arXiv subjects

Anna Lisa Varri

Publications and source records attributed to Anna Lisa Varri.

31 records · Page 2Linked to original sources

arXiv2017

The Kinematic Richness of Star Clusters I. Isolated Spherical Models with Primordial Anisotropy

We investigate the dynamical evolution of isolated equal-mass star cluster models by means of direct N-body simulations, primarily focusing on the effects of the presence of primordial anisotropy in the velocity space. We found evidence of the existence of a monotonic relationship between the moment of core collapse and the amount and flavour of anisotropy in the stellar system. Specifically, equilibria characterised by the same initial structural properties (Plummer density profile) and with different degrees of tangentially-biased (radially-biased) anisotropy, reach core collapse earlier (later) than isotropic models. We interpret this result in light of an accelerated (delayed) phase of the early evolution of collisional stellar systems "anisotropic-response"), which we have characterised both in terms of the evolution of the velocity moments and of a fluid model of two-body relaxation. For the case of the most tangentially anisotropic model the initial phase of evolution involves a catastrophic collapse of the inner part of the system which continues until an isotropic velocity distribution is reached. This study represents a first step towards a comprehensive investigation of the role played by kinematic richness in the long-term dynamical evolution of collisional systems.

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arXiv2017

Stellar envelopes of globular clusters embedded in dark mini-haloes

We show that hard encounters in the central regions of globular clusters embedded in dark matter (DM) haloes necessarily lead to the formation of gravitationally-bound stellar envelopes that extend far beyond the nominal tidal radius of the system. Using statistical arguments and numerical techniques we derive the equilibrium distribution function of stars ejected from the centre of a non-divergent spherical potential. Independently of the velocity distribution with which stars are ejected, GC envelopes have density profiles that approach asymptotically $ρ\sim r^{-4}$ at large distances and become isothermal towards the centre. Adding a DM halo component leaves two clear-cut observational signatures: (i) a flattening, or slightly increase of the projected velocity dispersion profile at large distances, and (ii) an outer surface density profile that is systematically shallower than in models with no dark matter.

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arXiv2017

Kinematical evolution of tidally limited star clusters: rotational properties

We present the results of a set of N-body simulations following the long-term evolution of the rotational properties of star cluster models evolving in the external tidal field of their host galaxy, after an initial phase of violent relaxation. The effects of two-body relaxation and escape of stars lead to a redistribution of the ordered kinetic energy from the inner to the outer regions, ultimately determining a progressive general loss of angular momentum; these effects are reflected in the overall decline the rotation curve as the cluster evolves and loses stars. We show that all of our models share the same dependence of the remaining fraction of the initial rotation on the fraction of the initial mass lost. As the cluster evolves and loses part of its initial angular momentum, it becomes increasingly dominated by random motions, but even after several tens of relaxation times, and losing a significant fraction of its initial mass, a cluster can still be characterized by a non-negligible ratio of the rotational velocity to the velocity dispersion. This result is in qualitative agreement with the recently observed kinematical complexity which characterizes several Galactic globular clusters.

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arXiv2017

An Approximate Analytic Model of a Star Cluster with Potential Escapers

In the context of a star cluster moving on a circular galactic orbit, a "potential escaper" is a cluster star that has orbital energy greater than the escape energy, and yet is confined within the Jacobi radius of the stellar system. On the other hand analytic models of stellar clusters typically have a truncation energy equal to the cluster escape energy, and therefore explicitly exclude these energetically unbound stars. Starting from the landmark analysis performed by Henon of periodic orbits of the circular Hill equations, we present a numerical exploration of the population of "non-escapers", defined here as those stars which remain within two Jacobi radii for several galactic periods, with energy above the escape energy. We show that they can be characterised by the Jacobi integral and two further approximate integrals, which are based on perturbation theory and ideas drawn from Lidov-Kozai theory. Finally we use these results to construct an approximate analytic model that includes a phase space description of a population resembling that of potential escapers, in addition to the usual bound population.

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arXiv2016

Kinematical evolution of tidally limited star clusters: the role of retrograde stellar orbits

The presence of an external tidal field often induces significant dynamical evolutionary effects on the internal kinematics of star clusters. Previous studies investigating the restricted three-body problem with applications to star cluster dynamics have shown that unbound stars on retrograde orbits (with respect to the direction of the cluster's orbit) are more stable against escape than prograde orbits, and predicted that a star cluster might acquire retrograde rotation through preferential escape of stars on prograde orbits. In this study we present evidence of this prediction, but we also illustrate that there are additional effects that cannot be accounted for by the preferential escape of prograde orbits alone. Specifically, in the early evolution, initially underfilling models increase their fraction of retrograde stars without losing significant mass, and acquire a retrograde angular velocity. We attribute this effect to the development of preferentially eccentric/radial orbits in the outer regions of star clusters as they are expanding into their tidal limitation. We explore the implications of the evolution of the fraction of prograde and retrograde stars for the evolution of the cluster internal rotation, and its dependence on the initial structural properties. Although all the systems studied here evolve towards an approximately solid-body internal rotation with angular velocity equal to about half of the angular velocity of the cluster orbital motion around the host galaxy, the evolutionary history of the radial profile of the cluster internal angular velocity depends on the cluster initial structure.

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arXiv2016

Spatial and kinematic segregation in star cluster merger remnants

Globular clusters which exhibit chemical and dynamical complexity have been suggested to be the stripped nuclei of dwarf galaxies (e.g., M54, $ω$ Cen). We use $N$-body simulations of nuclear star clusters forming via the mergers of star clusters to explore the persistence of substructure in the phase space. We find that the observed level of differentiation is difficult to reconcile with the observed if nuclear clusters form wholly out of the mergers of star clusters. Only the star clusters that merged most recently retain sufficiently distinct kinematics to be distinguishable from the rest of the nuclear cluster though the critical factor is the number of merger events not the elapsed time. In situ star formation must therefore be included to explain the observed properties of nuclear star clusters, in good agreement with previous results.

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arXiv2016

Testing lowered isothermal models with direct N-body simulations of globular clusters

Several self-consistent models have been proposed, aiming at describing the phase space distribution of stars in globular clusters. This study explores the ability of the recently proposed LIMEPY models (Gieles & Zocchi) to reproduce the dynamical properties of direct N-body models of a cluster in a tidal field, during its entire evolution. These dynamical models include prescriptions for the truncation and the degree of radially-biased anisotropy contained in the system, allowing us to explore the interplay between the role of anisotropy and tides in various stages of the life of star clusters. We show that the amount of anisotropy in an initially tidally underfilling cluster increases in the pre-collapse phase, and then decreases with time, due to the effect of the external tidal field on its spatial truncation. This is reflected in the correspondent model parameters, and the best-fit models reproduce the main properties of the cluster at all stages of its evolution, except for the phases immediately preceding and following core collapse. We also notice that the best-fit LIMEPY models are significantly different from isotropic King models, especially in the first part of the evolution of the cluster. Our results put limits on the amount of radial anisotropy that can be expected for clusters evolving in a tidal field, which is important to understand other factors that could give rise to similar observational signatures, such as the presence of an intermediate-mass black hole.

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arXiv2015

Velocity anisotropy in tidally limited star clusters

We explore the long-term evolution of the anisotropy in the velocity space of star clusters starting with different structural and kinematical properties. We show that the evolution of the radial anisotropy strength and its radial variation within a cluster contain distinct imprints of the cluster initial structural properties, dynamical history, and of the external tidal field of its host galaxy. Initially isotropic and compact clusters with small initial values of the ratio of the half-mass to Jacobi radius, $r_h/r_J$, develop a strong radial anisotropy during their long-term dynamical evolution. Many clusters, if formed with small values of $r_h/r_J$, should now be characterized by a significant radial anisotropy increasing with the distance from the cluster centre, reaching its maximum at a distance between 0.2 $r_J$ and 0.4 $r_J$, and then becoming more isotropic or mildly tangentially anisotropic in the outermost regions. A similar radial variation of the anisotropy can also result from an early violent relaxation phase. In both cases, as a cluster continues its evolution and loses mass, the anisotropy eventually starts to decrease and the system evolves toward an isotropic velocity distribution. However, in order to completely erase the strong anisotropy developed by these compact systems during their evolution, they must be in the advanced stages of their evolution and lose a large fraction of their initial mass. Clusters that are initially isotropic and characterized by larger initial values of $r_h/r_J$, on the other hand, never develop a significant radial anisotropy.

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arXiv2015

Evolution of star clusters on eccentric orbits

We study the evolution of star clusters on circular and eccentric orbits using direct $N$-body simulations. We model clusters with initially $N=8{\rm k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same $N$ on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semi-major axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the Galactic mass profile. From both sets of simulations we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.

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arXiv2015

Neutron star natal kicks and the long-term survival of star clusters

We investigate the dynamical evolution of a star cluster in an external tidal field by using N-body simulations, with focus on the effects of the presence or absence of neutron star natal velocity kicks.We show that, even if neutron stars typically represent less than 2% of the total bound mass of a star cluster, their primordial kinematic properties may affect the lifetime of the system by up to almost a factor of four. We interpret this result in the light of two known modes of star cluster dissolution, dominated by either early stellar evolution mass loss or two-body relaxation. The competition between these effects shapes the mass loss profile of star clusters, which may either dissolve abruptly ("jumping"), in the pre-core-collapse phase, or gradually ("skiing"), after having reached core collapse.

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arXiv2014

The inefficiency of satellite accretion in forming extended star clusters

The distinction between globular clusters and dwarf galaxies has been progressively blurred by the recent discoveries of several extended star clusters, with size (20-30 pc) and luminosity (-6 < Mv < -2) comparable to the one of faint dwarf spheroidals. In order to explain their sparse structure, it has been suggested that they formed as star clusters in dwarf galaxy satellites that later accreted onto the Milky Way. If these clusters form in the centre of dwarf galaxies, they evolve in a tidally-compressive environment where the contribution of the tides to the virial balance can become significant, and lead to a super-virial state and subsequent expansion of the cluster, once removed. Using N-body simulations, we show that a cluster formed in such an extreme environment undergoes a sizable expansion, during the drastic variation of the external tidal field due to the accretion process. However, we show that the expansion due to the removal of the compressive tides is not enough to explain the observed extended structure, since the stellar systems resulting from this process are always more compact than the corresponding clusters that expand in isolation due to two-body relaxation. We conclude that an accreted origin of extended globular clusters is unlikely to explain their large spatial extent, and rather favor the hypothesis that such clusters are already extended at the stage of their formation.

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arXiv2014

Kinematical fingerprints of star cluster early dynamical evolution

We study the effects of the external tidal field on the violent relaxation phase of star clusters dynamical evolution, with particular attention to the kinematical properties of the equilibrium configurations emerging at the end of this phase.We show that star clusters undergoing the process of violent relaxation in the tidal field of their host galaxy can acquire significant internal differential rotation and are characterized by a distinctive radial variation of the velocity anisotropy. These kinematical properties are the result of the symmetry breaking introduced by the external tidal field in the collapse phase and of the action of the Coriolis force on the orbit of the stars. The resulting equilibrium configurations are characterized by differential rotation, with a peak located between one and two half-mass radii. As for the anisotropy, similar to clusters evolving in isolation, the systems explored in this Letter are characterized by an inner isotropic core, followed by a region of increasing radial anisotropy. However for systems evolving in an external tidal field the degree of radial anisotropy reaches a maximum in the cluster intermediate regions and then progressively decreases, with the cluster outermost regions being characterized by isotropy or a mild tangential anisotropy. Young or old but less-relaxed dynamically young star clusters may keep memory of these kinematical fingerprints of their early dynamical evolution.

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arXiv2013

The flattening of globular clusters: internal rotation or velocity anisotropy?

Internal rotation is considered to play a major role in determining the structure and dynamics of some globular clusters. We present a dynamical analysis of the photometry and three-dimensional kinematics of 47 Tuc and omega Cen, by means of a new family of self-consistent axisymmetric rotating models. The combined use of line-of-sight velocities and proper motions allows us to obtain a global description of the internal dynamical structure of the objects together with an estimate of their dynamical distances. The well-relaxed cluster 47 Tuc is very well interpreted by our dynamical models; in particular, internal rotation is found to explain the observed morphology. For the partially relaxed cluster omega Cen, the selected model provides a good representation of its complex three-dimensional kinematics, in general qualitative agreement with the observed anisotropy profile, which is characterized by tangential anisotropy in the outer parts; discrepancies are found between the observed and the expected ellipticity profile and are ascribed to the presence of a high degree of radial anisotropy in the intermediate region and to its interplay with rotation.

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