Enrico Vesperini

Formation and dynamical evolution of multiple stellar generations in globular clusters

We study the formation and dynamical evolution of clusters with multiple stellar generations. Observational studies have found that some globular clusters host a population of second generation (SG) stars which show chemical anomalies and must have formed from gas containing matter processed in the envelopes of first generation (FG) cluster stars. We study the SG formation process by means of 1D hydrodynamical simulations, starting from a FG already in place and assuming that the SG is formed by the gas ejected by the Asymptotic Giant Branch (AGB) stars. This gas collects in a cooling flow into the cluster core, where it forms SG stars. The SG subsystem emerging from this process is initially strongly concentrated in the cluster innermost regions and its structural properties are largely independent of the FG initial properties. We also present the results of a model in which pristine gas contributes to the SG formation. In this model a very helium-rich SG population and one with a moderate helium enrichment form; the resulting SG bimodal helium distribution resembles that observed for SG stars in NGC 2808. By means of N-body simulations, we then study the two-population cluster dynamical evolution and mass loss. In our simulations, a large fraction of FG stars are lost early in the cluster evolution due to the expansion and stripping of the cluster outer layers resulting from early mass loss associated with FG SN ejecta. The SG population, initially concentrated in the innermost cluster regions, is largely unscathed by this early mass loss, and this early evolution leads to values of the number ratio of SG to FG stars consistent with observations. We also demonstrate possible evolutionary routes leading to the loss of most of the FG population, leaving an SG-dominated cluster. As the cluster evolves and the two populations mix, the local ratio of SG to FG stars, initially a decreasing function of radius, tends to a constant value in the inner parts of the cluster. Until mixing is complete, the radial profile of this number ratio is characterized by a flat inner part and a declining portion in the outer cluster regions.

Abundance patterns of multiple populations in globular clusters: a chemical evolution model based on yields from AGB ejecta

A large number of spectroscopic studies have provided evidence of the presence of multiple populations in globular clusters by revealing patterns in the stellar chemical abundances. This paper is aimed at studying the origin of these abundance patterns. We explore a model in which second generation (SG) stars form out of a mix of pristine gas and ejecta of the first generation of asymptotic giant branch stars. We first study the constraints imposed by the spectroscopic data of SG stars in globular clusters on the chemical properties of the asymptotic and super asymptotic giant branch ejecta. With a simple one-zone chemical model, we then explore the formation of the SG population abundance patterns focussing our attention on the Na-O, Al-Mg anticorrelations and on the helium distribution function. We carry out a survey of models and explore the dependence of the final SG chemical properties on the key parameters affecting the gas dynamics and the SG formation process. Finally, we use our chemical evolution framework to build specific models for NGC 2808 and M4, two Galactic globular clusters which show different patterns in the Na–O and Mg–Al anticorrelation and have different helium distributions. We find that the amount of pristine gas involved in the formation of SG stars is a key parameter to fit the observed O–Na and Mg–Al patterns. The helium distribution function for these models is in general good agreement with the observed one. Our models, by shedding light on the role of different parameters and their interplay in determining the final SG chemical properties, illustrate the basic ingredients, constraints and problems encountered in this self-enrichment scenario which must be addressed by more sophisticated chemical and hydrodynamic simulations.

Dynamical age differences among coeval star clusters as revealed by blue stragglers

Globular star clusters that formed at the same cosmic time may have evolved rather differently from the dynamical point of view (because that evolution depends on the internal environment) through a variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre. Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different ‘dynamical ages’). Blue straggler stars have masses greater than those at the turn-off point on the main sequence and therefore must be the result of either a collision or a mass-transfer event. Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties.

TIDAL DISRUPTION, GLOBAL MASS FUNCTION, AND STRUCTURAL PARAMETER EVOLUTION IN STAR CLUSTERS

We present a unified picture for the evolution of star clusters on the two-body relaxation timescale. We use direct N-body simulations of star clusters in a galactic tidal field starting from different multimass King models, up to 10% of primordial binaries and up to N tot = 65, 536 particles. An additional run also includes a central Intermediate Mass Black Hole. We find that for the broad range of initial conditions we have studied the stellar mass function of these systems presents a universal evolution, which depends only on the fractional mass loss. The structure of the system, as measured by the core to half-mass radius ratio, also evolves toward a universal state, which is set by the efficiency of heating on the visible population of stars induced by dynamical interactions in the core of the system. Interactions with dark remnants (white dwarfs, neutron stars, and stellar mass black holes) are dominant over the heating induced by a moderate population of primordial binaries (3%-5%), especially under the assumption that most of the neutron stars and black holes are retained in the system. All our models without primordial binaries undergo a deep gravothermal collapse in the radial mass profile. However, their projected light distribution can be well fitted by medium concentration King models (with parameter W 0 ~ 8), even though there tends to be an excess over the best fit for the innermost points of the surface brightness. This excess is consistent with a shallow cusp in the surface brightness (? ~ R ?? with ? ~ 0.4-0.7), like it has been observed for many globular clusters from high-resolution Hubble Space Telescope imaging. Generally, fitting a King profile to derive the structural parameters yields to larger fluctuations in the core size than defining the core as the radius where the surface brightness is one half of its central value. Classification of core-collapsed globular clusters based on their surface brightness profile may thus fail in systems that appear to have already bounced back to lower concentrations, particularly if the angular resolution of the observations is limited and the core is not well resolved.

Evidence for two populations of Galactic globular clusters from the ratio of their half-mass to Jacobi radii

We investigate the ratio between the half-mass radii r(h) of Galactic globular clusters and their Jacobi radii r(J) given by the potential of the Milky Way and show that clusters with galactocentric distances R(GC) > 8 kpc fall into two distinct groups: one group of compact, tidally underfilling clusterswith r(h)/r(J) < 0.05 and another group of tidally filling clusters which have 0.1 < r(h)/r(J) < 0.3. We find no correlation between the membership of a particular cluster in one of these groups and its membership in the old or younger halo population. Based on the relaxation times and orbits of the clusters, we argue that compact clusters and most clusters in the inner Milky Way were born compact with half-mass radii r(h) < 1 pc. Some of the tidally filling clusters might have formed compact as well, but the majority likely formed with large half-mass radii. Galactic globular clusters therefore show a similar dichotomy as was recently found for globular clusters in dwarf galaxies and for young star clusters in the Milky Way. It seems likely that some of the tidally filling clusters are evolving along the main-sequence line of clusters recently discovered by Kupper et al. (2008) and are in the process of dissolution.

EFFECTS OF PRIMORDIAL MASS SEGREGATION ON THE DYNAMICAL EVOLUTION OF STAR CLUSTERS

In this paper, we use N-body simulations to study the effects of primordial mass segregation on the early and long-term evolution of star clusters. Our simulations show that in segregated clusters early mass loss due to stellar evolution triggers a stronger expansion than for unsegregated clusters. Tidally limited, strongly segregated clusters may dissolve rapidly as a consequence of this early expansion, while segregated clusters initially underfilling their Roche lobe can survive the early expansion and have a lifetime similar to that of unsegregated clusters. Long-lived initially segregated clusters tend to have looser structure and reach core collapse later in their evolution than initially unsegregated clusters. We have also compared the effects of dynamical evolution on the global stellar mass function (MF) of low-mass main-sequence stars. In all cases, the MF flattens as the cluster loses stars. The amount of MF flattening induced by a given amount of mass loss in a rapidly dissolving initially segregated cluster is less than for an unsegregated cluster. The evolution of the MF of a long-lived segregated cluster, on the other hand, is very similar to that of an initially unsegregated cluster.

Formation of multiple populations in globular clusters: constraints on the dilution by pristine gas

The star-to-star differences in the abundance of light elements observed in the globular clusters (GCs) can be explained assuming that a second generation (SG) of stars form in the gas ejected by the asymptotic giant branch (AGB) stars belonging to a first stellar generation. However, while Na and O appear to be anticorrelated in the cluster stars, from the stellar models they turn out to be correlated in the AGB ejecta. In order to reconcile the stellar theory with the observational findings, all the GC models invoke an early dilution of AGB ejecta with pristine gas occurring during the SG formation. Despite a vast consensus about the occurrence of such a dilution, the physical process behind it is still unknown. In the present paper we set some general constraints on the pristine gas dynamics and on the possible amount of pristine gas involved in the SG formation, making use of a one-zone chemical model. We find that such a dilution is a necessary ingredient in the SG star formation to explain the observed abundance patterns. We confirm the conclusion of our previous works showing that clusters must have been initially much more massive. We also show that models assuming that clusters had an initial mass similar to their current one, and adopting a large fraction of pristine gas to form SG stars, fail to reproduce the observed Na–O anticorrelation and are not viable. We finally show that the dilution event should be restricted in time, rather than extended for the full duration of SG formation.

The fraction of globular cluster second-generation stars in the Galactic halo

Many observational studies have revealed the presence of multiple stellar generations in Galactic globular clusters. These studies suggest that second-generation stars make up a significant fraction of the current mass of globular clusters, with the second-generation mass fraction ranging from ~50% to 80% in individual clusters. In this Letter, we carry out hydrodynamical simulations to explore the dependence of the mass of second-generation stars on the initial mass and structural parameters and stellar initial mass function (IMF) of the parent cluster. We then use the results of these simulations to estimate the fraction f SG,H of the mass of the Galactic stellar halo composed of second-generation stars that originated in globular clusters. We study the dependence of f SG,H on the parameters of the IMF of the Galactic globular cluster system. For a broad range of initial conditions, we find that the fraction of mass of the Galactic stellar halo in second-generation stars is always small, f SG,H < 4%-6% for a Kroupa-1993 IMF and f SG,H < 7%-9% for a Kroupa-2001 IMF.

The ages of globular clusters in NGC 4365 revisited with deep HST observations

We present new Hubble Space Telescope (HST) NIC3, near-infrared H-band photometry of globular clusters (GCs) around NGC 4365 and NGC 1399 in combination with archival HST WFPC2 and ACS optical data. We find that NGC 4365 has a number of globular clusters with bluer optical colors than expected for their red optical-to-near-infrared colors and an old age. The only known way to explain these colors is with a significant population of intermediate-age (2-8 Gyr) clusters in this elliptical galaxy. On the other hand, our result for NGC 1399 is in agreement with previous spectroscopic work that suggests that its clusters have a large metallicity spread and are nearly all old. In the literature, there are various results from spectroscopic studies of modest samples of NGC 4365 globular clusters. The spectroscopic data allow for either the presence or absence of a significant population of intermediate-age clusters, given the index uncertainties indicated by comparing objects in common between these studies and the few spectroscopic candidates with optical-to-near-IR colors indicative of intermediate ages. Our new near-IR data of the NGC 4365 GC system with a much higher signal-to-noise ratio agree well with earlier published photometry, and both give strong evidence of a significant intermediate-age component. The agreement between the photometric and spectroscopic results for NGC 1399 and other systems lends further confidence to this conclusion and to the effectiveness of the near-IR technique.

The oxygen versus sodium (anti)correlation(s) in ω Cen

Recent examination of large samples of ω Cen giants shows that, as in mono-metallic globular clusters, sodium versus oxygen anticorrelation is present within each subset of stars with iron content in the range –1.9 [Fe/H] –1.3. These findings suggest that, while the second generation formation history in ω Cen is more complex than that of mono-metallic clusters, it shares some key steps with those simpler clusters. In addition, the giants in the range –1.3 –1.3 in ω Cen are likely to have formed directly from the pure ejecta of massive AGBs of the same metallicities. This is possible if the massive AGBs of [Fe/H] > –1.3 in the progenitor system evolve when all the pristine gas surrounding the cluster has been exhausted by the previous star formation events, or the protocluster interaction with the Galaxy caused the loss of a significant fraction of its mass, or of its dark matter halo, and the supernova ejecta have been able to clear the gas out of the system. The absence of dilution in the relatively metal-rich populations lends further support to a scenario of the formation of second generation stars in cooling flows from massive AGB progenitors. We suggest that the entire formation of ω Cen took place in a few 108 yr, and discuss the problem of a prompt formation of s-process elements.