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We examine the level of substructure and mass segregation in the massive, young cluster Westerlund 1. We find that it is relatively smooth, with little or no mass segregation, but with the massive stars in regions of significantly higher than average surface density. While an expanding or bouncing-back scenario for the evolution of Westerlund 1 cannot be ruled out, we argue that the most natural model to explain these observations is one in which Westerlund 1 formed with no primordial mass segregation and at a similar or larger size than we now observe., Comment: Accepted for publication in MNRAS (11 pages, 4 figures)

We present deep Hubble Space Telescope/Wide Field and Planetary Camera 2 photometry of the young HD 97950 star cluster in the giant H {\sc ii} region NGC 3603. The data were obtained in 1997 and 2007 permitting us to derive membership based on proper motions of the stars. Our data are consistent with an age of 1 Myr for the HD 97950 cluster. A possible age spread, if present in the cluster, appears to be small. The global slope of the incompleteness-corrected mass function for member stars within 60$"$ is $\rm \Gamma=-0.88\pm0.15$, which is flatter than the value of a Salpeter slope of -1.35. The radially varying mass function shows pronounced mass segregation ranging from slopes of $-0.26 \pm 0.32$ in the inner $5"$ to $-0.94\pm 0.36$ in the outermost annulus ($40"$ -- $60"$). Stars more massive than 50 M$_{\odot}$ are found only in the cluster center. The $\Lambda$ minimum spanning tree technique confirms significant mass segregation down to 30 M$_{\odot}$. The dependence of $\Lambda$ on mass, i.e., that high-mass stars are more segregated than low mass stars, and the (weak) dependence of the velocity dispersion on stellar mass might imply that the mass segregation is dynamical in origin. While primordial segregation cannot be excluded, the properties of the mass segregation indicate that dynamical mass segregation may have been the dominant process for segregation of high-mass stars., Comment: 11 pages, 6 figures, ApJ accepted 2012

We investigate how the properties of escaping stars are related to the initial conditions of their birth clusters. We find that the number of escaping stars, their spatial distribution, and their kinematics show a dependence on the initial conditions of the host cluster (substructure and virial ratio). Thus the properties of escaping stars can be used to inform us of the initial conditions of star formation, and also provide a window into the dynamical history of star clusters. The ESA Gaia mission will make observations of the positions and proper motions of these escaping stars at the required accuracy to allow us to investigate the dynamical evolution of local star clusters and provide an important insight into the initial conditions of star formation., Comment: 4 pages, 2 figures. Accepted for publication in MNRAS Jan 2012

We investigate the formation of protostellar clusters during the collapse of dense molecular cloud cores with a focus on the evolution of potential and kinetic energy, the degree of substructure, and the early phase of mass segregation. Our study is based on a series of hydrodynamic simulations of dense cores, where we vary the initial density profile and the initial turbulent velocity. In the three-dimensional adaptive mesh refinement simulations, we follow the dynamical formation of filaments and protostars until a star formation efficiency of 20%. Despite the different initial configurations, the global ensemble of all protostars in a setup shows a similar energy evolution and forms sub-virial clusters with an energy ratio $E_\mathrm{kin}/|E_\mathrm{pot}|\sim0.2$. Concentrating on the innermost central region, the clusters show a roughly virialised energy balance. However, the region of virial balance only covers the innermost $\sim10-30%$ of all the protostars. In all simulations with multiple protostars, the total kinetic energy of the protostars is higher than the kinetic energy of the gas cloud, although the protostars only contain 20% of the total mass. The clusters vary significantly in size, mass, and number of protostars, and show different degrees of substructure and mass segregation. Flat density profiles and compressive turbulent modes produce more subclusters then centrally concentrated profiles and solenoidal turbulence. We find that dynamical relaxation and hence dynamical mass segregation is very efficient in all cases from the very beginning of the nascent cluster, i.e., during a phase when protostars are constantly forming and accreting., Comment: 19 pages, MNRAS accepted

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., Comment: 12 pages, 7 figures; accepted for publication in MNRAS

We investigate the formation and evolution of high-order massive star multiples similar to the Trapezium in the Orion Nebula Cluster. We perform ensembles of N-body simulations of the evolution of N=1000 Orion-like clusters with initial conditions ranging from cool and clumpy to relatively smooth and relaxed. We find that trapezium-like systems are frequently formed in the first 2 Myr in initially cool and clumpy clusters and can survive for significant amounts of time in such clusters. We also find that these systems are highly dynamical entities, constantly interacting with the surrounding cluster, changing their appearance and membership regularly. The eventual decay of trapezium-like systems can even destroy the host cluster. We argue that the current state of any trapezium-like system is transient and care should be taken when analysing and drawing conclusions from a single snapshot in the life of a highly dynamic object., Comment: Accepted for publication in MNRAS. Supplementary material can be found at ftp://hydra.shef.ac.uk/pub/spg/TRAP_SUPLIMENTARY.pdf

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 lengths 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., Comment: 10 pages, 8 figures, accepted for publication in MNRAS

Observations and theory both suggest that star clusters form sub-virial (cool) with highly sub-structured distributions. We perform a large ensemble of N-body simulations of moderate-sized (N=1000) cool, fractal clusters to investigate their early dynamical evolution. We find that cool, clumpy clusters dynamically mass segregate on a short timescale, that Trapezium-like massive higher-order multiples are commonly formed, and that massive stars are often ejected from clusters with velocities > 10 km/s (c.f. the average escape velocity of 2.5 km/s). The properties of clusters also change rapidly on very short timescales. Young clusters may also undergo core collapse events, in which a dense core containing massive stars is hardened due to energy losses to a halo of lower-mass stars. Such events can blow young clusters apart with no need for gas expulsion. The warmer and less substructured a cluster is initially, the less extreme its evolution., Comment: Accepted for publication in MNRAS; supplementary material can be downloaded at http://sgoodwin.staff.shef.ac.uk/all_plots.pdf.gz

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected. We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a `mass segregation ratio' \Lambda_{MSR}=8.0 \pm 3.5 (where \Lambda_{MSR}=1 is no mass segregation) down to 16 \Msun, and also that the ONC is mass segregated at a lower level (~2.0 \pm 0.5) down to 5 \Msun. Below 5 \Msun we find no evidence for any further mass segregation in the ONC., Comment: Accepted in MNRAS