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.

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