We report results of a large set of N-body calculations aimed to study the evolution of multi-mass star clusters in external tidal fields. Our clusters start with the same initial mass-functions, but varying particle numbers, orbital types and density profiles. Our main focus is to study how the stellar mass-function and other cluster parameters change under the combined influence of stellar evolution, two-body relaxation and the external tidal field. We find that the lifetimes of star clusters moving on similar orbits scale as T sim T_RH^x, where T_RH is the relaxation time, and the exponent x depends on the initial concentration of the cluster and is around x approx 0.75. From the results for the lifetimes, we predict that between 53% to 67% of all galactic globular clusters will be destroyed within the next Hubble time. Low-mass stars are preferentially lost and the depletion is strong enough to turn initially increasing mass-functions into mass-functions which decrease towards the low-mass end. The details of this depletion are insensitive to the starting condition of the cluster. The preferential depletion of low-mass stars from star clusters leads to a decrease of their mass-to-light ratios except for a short period close to final dissolution. The fraction of compact remnants is increasing throughout the evolution and they are more strongly concentrated towards the cluster cores than main-sequence stars. For a sample of galactic globular clusters with well observed parameters, we find a correlation between the observed slope of the mass-function and the lifetimes predicted by us. It seems possible that galactic globular clusters started with a mass-function similar to what one observes for the average mass-function of the galactic disc and bulge. (Abridged)Comment: 22 pages, 26 figures,accepted for publication in MNRA
We have derived the mean proper motions and space velocities of 154 Galactic globular clusters and the velocity dispersion profiles of 141 globular clusters based on a combination of Gaia DR2 proper motions with ground-based line-of-sight velocities. Combining the velocity dispersion profiles derived here with new measurements of the internal mass functions allows us to model the internal kinematics of 144 clusters, more than 90% of the currently known Galactic globular cluster population. We also derive the initial cluster masses by calculating the cluster orbits backwards in time applying suitable recipes to account for mass loss and dynamical friction. We find a correlation between the stellar mass function of a globular cluster and the amount of mass lost from the cluster, pointing to dynamical evolution as one of the mechanisms shaping the mass function of stars in clusters. The mass functions also show strong evidence that globular clusters started with a bottom-light initial mass function. Our simulations show that the currently surviving globular cluster population has lost about 80% of its mass since the time of formation. If globular clusters started from a log-normal mass function, we estimate that the Milky Way contained about 500 globular clusters initially, with a combined mass of about 2.5 · 10 8 M ⊙ . For a power-law initial mass function, the initial mass in globular clusters could have been a factor of three higher.
We have carried out a large set of N‐body simulations studying the effect of residual‐gas expulsion on the survival rate, and final properties of star clusters. We have varied the star formation efficiency (SFE), gas expulsion time‐scale and strength of the external tidal field, obtaining a three‐dimensional grid of models which can be used to predict the evolution of individual star clusters or whole star cluster systems by interpolating between our runs. The complete data of these simulations are made available on the internet. Our simulations show that cluster sizes, bound mass fraction and velocity profile are strongly influenced by the details of the gas expulsion. Although star clusters can survive SFEs as low as 10 per cent if the tidal field is weak and the gas is removed only slowly, our simulations indicate that most star clusters are destroyed or suffer dramatic loss of stars during the gas removal phase. Surviving clusters have typically expanded by a factor of 3 or 4 due to gas removal, implying that star clusters formed more concentrated than as we see them today. Maximum expansion factors seen in our runs are around 10. If gas is removed on time‐scales smaller than the initial crossing time, star clusters acquire strongly radially anisotropic velocity dispersions outside their half‐mass radii. Observed velocity profiles of star clusters can therefore be used as a constraint on the physics of cluster formation.
We have determined masses, stellar mass functions and structural parameters of 112 Milky Way globular clusters by fitting a large set of N -body simulations to their velocity dispersion and surface density profiles. The velocity dispersion profiles were calculated based on a combination of more than 15,000 high-precision radial velocities which we derived from archival ESO/VLT and Keck spectra together with ∼ 20, 000 published radial velocities from the literature. Our fits also include the stellar mass functions of the globular clusters, which are available for 47 clusters in our sample, allowing us to self-consistently take the effects of mass segregation and ongoing cluster dissolution into account. We confirm the strong correlation between the global mass functions of globular clusters and their relaxation times recently found by . We also find a correlation of the escape velocity from the centre of a globular cluster and the fraction of first generation stars (FG) in the cluster recently derived for 57 globular clusters by Milone et al. (2017), but no correlation between the FG star fraction and the global mass function of a globular cluster. This could indicate that the ability of a globular cluster to keep the wind ejecta from the polluting star(s) is the crucial parameter determining the presence and fraction of second generation stars and not its later dynamical mass loss.
We know from observations that globular clusters are very efficient catalysts in forming unusual short-period binary systems or their offspring, such as low-mass X-ray binaries (LMXBs; neutron stars accreting matter from low-mass stellar companions), cataclysmic variables (CVs; white dwarfs accreting matter from stellar companions), and millisecond pulsars (MSPs; rotating neutron stars with spin periods of a few ms). Although there has been little direct evidence, the overabundance of these objects in globular clusters has been attributed by numerous authors to the high densities in the cores, which leads to an increase in the formation rate of exotic binary systems through close stellar encounters. Many such close binary systems emit X-radiation at low luminosities (L_x < 10^{34} erg/s) and are being found in large numbers through observations with the Chandra X-ray Observatory. Here we present conclusive observational evidence for a link between the number of close binaries observed in X-rays in a globular cluster and the stellar encounter rate of the cluster. We also make an estimate of the total number of LMXBs in globular clusters in our Galaxy.Comment: 11 pages, 1 b&w figure, 1 color figur
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