Velocity anisotropy in tidally limited star clusters

Abstract

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.

Kinematical evolution of multiple stellar populations in star clusters

“…The less concentrated and more tidally filling 1G population never develops a strong radial anisotropy in the velocity space. As in the previous case, this behaviour is in agreement with the findings of Tiongco et al (2016a) for tidally filling systems.…”

“…Drawing parallels to the results of Tiongco et al (2016a), we find that the evolution of the anisotropy profile of the 1G population is similar to that of a tidally filling system, while the evolution of the anisotropy of the more compact 2G subsystem is similar to that of a tidally underfilling case. Specifically, as the 2G population expands due to two-body relaxation, it populates the outer halo with 2G stars on primarily radial orbits; this is clearly seen in Fig.…”

The properties of energetically unbound stars in stellar clusters

“…It has been shown that simulations of GCs with dense starting conditions develop radial anisotropy (Sollima et al 2015;Zocchi et al 2016) but those with larger initial r hm /rJ, similar to our initial conditions, do not develop any radial anisotropy and instead show tangential anisotropy near the tidal radius (Baumgardt & Makino 2003). This is thought to be due to the balance between the preferential production and preferential loss of radial orbits: two-body interactions predominantly scatter stars outwards on radial orbits, and these stars then escape more easily than those on other orbits (Takahashi, Lee & Inagaki 1997, Tiongco, Vesperini & Varri 2016a.…”

The orbital anisotropy profiles of nearby globular clusters from Gaia Data Release 2

“…The cases where radial anisotropy is observed in the inner regions of the cluster (ω Cen, M 3, M 13, M 15 and 47 Tuc) are likely examples of clusters that either formed tidally under-filling, are dynamically young, have undergone core collapse, or are strongly affected by the presence of multiple populations (Tiongco et al 2016;Zocchi et al 2017;Milone et al 2018). ω Cen has one of the longest relaxation times of any cluster (Harris 1996).…”

“…M 13 and M 15 are both clusters that are tidally underfilling at their current location, but tidally filling at pericenter. Hence these clusters were even more under-filling in the past and were therefore able to develop a strong anisotropy profile early in their dynamical lifetimes (Tiongco et al 2016). While tides have likely helped remove some stars on radial orbits in the outer regions of the clusters, the majority of the cluster has remained tidally unaffected.…”