arXiv subjects

Anna Lisa Varri

Publications and source records attributed to Anna Lisa Varri.

At least 19 recordsLinked to original sources

arXiv2026

ROLLIN': Rotating globular cluster simulations II. The complex morphology of globular clusters driven by multi-scale dynamics

Globular clusters (GCs) are inherently non-spherical systems that in many cases show internal rotation. Typically, rotation is considered the main driver of GC morphology; however, the relationship between ellipticity and rotational support is not a simple one-to-one mapping, and other multi-scale dynamical processes may contribute. We investigate how morphology evolves in realistic models of rotating GCs, and how it correlates with key physical ingredients, including mass loss, stellar evolution, external tidal fields, and two-body relaxation. Using the \texttt{ROLLIN'} suite of direct N-body simulations, we measure the intrinsic ellipticity and triaxiality of our models using the second-moment tensor method, and explore their evolution and the physical mechanisms driving them. We find that early GC evolution can be dominated by dynamical instabilities driven by internal rotation and velocity anisotropy, leading to bar-like structures that rapidly erode due to collisional effects around the time of the first core collapse. These bars are stronger and longer-lived ($\lesssim 800,\mathrm{Myr}$) in strongly rotating clusters with longer relaxation times and subject to stellar evolution. In the long term, clusters evolve toward less flattened and gradually triaxial configurations, particularly when they experience stronger mass loss, are more tidally filling and isotropic, and have lower rotational support. Our models provide a physical explanation for the observational $V/\sigma$--ellipticity relation and demonstrate that morphology can serve as a reliable tracer of the dynamical state of GCs. Initially retrograde, dense, and inclined rotating models deviate from this relation, providing a physical explanation for observational outliers. This framework will aid the interpretation of GC evolution in upcoming large-scale photometric surveys.

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arXiv2026

The stability of radially anisotropic rotating stellar systems with a central density cusp

We investigate the interplay between radial velocity anisotropy and internal rotation in self-gravitating systems characterised by initial spherical symmetry and a moderate density cusp. We study the stability properties of such configurations to disentangle the impact of anisotropy, rotation, and density structure on the formation of triaxial stellar systems. We perform a set of collisionless $N$-body simulations starting from initial equilibria with a phase space distribution function of the class introduced by Osipkov and Merritt, modified to impose a net global angular momentum with the Lynden-Bell daemon protocol. We analyse the growth of the density and phase space distribution modes, as well as the axial ratios and triaxiality index of the final configurations. We find that internal rotation has a mitigating effect on the strength of the radial orbit instability in radially anisotropic models with Fridman-Polyachenko-Shukhman index close to its value for consistency, while it slightly enhances the onset of the instability in nearly stable models. From the analysis of the growth rate of the density modes, we also find that an inner bar, though unstable for maximally rotating initial conditions, is formed even in systems with initial profiles with a central density cusp.

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arXiv2025

Tidally Perturbed, Rotating Stellar Systems: Asynchronous Equilibria

We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised description of globular clusters that rotate asynchronously with respect to their orbital motion around a host galaxy. Model construction proceeds by extension of the truncated King models, using a newly defined asynchronicity parameter to couple the tidal and rotational perturbations. The method of matched asymptotic expansion is used to derive a global solution to the free boundary problem posed by the corresponding set of Poisson-Laplace equations. We explore the relevant parameter space and outline the intrinsic properties of the resulting models, both structural and kinematic. Their triaxial configuration, characterised by extension in the direction of the galactic centre and flattening toward the orbital plane, is found to depart further from spherical symmetry for larger values of the asynchronicity parameter. We hope that these simplified analytical models serve as useful tools for investigating the interplay of tidal and rotational effects, providing an equilibrium description that complements, and may serve as a basis for, more realistic numerical simulations.

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arXiv2025

Evolution of the kinematic properties of rotating multiple-population globular clusters

Globular clusters (GCs) host multiple stellar populations differing in their chemical and dynamical properties. A number of models for the formation of multiple populations predict that the subsystem of second generation (SG) stars is characterized by a more centrally concentrated spatial distribution and a more rapid rotation than the system of first generation (FG) stars. We present the results of N-body simulations exploring the long-term dynamical evolution of rotating multiple-population GCs. We study the evolution of systems starting with four different orientations of the GC's total internal angular momentum vector relative to the orbital angular momentum. We explore the evolution driven by two-body relaxation and the effects of the GC's interaction with the galactic tidal field. We focus on the kinematic differences between the two generations and we quantify them by exploring the FG and SG rotation velocity and angular momenta. We find that kinematic differences between the generations persist for most of the GCs' lifetimes, although the strength of these differences decreases after a few relaxation times. The differences can be seen most clearly in the lowest-mass stars. We find that the GCs' internal angular momentum gradually aligns with the orbital angular momentum, although there is little difference in this alignment between the FG and SG systems. We also find that stars in the GC's outer regions align with the orbital angular momentum vector more rapidly than those in the inner regions leading to a variation of the orientation of the internal angular momentum with the clustercentric distance. The alignment between internal angular momentum and orbital angular momentum occurs more rapidly for low-mass stars. We study the evolution of the anisotropy in the velocity distribution and find the SG to be characterized by a stronger radial anisotropy than the FG.(abridged)

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arXiv2024

Dynamics of star clusters with tangentially anisotropic velocity distribution

Recent high-precision observations with HST and Gaia enabled new investigations of the internal kinematics of star clusters (SCs) and the dependence of kinematic properties on the stellar mass. These studies raised new questions about the dynamical evolution of self-gravitating stellar systems. We aim to develop a more complete theoretical understanding of how various kinematical properties of stars affect the global dynamical development of their host SCs. We perform N-body simulations of SCs with isotropic, radially anisotropic and tangentially anisotropic initial velocity distributions. We also study the effect of an external Galactic tidal field. We find three main results. First, compared to the conventional, isotropic case, the relaxation processes are accelerated in the tangentially anisotropic models and, in agreement with our previous investigations, slower in the radially anisotropic ones. This leads to, e.g., more rapid mass segregation in the central regions of the tangential models or their earlier core collapse. Second, although all SCs become isotropic in the inner regions after several relaxation times, we observe differences in the anisotropy profile evolution in the outer cluster regions - all tidally filling models gain tangential anisotropy there while the underfilling models become radially anisotropic. Third, we observe different rates of evolution towards energy equipartition (EEP). While all SCs evolve towards EEP in their inner regions (regardless of the filling factor), the outer regions of the tangentially anisotropic and isotropic models are evolving to an "inverted" EEP (i.e., the high-mass stars having higher velocity dispersion than the low-mass ones). The extent (both spatial and temporal) of this inversion can be attributed to the initial velocity anisotropy - it grows with increasing tangential anisotropy and decreases as the radial anisotropy rises.

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arXiv2022

Linking the Internal Properties of Infant Globular Clusters to their Formation Environments

We investigate the formation of infant globular cluster (GC) candidates in high-resolution cosmological simulations from the First Billion Years (FiBY) project. By analysing the evolution of the systems in the energy and angular momentum plane, we identify the redshift at which the infant GCs first became gravitationally bound, and we find evidence of radial infall of their gaseous and stellar components. The collapse appears to be driven by internal self-gravity, however, the initial trigger is sourced from the external environment. The phase space behaviour of the infant GCs also allows us to identify some characteristic groupings of objects. Such a classification based on internal properties appears to be reflected in the formation environment: GC candidates that belong to the same class are found in host galaxies of similar morphology, with the majority of the infant GCs located in clumpy, irregular proto-galaxies. Finally, through the inspection of two GC candidates that contain only stars by z = 6, we find that supernova feedback is the main physical mechanism behind their dearth of gas and that the systems subsequently respond with an approximately adiabatic expansion. Such infant GC candidates already resemble the GCs we currently observe in the local Universe.

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arXiv2022

Long-term evolution of multimass rotating star clusters

We investigate the long-term dynamical evolution of the internal kinematics of multimass rotating star clusters. We have performed a set of N-body simulations to follow the internal evolution of clusters with different degrees of initial rotation and have explored the evolution of the rotational velocity, the degree of energy equipartition, and anisotropy in the velocity distribution. Our simulations show that: 1) as the cluster evolves, the rotational velocity develops a dependence on the stellar mass with more massive stars characterised by a more rapid rotation and a peak in the rotation curve closer to the cluster centre than low-mass stars; 2) the degree of energy equipartition in the cluster's intermediate and outer regions depends on the component of the velocity dispersion measured; for more rapidly rotating clusters, the evolution towards energy equipartition is more rapid in the direction of the rotational velocity; 3) the anisotropy in the velocity distribution is stronger for massive stars; 4) both the degree of mass segregation and energy equipartition are characterised by spatial anisotropy; they have a dependence on both $R$ and $z$, correlated with the flattening in the spatial variation of the cluster's density and velocity dispersion, as shown by 2D maps of the mass segregation and energy equipartition on the ($R$-$z$) meridional plane.

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arXiv2022

Early dynamical evolution of rotating star clusters in a tidal field

In order to explore how the early internal rotational properties of star clusters are affected by the external potential of their host galaxies, we have run a suite of $N$-body simulations following the early dynamical evolution and violent relaxation of rotating star clusters embedded in a tidal field. Our study focuses on models for which the cluster's rotation axis has a generic orientation relative to the torque of the tidal field. The interaction between the violent relaxation process, angular momentum of the cluster, and the external torque creates a complex kinematic structure within the cluster, most prominently a radial variation in the position of the rotation axis along both the polar and azimuthal directions. We also examine the cluster's velocity dispersion anisotropy and show that the projected anisotropy may be affected by the variation of the rotation axis directions within the cluster; the combination of projection effects and the complex kinematical features may result in the measurement of tangential anisotropy in the cluster's inner regions. We also characterize the structural properties of our clusters as a function of their initial rotation and virial ratio and find that clusters may develop a triaxial morphology and a radial variation of the minor axis not necessarily aligned with the rotation axis. Finally, we examine the long-term evolution of these complex kinematic features.

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arXiv2022

Forward and Back: Kinematics of the Palomar 5 Tidal Tails

The tidal tails of Palomar 5 (Pal 5) have been the focus of many spectroscopic studies in an attempt to identify individual stars lying along the stream and characterise their kinematics. The well-studied trailing tail has been explored out to a distance of 15^\text{o} from the cluster centre, while less than four degrees have been examined along the leading tail. In this paper, we present results of a spectroscopic study of two fields along the leading tail that we have observed with the AAOmega spectrograph on the Anglo-Australian telescope. One of these fields lies roughly 7^\text{o} along the leading tail, beyond what has been previously been explored spectroscopically. Combining our measurements of kinematics and line strengths with Pan-STARRS1 photometric data and Gaia EDR3 astrometry, we adopt a probabilistic approach to identify 16 stars with high probability of belonging to the Pal 5 stream. Eight of these stars lie in the outermost field and their sky positions confirm the presence of ``fanning'' in the leading arm. We also revisit previously-published radial velocity studies and incorporate Gaia EDR3 astrometry to remove interloping field stars. With a final sample of 109 {\it bona fide} Pal 5 cluster and tidal stream stars, we characterise the 3D kinematics along the the full extent of the system. We provide this catalogue for future modeling work.

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arXiv2021

Central Dynamics of Multi-mass Rotating Star Clusters

We investigate the evolutionary nexus between the morphology and internal kinematics of the central regions of collisional, rotating, multi-mass stellar systems, with special attention to the spatial characterisation of the process of mass segregation. We report results from idealized, purely $N$-body simulations that show multi-mass, rotating, and spherical systems rapidly form an oblate, spheroidal massive core, unlike single-mass rotating or multi-mass non-rotating configurations with otherwise identical initial properties, indicating that this evolution is a result of the interplay between the presence of a mass spectrum and angular momentum. This feature appears to be long-lasting, preserving itself for several relaxation times. The degree of flattening experienced by the systems is directly proportional to the initial degree of internal rotation. In addition, this morphological effect has a clear characterisation in terms of orbital architecture, as it lowers the inclination of the orbits of massive stars. We offer an idealised dynamical interpretation that could explain the mechanism underpinning this effect and we highlight possible useful implications, from kinematic hysteresis to spatial distribution of dark remnants in dense stellar systems.

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arXiv2021

$l=1$: Weinberg's weakly damped mode in an $N$-body model of a spherical stellar system

Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever application of the matrix method of linear stability, that they may be nearly unstable, in the sense of possessing {\sl weakly} damped modes of oscillation. He also demonstrated the presence of such a mode in an $N$-body model by endowing it with initial conditions generated from his perturbative solution. In the present paper we provide evidence for the presence of this same mode in $N$-body simulations of the King $W_0 = 5$ model, in which the initial conditions are generated by the usual Monte Carlo sampling of the King distribution function. It is shown that the oscillation of the density centre correlates with variations in the structure of the system out to a radius of about 1 virial radius, but anticorrelates with variations beyond that radius. Though the oscillations appear to be continually reexcited (presumably by the motions of the particles) we show by calculation of power spectra that Weinberg's estimate of the period (strictly, $2π$ divided by the real part of the eigenfrequency) lies within the range where the power is largest. In addition, however, the power spectrum displays another very prominent feature at shorter periods, around 5 crossing times.

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arXiv2021

The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation

We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, a la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) which have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system which have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesised with an existing theoretical framework, and used to consider the old question of constructing a stability criterion.

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arXiv2020

The First Billion Years Project: Finding Infant Globular Clusters at z=6

We explored a suite of high-resolution cosmological simulations from the First Billion Years Project (FiBY) at $z \geq 6$. All substructures within the simulations have been identified with the SUBFIND algorithm. From our analysis, two distinct groups of objects emerge. We hypothesise that the substructures in the first group, which appear to have a high baryon fraction ($f_{\rm b} \geq 0.95$), are possible infant GC candidates. Objects belonging to the second group have a high stellar fraction ($f_{\rm star} \geq 0.95$) and show a potential resemblance to infant ultra-faint dwarf galaxies. The high baryon fraction objects identified in this study are characterised by a stellar content similar to the one observed in present-day GCs, but they still contain a high gas fraction ($f_{\rm gas} \sim 0.95$) and a relatively low amount of dark matter. They are compact, dense systems. Their sizes are consistent with recent estimates based on the first observations of possible proto-GCs at high redshifts. These types of infant GC candidates appear to be more massive and more abundant in massive host galaxies, indicating that the assembly of galaxies via mergers may play an important role in building several GC-host scaling relations. Specifically, we express the relation between the mass of the most massive infant GC and its host stellar mass as $\log(M_{\rm cl}) = (0.31\pm0.15)\log(M_{\rm *,gal} + (4.17\pm1.06)$. We also report a new relation between the most massive infant GC and the parent specific star formation rate of the form $\log(M_{\rm cl}) = (0.85\pm0.30)\log(sSFR) + α$ that describes the data at both low and high redshift. Finally, we assess the present-day GC mass (GC number) -- halo mass relation offers a satisfactory description of the behaviour of our infant GC candidates at high redshift, suggesting that such a relation may be set at formation.

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arXiv2019

Kinematical evolution of multiple stellar populations in star clusters

We present the results of a suite of \Nbody simulations aimed at understanding the fundamental aspects of the long-term evolution of the internal kinematics of multiple stellar populations in globular clusters. Our models enable us to study the cooperative effects of internal, relaxation-driven processes and external, tidally-induced perturbations on the structural and kinematic properties of multiple-population globular clusters. To analyse the dynamical behaviour of the multiple stellar populations in a variety of spin-orbit coupling conditions, we have considered three reference cases in which the tidally perturbed star cluster rotates along an axis oriented in different directions with respect to the orbital angular momentum vector. We focus specifically on the characterisation of the evolution of the degree of differential rotation and anisotropy in the velocity space, and we quantify the process of spatial and kinematic mixing of the two populations. In light of recent and forthcoming explorations of the internal kinematics of this class of stellar systems by means of line-of sight and astrometric measurements, we also investigate the implications of projection effects and spatial distribution of the stars adopted as tracers. The kinematic and structural richness emerging from our models further emphasises the need and the importance of observational studies aimed at building a complete kinematical picture of the multiple population phenomenon.

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arXiv2019

Spherical models of star clusters with potential escapers

An increasing number of observations of the outer regions of globular clusters (GCs) have shown a flattening of the velocity dispersion profile and an extended surface density profile. Formation scenarios of GCs can lead to different explanations of these peculiarities, therefore the dynamics of stars in the outskirts of GCs are an important tool in tracing back the evolutionary history and formation of star clusters. One possible explanation for these features is that GCs are embedded in dark matter halos. Alternatively, these features are the result of a population of energetically unbound stars that can be spatially trapped within the cluster, known as potential escapers (PEs). We present a prescription for the contribution of these energetically unbound members to a family of self-consistent, distribution function-based models, which, for brevity, we call the Spherical Potential Escapers Stitched (SPES) models. We show that, when fitting to mock data of bound and unbound stars from an N-body model of a tidally-limited star cluster, the SPES models correctly reproduce the density and velocity dispersion profiles up to the Jacobi radius, and they are able to recover the value of the Jacobi radius itself to within 20%. We also provide a comparison to the number density and velocity dispersion profiles of the Galactic cluster 47 Tucanae. Such a case offers a proof of concept that an appropriate modelling of PEs is essential to accurately interpret Gaia data in the outskirts of GCs, and, in turn, to formulate meaningful present-day constraints for GC formation scenarios in the early universe.

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arXiv2019

Mapping the stability of stellar rotating spheres via linear response theory

Rotation is ubiquitous in the Universe, and recent kinematic surveys have shown that early type galaxies and globular clusters are no exception. Yet the linear response of spheroidal rotating stellar systems has seldom been studied. This paper takes a step in this direction by considering the behaviour of spherically symmetric systems with differential rotation. Specifically, the stability of several sequences of Plummer spheres is investigated, in which the total angular momentum, as well as the degree and flavour of anisotropy in the velocity space are varied. To that end, the response matrix method is customised to spherical rotating equilibria. The shapes, pattern speeds and growth rates of the systems' unstable modes are computed. Detailed comparisons to appropriate N-body measurements are also presented. The marginal stability boundary is charted in the parameter space of velocity anisotropy and rotation rate. When rotation is introduced, two sequences of growing modes are identified corresponding to radially and tangentially-biased anisotropic spheres respectively. For radially anisotropic spheres, growing modes occur on two intersecting surfaces (in the parameter space of anisotropy and rotation), which correspond to fast and slow modes, depending on the net rotation rate. Generalised, approximate stability criteria are finally presented.

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arXiv2018

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.

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arXiv2018

The complex kinematics of rotating star clusters in a tidal field

We broaden the investigation of the dynamical properties of tidally perturbed, rotating star clusters by relaxing the traditional assumptions of coplanarity, alignment, and synchronicity between the internal and orbital angular velocity vector of their initial conditions. We show that the interplay between the internal evolution of these systems and their interaction with the external tidal field naturally leads to the development of a number of evolutionary features in their three-dimensional velocity space, including a precession and nutation of the global rotation axis and a variation of its orientation with the distance from the cluster centre. In some cases, such a radial variation may manifest itself as a counter-rotation of the outermost regions relative to the inner ones. The projected morphology of these systems is characterized by a non-monotonic ellipticity profile and, depending on the initial inclination of the rotation axis, it may also show a twisting of the projected isodensity contours. These results provide guidance in the identification of non-trivial features which may emerge in upcoming investigations of star cluster kinematics and a dynamical framework to understand some of the complexities already hinted by recent observational studies.

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