongoing interactions and tidal heating. We show that the observational results are generally consistent with those found in $N$-body simulations following the cluster violent relaxation phase strongly suggesting that the system is a massive cluster in the early assembly stages. This is the second structure with these properties identified in our Galaxy and, following the nomenclature of our previous work, we named it LISCA II.

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arXiv2022

The ESO-VLT MIKiS survey reloaded: velocity dispersion profile and rotation curve of NGC 1904

We present an investigation of the internal kinematic properties of M79 (NGC 1904). Our study is based on radial velocity measurements obtained from the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters for more than 1700 individual stars distributed between $\sim 0.3^{\prime\prime}$ and $770^{\prime\prime}$ ($\sim14$ three-dimensional half-mass radii), from the center. Our analysis reveals the presence of ordered line-of-sight rotation with a rotation axis almost aligned along the East-West direction and a velocity peak of $1.5$ km s$^{-1}$ at $\sim 70^{\prime\prime}$ from the rotation axis. The velocity dispersion profile is well described by the same King model that best fits the projected density distribution, with a constant central plateau at $σ_0\sim 6$ km s$^{-1}$. To investigate the cluster rotation in the plane of the sky, we have analyzed the proper motions provided by the Gaia EDR3, finding a signature of rotation with a maximum amplitude of $\sim 2.0$ km s$^{-1}$ at $\sim 80^{\prime\prime}$ from the cluster center. Analyzing the three-dimensional velocity distribution, for a sub-sample of 130 stars, we confirm the presence of systemic rotation and find a rotation axis inclination angle of $37$° with respect to the line-of-sight. As a final result, the comparison of the observed rotation curves with the results of a representative N-body simulation of a rotating star cluster shows that the present-day kinematic properties of NGC 1904 are consistent with those of a dynamically old system that has lost a significant fraction of its initial angular momentum.

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arXiv2021

Early dynamics and violent relaxation of multi-mass rotating star clusters

We present the results of a study aimed at exploring, by means of N-body simulations, the evolution of rotating multi-mass star clusters during the violent relaxation phase, in the presence of a weak external tidal field. We study the implications of the initial rotation and the presence of a mass spectrum for the violent relaxation dynamics and the final properties of the equilibria emerging at the end of this stage. Our simulations show a clear manifestation of the evolution towards spatial mass segregation and evolution towards energy equipartition during and at the end of the violent relaxation phase. We study the final rotational kinematics and show that massive stars tend to rotate more rapidly than low-mass stars around the axis of cluster rotation. Our analysis also reveals that during the violent relaxation phase, massive stars tend to preferentially segregate into orbits with angular momentum aligned with the cluster's angular momentum, an effect previously found in the context of the long-term evolution of star clusters driven by two-body relaxation.

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arXiv2021

First phase space portrait of a hierarchical stellar structure in the Milky Way

We present the first detailed observational picture of a possible ongoing massive cluster hierarchical assembly in the Galactic disk as revealed by the analysis of the stellar full phase-space (3D positions and kinematics and spectro-photometric properties) of an extended area ($6^{\circ}$ diameter) surrounding the well-known $\it h$ and $χ$ Persei double stellar cluster in the Perseus Arm. Gaia-EDR3 shows that the area is populated by seven co-moving clusters, three of which were previously unknown, and by an extended and quite massive ($M\sim10^5 M_{\odot}$) halo. All stars and clusters define a complex structure with evidence of possible mutual interactions in the form of intra-cluster over-densities and/or bridges. They share the same chemical abundances (half-solar metallicity) and age ($t\sim20$ Myr) within a small confidence interval and the stellar density distribution of the surrounding diffuse stellar halo resembles that of a cluster-like stellar system. The combination of these evidences suggests that stars distributed within a few degrees from $\it h$ and $χ$ Persei are part of a common, sub-structured stellar complex that we named LISCA I. Comparison with results obtained through direct $N$-body simulations suggest that LISCA I may be at an intermediate stage of an ongoing cluster assembly that can eventually evolve in a relatively massive (a few $10^5 M_{\odot}$) stellar system. We argue that such cluster formation mechanism may be quite efficient in the Milky Way and disk-like galaxies and, as a consequence, it has a relevant impact on our understanding of cluster formation efficiency as a function of the environment and redshift.

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arXiv2017

Three candidate double clusters in the LMC: truth or dare?

The Large Magellanic Cloud (LMC) hosts a large number of candidate stellar cluster pairs. Binary stellar clusters provide important clues about cluster formation processes and the evolutionary history of the host galaxy. However, to properly extract and interpret this information, it is crucial to fully constrain the fraction of real binary systems and their physical properties. Here we present a detailed photometric analysis based on ESO-FORS2 images of three candidate cluster multiplets in the LMC, namely SL349-SL353, SL385-SL387-NGC1922 and NGC1836-BRHT4b-NGC1839. For each cluster we derived ages, structural parameters and morphological properties. We have also estimated the degree of filling of their Roche lobe, as an approximate tool to measure the strength of the tidal perturbations induced by the LMC. We find that the members of the possible pairs SL349-SL353 and BRHT4b-NGC1839 have a similar age ($t = 1.00 \pm 0.12$ Gyr and $t = 140 \pm 15$ Myr, respectively), thus possibly hinting to a common origin of their member systems We also find that all candidate pairs in our sample show evidence of intra-cluster overdensities that can be a possible indication of real binarity. Particularly interesting is the case of SL349-SL353. In fact, SL353 is relatively close to the condition of critical filling, thus suggesting that these systems might actually constitute an energetically bound pair. It is therefore key to pursue a detailed kinematic screening of such clusters, without which, at present, we do not dare making a conclusive statement about the true nature of this putative pair.

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arXiv2017

Hubble Space Telescope Proper Motion (HSTPROMO) Catalogs of Galactic Globular Clusters. V. The rapid rotation of 47 Tuc traced and modeled in three dimensions

High-precision proper motions of the globular cluster 47 Tuc have allowed us to measure for the first time the cluster rotation in the plane of the sky and the velocity anisotropy profile from the cluster core out to about 13'. These profiles are coupled with prior measurements along the line of sight and the surface-brightness profile, and fit all together with self-consistent models specifically constructed to describe quasi-relaxed stellar systems with realistic differential rotation, axisymmetry and pressure anisotropy. The best-fit model provides an inclination angle i between the rotation axis and the line-of-sight direction of 30 deg, and is able to simultaneously reproduce the full three-dimensional kinematics and structure of the cluster, while preserving a good agreement with the projected morphology. Literature models based solely on line-of-sight measurements imply a significantly different inclination angle (i=45 deg), demonstrating that proper motions play a key role in constraining the intrinsic structure of 47 Tuc. Our best-fit global dynamical model implies an internal rotation higher than previous studies have shown, and suggests a peak of the intrinsic V/sigma ratio of ~0.9 at around two half-light radii, with a non-monotonic intrinsic ellipticity profile reaching values up to 0.45. Our study unveils a new degree of dynamical complexity in 47 Tuc, which may be leveraged to provide new insights into the formation and evolution of globular clusters.

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arXiv2016

Differences in the rotational properties of multiple stellar populations in M 13: a faster rotation for the "extreme" chemical subpopulation

We use radial velocities from spectra of giants obtained with the WIYN telescope, coupled with existing chemical abundance measurements of Na and O for the same stars, to probe the presence of kinematic differences among the multiple populations of the globular cluster (GC) M13. To characterise the kinematics of various chemical subsamples, we introduce a method using Bayesian inference along with an MCMC algorithm to fit a six-parameter kinematic model (including rotation) to these subsamples. We find that the so-called "extreme" population (Na-enhanced and extremely O-depleted) exhibits faster rotation around the centre of the cluster than the other cluster stars, in particular when compared to the dominant "intermediate" population (moderately Na-enhanced and O-depleted). The most likely difference between the rotational amplitude of this extreme population and that of the intermediate population is found to be $\sim$4 km s$^{-1}$, with a 98.4% probability that the rotational amplitude of the extreme population is larger than that of the intermediate population. We argue that the observed difference in rotational amplitudes, obtained when splitting subsamples according to their chemistry, is not a product of the long-term dynamical evolution of the cluster, but more likely a surviving feature imprinted early in the formation history of this GC and its multiple populations. We also find an agreement (within uncertainties) in the inferred position angle of the rotation axis of the different subpopulations considered. We discuss the constraints that these results may place on various formation scenarios.

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arXiv2016

A novel look at energy equipartition in globular clusters

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 of the systems. This simple parametrization successfully captures the behaviour of the velocity dispersion at lower as well as higher stellar masses, that is, the regime where the system is expected to approach full equipartition. We find a tight correlation between the degree of equipartition reached by a GC and its dynamical state, indicating that clusters that are more than about 20 core relaxation times old, have reached a maximum degree of equipartition. This equipartition$-$dynamical state relation can be used as a tool to characterize the relaxation condition of a cluster with a kinematic measure of the $m_\mathrm{eq}$ parameter. Vice versa, the mass-dependence of the kinematics can be predicted knowing the relaxation time solely on the basis of photometric measurements. Moreover, any deviations from this tight relation could be used as a probe of a peculiar dynamical history of a cluster. Finally, our novel approach is important for the interpretation of state-of-the-art Hubble Space Telescope proper motion data, for which the mass dependence of kinematics can now be measured, and for the application of modeling techniques which take into consideration multi-mass components and mass segregation.

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arXiv2015

Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era

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/over-estimated up to 50% 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 center 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.

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arXiv2013

On the density profile of the globular cluster M92

We present new number density and surface brightness profiles for the globular cluster M92 (NGC 6341). These profiles are calculated from optical images collected with the CCD mosaic camera MegaCam at the Canada-France-Hawaii-Telescope and with the Advanced Camera for Surveys on the Hubble Space Telescope. The ground-based data were supplemented with the Sloan Digital Sky Survey photometric catalog. Special care was taken to discriminate candidate cluster stars from field stars and to subtract the background contamination from both profiles. By examining the contour levels of the number density, we found that the stellar distribution becomes clumpy at radial distances larger than about 13 arcminutes, and there is no preferred orientation of contours in space. We performed detailed fits of King and Wilson models to the observed profiles. The best-fit models underestimate the number density inside the core radius. Wilson models better represent the observations, in particular in the outermost cluster regions: the good global agreement of these models with the observations suggests that there is no need to introduce an extra-tidal halo to explain the radial distribution of stars at large radial distances. The best-fit models for the number density and the surface brightness profiles are different, even though they are based on the same observations. Additional tests support the evidence that this fact reflects the difference in the radial distribution of the stellar tracers that determine the observed profiles (main sequence stars for the number density, bright evolved stars for the surface brightness).

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arXiv2012

Self-consistent models of quasi-relaxed rotating stellar systems

Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The second is characterized by differential rotation, designed to be rigid in the central regions and to vanish in the outer parts, where the energy truncation becomes effective. The models are constructed by solving the nonlinear Poisson equation for the self-consistent mean-field potential. For rigidly rotating configurations, the solutions are obtained by an asymptotic expansion on the rotation strength parameter. The differentially rotating models are constructed by means of an iterative approach based on a Legendre series expansion of the density and the potential. The two classes of models exhibit complementary properties. The rigidly rotating configurations are flattened toward the equatorial plane, with deviations from spherical symmetry that increase with the distance from the center. For models of the second family, the deviations from spherical symmetry are strongest in the central region, whereas the outer parts tend to be quasi-spherical. The relevant parameter spaces are explored and the intrinsic and projected structural properties are described. Special attention is given to the effect of different options for the truncation of the distribution function in phase space. Models in the moderate rotation regime are best suited to applications to globular clusters. For general interest in stellar dynamics, at high values of the rotation strength the differentially rotating models exhibit a toroidal core embedded in a quasi-spherical configuration. Physically simple analytical models of the kind presented here provide insights into dynamical mechanisms and may be a basis for more realistic investigations with the help of N-body simulations.

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arXiv2012

A dynamical study of Galactic globular clusters under different relaxation conditions

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 relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^(ν) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field.

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arXiv2009

Properties of quasi-relaxed stellar systems in an external tidal field

In a previous paper, we have constructed a family of self-consistent triaxial models of quasi-relaxed stellar systems, shaped by the tidal field of the hosting galaxy, as an extension of the well-known spherical King models. For a given tidal field, the models are characterized by two physical scales (such as total mass and central velocity dispersion) and two dimensionless parameters (the concentration parameter and the tidal strength). The most significant departure from spherical symmetry occurs when the truncation radius of the corresponding spherical King model is of the order of the tidal radius, which, for a given tidal strength, is set by the maximum concentration value admitted. For such maximally extended (or "critical") models the outer boundary has a generally triaxial shape, given by the zero-velocity surface of the relevant Jacobi integral, which is basically independent of the concentration parameter. In turn, the external tidal field can give rise to significant global departures from spherical symmetry (as measured, for example, by the quadrupole of the mass distribution of the stellar system) only for low-concentration models, for which the allowed maximal value of the tidal strength can be relatively high. In this paper we describe in detail the intrinsic and the projected structure and kinematics of the models, covering the entire parameter space, from the case of sub-critical (characterized by "underfilling" of the relevant Roche volume) to that of critical models. The intrinsic properties can be a useful starting point for numerical simulations and other investigations that require initialization of a stellar system in dynamical equilibrium. The projected properties are a key step in the direction of a comparison with observed globular clusters and other candidate stellar systems.

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arXiv2008

The construction of non-spherical models of quasi-relaxed stellar systems

Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a "frozen" external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to two orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified non-spherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the non-spherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy.

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