Dynamical evolution and spatial mixing of multiple population globular clusters

Abstract

Numerous spectroscopic and photometric observational studies have provided strong evidence for the widespread presence of multiple stellar populations in globular clusters. In this paper we study the long-term dynamical evolution of multiple-population clusters, focusing on the evolution of the spatial distributions of the first-(FG) and second-generation (SG) stars. In previous studies we have suggested that SG stars formed from the ejecta of FG AGB stars are expected initially to be concentrated in the cluster inner regions. Here, by means of N -body simulations, we explore the time scales and the dynamics of the spatial mixing of the FG and the SG populations and their dependence on the SG initial concentration.Our simulations show that, as the evolution proceeds, the radial profile of the SG/FG number ratio, N SG /N F G , is characterized by three regions: 1) a flat inner part; 2) a declining part in which FG stars are increasingly dominant; and 3) an outer region where the N SG /N F G profile flattens again (the N SG /N F G profile may rise slightly again in the outermost cluster regions). Until mixing is complete and the N SG /N F G profile is flat over the entire cluster, the radial variation of N SG /N F G implies that the fraction of SG stars determined by observations covering a limited range of radial distances is not, in general, equal to the SG global fraction, (N SG /N F G ) glob . The distance at which N SG /N F G equals (N SG /N F G ) glob is approximately between 1 and 2 cluster half-mass radii. The time scale for complete mixing depends on the SG initial concentration, but in all cases complete mixing is expected only for clusters in advanced evolutionary phases, having lost at least 60-70 percent of their mass due to two-body relaxation (in addition to the early FG loss due to the cluster expansion triggered by SNII ejecta and gas expulsion).The results of our simulations suggest that in many Galactic globular clusters the SG should still be more spatially concentrated than the FG.

Multiple Stellar Populations of Globular Clusters from Homogeneous Ca-CN Photometry. II. M5 (NGC 5904) and a New Filter System*

“…The large FOV is critical in the statistical study of the MSPs in GCs and in understanding the formation of such GCs. For example, Vesperini et al (2013) discussed that the local relative number ratio between the MSPs can be different from the global number ratio until the achievement of the complete mixing. Therefore the large area of the spatial coverage is essential to ensure the correct population number ratios, although M5 does not show any radial gradient in the population number ratio.…”

“…However, the recent N -body numerical simulations by Vesperini et al (2013), for example, showed that the time required to achieve the complete mixing can be about at least 20 half-mass relaxation time. During the course of the long-term dynamical evolution of GCs with MSPs, any structural differences between the MSPs are expected to be gradually eliminated.…”

“…The moving average shows some small scale local fluctuations but does not show any large scale gradient in the figure, i.e., no radial CN gradient in M5 (e.g., see Chun & Freeman 1979, for the radial CN variation in NGC 104). It is thought that the flat number ratio against the radial distance between the two populations up to more than 5r h may suggest that M5 is already in the stage of complete mixing (e.g., see Vesperini et al 2013). …”

G2C2 – IV. A novel approach to study the radial distributions of multiple populations in Galactic globular clusters

“…While most GC formation scenarios predict that the second and further generations will have different radial distribution from the primordial cluster populations, usually in the sense of being more centrally concentrated, we find that there is little evidence that this is generally true, if we use HB stars as tracers of He enriched population, a feature that should accompany the light element enhancement typical of the secondary stellar generations. Although in some cases we expect that the stellar populations will have been thoroughly mixed by dynamical evolution, including the possible effects of disk shocking, simulations of Vesperini et al (2013) predict that original population gradients will not have been erased by the present time in many GCs.…”

Evidence of tidal distortions and mass-loss from the old open cluster NGC 6791

“…In this Section we attempt to estimate the total mass lost by NGC 6791 during its evolution and derive its original mass. While many recipes can be used for this purpose (e.g., Vesperini et al 2013), we adopted the approach described by Lamers et al (2005). It has the advantage of describing the way the mass of a cluster decreases with time by means of relatively simple analytic expressions.…”