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.Comment: 5 pages, 4 figures, accepted for publication in MNRA

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.Comment: 5 pages, 4 figures, 1 table. Accepted for publication in MNRAS Letter

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.Comment: 5 pages 4 figures. Accepted for publication in MNRAS Letter

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.Comment: 7 pages, 8 figures, accepted for publication in the Monthly Notices of the Royal Astronomical Societ

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.Comment: 15 pages, 12 figures, accepted by MNRA

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.Comment: 13 pages, 12 figures, Accepted for publication in MNRA