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We have carried out a set of Monte Carlo simulations to study a number of fundamental aspects of the dynamical evolution of multiple stellar populations in globular clusters with different initial masses, fractions of second generation (2G) stars, and structural properties. Our simulations explore and elucidate: 1) the role of early and long-term dynamical processes and stellar escape in the evolution of the fraction of 2G stars and the link between the evolution of the fraction of 2G stars and various dynamical parameters; 2) the link between the fraction of 2G stars inside the cluster and in the population of escaping stars during a clusters dynamical evolution; 3) the dynamics of the spatial mixing of the first-generation (1G) and 2G stars and the details of the structural properties of the two populations as they evolve toward mixing; 4) the implications of the initial differences between the spatial distribution of 1G and 2G stars for the evolution of the anisotropy in the velocity distribution and the expected radial profile of the 1G and 2G anisotropy for clusters at different stages of their dynamical history; 5) the variation of the degree of energy equipartition of the 1G and the 2G populations as a function of the distance from the clusters centre and the clusters evolutionary phase.
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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, NSG/NFG, 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 NSG/NFG profile flattens again (the NSG/NFG profile may rise slightly again in the outermost cluster regions). The radial variation of NSG/NFG 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, (NSG/NFG)glob. The distance at which NSG/NFG equals (NSG/NFG)glob is approximately between 1 and 2 cluster half-mass radii. The results of our simulations suggest that in many Galactic globular clusters the SG should still be more spatially concentrated than the FG.[abridged]
We present the results of a study aimed at investigating the effects of dynamical evolution on the spatial distribution and mixing of primordial binary stars in multiple-population globular clusters. Multiple stellar population formation models predict that second-generation (SG) stars form segregated in the inner regions of a more extended first-generation (FG) cluster. Our study, based on the results of a survey of N-body simulations, shows that the spatial mixing process for binary stars is more complex than that of single stars since additional processes such as binary ionization, recoil and ejection following binary-single and binary-binary interactions play a key role in determining the spatial distribution of the population of surviving binaries. The efficiency and relative importance of these additional effects depends on the binary binding energy and determines the timescale of the spatial mixing of FG and SG binaries. Our simulations illustrate the role of ionization, recoil and ejection combined with the effects of mass segregation driven by two-body relaxation and show that the complex interplay of all these processes results in a significant extension of the time needed for the complete spatial mixing of FG and SG binaries compared to that of single stars. Clusters in which FG and SG single stars have already reached complete spatial mixing might be characterized by a significant radial gradient in the ratio of the FG-to-SG binary fraction. The implications of the delayed mixing of FG and SG binaries for the differences between the kinematics of the two populations are discussed.
Our current understanding of the stellar initial mass function and massive star evolution suggests that young globular clusters may have formed hundreds to thousands of stellar-mass black holes, the remnants of stars with initial masses from $sim 20 - 100, M_odot$. Birth kicks from supernova explosions may eject some black holes from their birth clusters, but most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of globular clusters containing large numbers of stellar black holes. We describe numerical results for 42 models, covering a range of realistic initial conditions, including up to $1.6times10^6$ stars. In almost all models we find that significant numbers of black holes (up to $sim10^3$) are retained all the way to the present. This is in contrast to previous theoretical expectations that most black holes should be ejected dynamically within a few Gyr. The main reason for this difference is that core collapse driven by black holes (through the Spitzer mass segregation instability) is easily reverted through three-body processes, and involves only a small number of the most massive black holes, while lower-mass black holes remain well-mixed with ordinary stars far from the central cusp. Thus the rapid segregation of stellar black holes does not lead to a long-term physical separation of most black holes into a dynamically decoupled inner core, as often assumed previously. Combined with the recent detections of several black hole X-ray binary candidates in Galactic globular clusters, our results suggest that stellar black holes could still be present in large numbers in many globular clusters today, and that they may play a significant role in shaping the long-term dynamical evolution and the present-day dynamical structure of many clusters.
Scaling relations for globular clusters (GC) differ from scaling relations for pressure supported (elliptical) galaxies. We show that two-body relaxation is the dominant mechanism in shaping the bivariate dependence of density on mass and Galactocentric distance for Milky Way GCs with masses <10^6 Msun, and it is possible, but not required, that GCs formed with similar scaling relations as ultra-compact dwarf galaxies. We use a fast cluster evolution model to fit a parameterised model for the initial properties of Milky Way GCs to the observed present-day properties. The best-fit cluster initial mass function is substantially flatter (power-law index alpha =- 0.6+/-0.2) than what is observed for young massive clusters (YMCs) forming in the nearby Universe (alpha =~-2). A slightly steeper CIMF is allowed when considering the metal-rich GCs separately (alpha =~-1.2+/-0.4$). If stellar mass loss and two-body relaxation in the Milky Way tidal field are the dominant disruption mechanisms, then GCs formed differently from YMCs.
We study the interaction of the early spherical GC wind powered by Type II supernovae (SNe II) with the surrounding ambient medium consisting of the gaseous disk of a star forming galaxy at redshift z ~> 2. The bubble formed by the wind eventually breaks out of the disk, and most of the wind moves directly out of the galaxy and is definitively lost. The fraction of the wind moving nearly parallel to the galactic plane carves a hole in the disk which will contract after the end of the SN activity. During the interval of time between the end of the SN explosions and the closure of the hole, very O-poor stars (the Extreme population) can form out of the super-AGB (asymptotic giant branch) ejecta collected in the GC center. Once the hole contracts, the AGB ejecta mix with the pristine gas, allowing the formation of stars with an oxygen abundance intermediate between that of the very O-poor stars and that of the pristine gas. We show that this mechanism may explain why Extreme populations are present only in massive clusters, and can also produce a correlation between the spread in helium and the cluster mass. Finally, we also explore the possibility that our proposed mechanism can be extended to the case of multiple populations showing bimodality in the iron content, with the presence of two populations characterized by a small difference in [Fe/H]. Such a result can be obtained taking into account the contribution of delayed SN II.
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