We model the dynamical evolution of star forming regions with a wide range of initial properties. We follow the evolution of the regions substructure using the Q-parameter, we search for dynamical mass segregation using the Lambda_MSR technique, and
we also quantify the evolution of local density around stars as a function of mass using the Sigma_LDR method. The amount of dynamical mass segregation measured by Lambda_MSR is generally only significant for subvirial and virialised, substructured regions - which usually evolve to form bound clusters. The Sigma_LDR method shows that massive stars attain higher local densities than the median value in all regions, even those that are supervirial and evolve to form (unbound) associations. We also introduce the Q-Sigma_LDR plot, which describes the evolution of spatial structure as a function of mass-weighted local density in a star forming region. Initially dense (>1000 stars pc^{-2}), bound regions always have Q >1, Sigma_LDR > 2 after 5Myr, whereas dense unbound regions always have Q < 1, Sigma_LDR > 2 after 5Myr. Less dense regions (<100 stars pc^{-2}) do not usually exhibit Sigma_LDR > 2 values, and if relatively high local density around massive stars arises purely from dynamics, then the Q-Sigma_LDR plot can be used to estimate the initial density of a star forming region.
We use N-body simulations of star cluster evolution to explore the hypothesis that short-lived radioactive isotopes found in meteorites, such as 26-Al, were delivered to the Suns protoplanetary disc from a supernova at the epoch of Solar System forma
tion. We cover a range of star cluster formation parameter space and model both clusters with primordial substructure, and those with smooth profiles. We also adopt different initial virial ratios - from cool, collapsing clusters to warm, expanding associations. In each cluster we place the same stellar population; the clusters each have 2100 stars, and contain one massive 25M_Sun star which is expected to explode as a supernova at about 6.6Myr. We determine the number of Solar (G)-type stars that are within 0.1 - 0.3pc of the 25M_Sun star at the time of the supernova, which is the distance required to enrich the protoplanetary disc with the 26-Al abundances found in meteorites. We then determine how many of these G-dwarfs are unperturbed `singletons; stars which are never in close binaries, nor suffer sub-100au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of twenty initially identical clusters is highly stochastic, with the supernova enriching over 10 G-dwarfs in some clusters, and none at all in others. Typically only ~25 per cent of clusters contain enriched, unperturbed singletons, and usually only 1 - 2 per cluster (from a total of 96 G-dwarfs in each cluster). The initial conditions for star formation do not strongly affect the results, although a higher fraction of supervirial (expanding) clusters would contain enriched G-dwarfs if the supernova occurred earlier than 6.6Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.
We determine the distribution of stellar surface densities, Sigma, from models of static and dynamically evolving star clusters with different morphologies, including both radially smooth and substructured clusters. We find that the Sigma distributio
n is degenerate, in the sense that many different cluster morphologies (smooth or substructured) produce similar cumulative distributions. However, when used in tandem with a measure of structure, such as the Q-parameter, the current spatial and dynamical state of a star cluster can be inferred. The effect of cluster dynamics on the Sigma distribution and the Q-parameter is investigated using N-body simulations and we find that, depending on the assumed initial conditions, the Sigma distribution can rapidly evolve from high to low densities in less than 5Myr. This suggests that the Sigma distribution can only be used to assess the current density of a star forming region, and provides little information on its initial density. However, if the Sigma distribution is used together with the Q-parameter, then information on the amount of substructure can be used as a proxy to infer the amount of dynamical evolution that has taken place. Substructure is erased quickly through dynamics, which can disrupt binary star systems and planets, as well as facilitate dynamical mass segregation. Therefore, dynamical processing in young star forming regions could still be significant, even without currently observed high densities.
Observations and theory suggest that star clusters can form in a subvirial (cool) state and are highly substructured. Such initial conditions have been proposed to explain the level of mass segregation in clusters through dynamics, and have also been
successful in explaining the origin of trapezium-like systems. In this paper we investigate, using N-body simulations, whether such a dynamical scenario is consistent with the observed binary properties in the Orion Nebula Cluster (ONC). We find that several different primordial binary populations are consistent with the overall fraction and separation distribution of visual binaries in the ONC (in the range 67 - 670 au), and that these binary systems are heavily processed. The substructured, cool-collapse scenario requires a primordial binary fraction approaching 100 per cent. We find that the most important factor in processing the primordial binaries is the initial level of substructure; a highly substructured cluster processes up to 20 per cent more systems than a less substructured cluster because of localised pockets of high stellar density in the substructure. Binaries are processed in the substructure before the cluster reaches its densest phase, suggesting that even clusters remaining in virial equilibrium or undergoing supervirial expansion would dynamically alter their primordial binary population. Therefore even some expanding associations may not preserve their primordial binary population.
We use the new minimum spanning tree (MST) method to look for mass segregation in the Taurus association. The method computes the ratio of MST lengths of any chosen subset of objects, including the most massive stars and brown dwarfs, to the MST leng
ths of random sets of stars and brown dwarfs in the cluster. This mass segregation ratio (Lambda_MSR) enables a quantitative measure of the spatial distribution of high-mass and low-mass stars, and brown dwarfs to be made in Taurus. We find that the most massive stars in Taurus are inversely mass segregated, with Lambda_MSR = 0.70 +/- 0.10 (Lambda_MSR = 1 corresponds to no mass segregation), which differs from the strong mass segregation signatures found in more dense and massive clusters such as Orion. The brown dwarfs in Taurus are not mass segregated, although we find evidence that some low-mass stars are, with an Lambda_MSR = 1.25 +/- 0.15. Finally, we compare our results to previous measures of the spatial distribution of stars and brown dwarfs in Taurus, and briefly discuss their implications.
Around 4% of O-stars are observed in apparent isolation, with no associated cluster, and no indication of having been ejected from a nearby cluster. We define an isolated O-star as a star > 17.5 M_odot in a cluster with total mass <100 M_odot which c
ontains no other massive (>10 M_odot) stars. We show that the fraction of apparently isolated O-stars is reproduced when stars are sampled (randomly) from a standard initial mass function and a standard cluster mass function of the form N(M) propto M^-2. This result is difficult to reconcile with the idea that there is a fundamental relationship between the mass of a cluster and the mass of the most massive star in that cluster. We suggest that such a relationship is a typical result of star formation in clusters, and that `isolated O-stars are low-mass clusters in which massive stars have been able to form.
