tokens: we find that the median total number of stars that are enriched per event is ∼13, which is comparable to the maximum number of G dwarfs (stars with similar mass to the Sun, 0.8–1.2 M ⊙ ) that were enriched in the more populous clusters studied in Parker et al. ( 2014a ) as are the fraction of enriched G-dwarf stars that were unperturbed (∼0.5 per cent). In an attempt to increase the fraction of enriched stars, we explore a host of initial conditions for the star clusters. However, we find that no initial conditions result in a significantly higher (more than twice) fraction of enriched stars. The principal reason for this is the effects of two-body relaxation. In order to enrich more than half of the stars in a low-mass cluster, the required stellar density at the time of the SN(e) explosion(s) corresponds to a radius of only ∼0.4 pc, which is impossible to achieve after 5 Myr of evolution. Two-body relaxation results from a stellar system attempting to reach dynamical equilibrium and even a moderately dense system (100 stars pc −3 ) such as our default model expands significantly in the first 10 Myr, as shown in Fig. 7 . Here, the coloured lines represent the median local stellar density with time in each of the 20 realizations of these initial conditions. The solid black line is the mean central density across all 20 simulations (where we define the central density as the density within the half-mass radius). Clearly, the clusters have expanded significantly before the SN explosions (shown by the vertical dashed lines). Figure 7. Evolution of the median local volume density in each simulation as a function of time. Coloured lines indicate each of the 20 simulations and the black line indicates the average central density. Vertical dashed grey lines indicate times of the SNe. Irrespective of the initial conditions, the clusters never attain significant enrichment because the initial density is either too high (and two-body relaxation causes significant expansion), or the initial density is so low that despite the initial subvirial motion of the stars, significant clustering of the stars never occurs. The fraction of enriched unperturbed G-dwarf stars across all initial conditions range between ∼0.07 and 0.55 per cent. 3.4 Low-mass clusters containing one massive star The second median cluster chosen from our Monte Carlo sampling contained 113 stars, of which 1 was massive (24 M ⊙ ), resulting in an SN explosion at ∼7 Myr. The same set of initial conditions are focused on (α vir = 0.3, r F = 1.0 pc and D = 1.6) before summarizing the others. An average of six stars were enriched by the SN, a similar number to the median cluster containing two massive stars. The dynamical interaction and cluster density histories were also similar, resulting in ∼0.1–0.4 per cent of G dwarfs being enriched and unperturbed. With almost identical enrichment fractions and dynamical histories, the difference between clusters containing one or two massive stars is
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O