The distribution of stellar masses that form together, the initial mass function (IMF), is one of the most important astrophysical distribution functions. The determination of the IMF is a very difficult problem because stellar masses cannot be measured directly and because observations usually cannot assess all stars in a population requiring elaborate bias corrections. Nevertheless, impressive advances have been achieved during the last decade, such that the shape of the IMF is reasonably well understood from low-mass brown dwarfs (BDs) to very massive stars. The case can be made for a rather universal form that can be well approximated by a two-part power-law function in the stellar regime. However, there exists a possible hint for a systematic variation with metallicity. From very elaborate observational surveys a picture is emerging according to which the binary properties of very-low-mass stars (VLMSs) and BDs may be fundamentally different from those of late-type stars implying the probable existence of a discontinuity in the IMF, but the surveys also appear to suggest the number of BDs per star to be independent of the physical conditions of current Galactic star formation. Star-burst clusters and thus globular cluster may, however, have a much larger abundance of BDs. Very recent advances have allowed the measurement of the physical upper stellar mass limit, which also appears to be disconcertingly robust to variations in metallicity. Furthermore, it now appears that star clusters are formed in a rather organised fashion from lowto high stellar masses, such that the most-massive stars just forming terminate further star-formation within the particular cluster. Populations formed from many star clusters, composite populations, would then have steeper IMFs (fewer massive stars per low-mass star) than the simple populations in the constituent clusters. A near invariant star-cluster mass function implies the maximal cluster mass to correlate with the galaxy-wide star-formation rate. This then leads to the result that the composite-stellar IMFs vary in dependence of galaxy type, with potentially dramatic implications for theories of galaxy formation and evolution.The simple and composite IMF 5 30 Dor cluster (R136) in the LMC, NGC 3603 in the MW, and the Arches cluster near the Galactic centre. The 30 Dor star-burst cluster (

The fraction of star formation that results in bound star clusters is influenced by the density spectrum in which stars are formed and by the response of the stellar structure to gas expulsion. We analyse hydrodynamical simulations of turbulent fragmentation in star-forming regions to assess the dynamical properties of the resulting population of stars and (sub)clusters. Stellar subclusters are identified using a minimum spanning tree algorithm. When considering only the gravitational potential of the stars and ignoring the gas, we find that the identified subclusters are close to virial equilibrium (the typical virial ratio Q_vir~0.59, where virial equilibrium would be Q_vir~0.5). This virial state is a consequence of the low gas fractions within the subclusters, caused by the accretion of gas onto the stars and the accretion-induced shrinkage of the subclusters. Because the subclusters are gas-poor, up to a length scale of 0.1-0.2 pc at the end of the simulation, they are only weakly affected by gas expulsion. The fraction of subclusters that reaches the high density required to evolve to a gas-poor state increases with the density of the star-forming region. We extend this argument to star cluster scales, and suggest that the absence of gas indicates that the early disruption of star clusters due to gas expulsion (infant mortality) plays a smaller role than anticipated, and is potentially restricted to star-forming regions with low ambient gas densities. We propose that in dense star-forming regions, the tidal shocking of young star clusters by the surrounding gas clouds could be responsible for the early disruption. This `cruel cradle effect' would work in addition to disruption by gas expulsion. We suggest possible methods to quantify the relative contributions of both mechanisms.Comment: 13 pages, 10 figures; Accepted for publication in MNRA

By analysing models of the young massive cluster R136 in 30 Doradus, set‐up using the herewith introduced and publicly made available code McLuster, we investigate and compare different methods for detecting and quantifying mass segregation and substructure in non‐seeing limited N‐body data. For this purpose we generate star cluster models with different degrees of mass segregation and fractal substructure and analyse them. We quantify mass segregation by measuring, from the projected 2D model data, the mass function slope in radial annuli, by looking for colour gradients in radial colour profiles, by measuring Allison’s Λ parameter and by determining the local stellar surface density around each star. We find that these methods for quantifying mass segregation often produce ambiguous results. Most reliable for detecting mass segregation is the mass function slope method, whereas the colour‐gradient method is the least practical in an R136‐like configuration. The other two methods are more sensitive to low degrees of mass segregation but are computationally much more demanding. We also discuss the effect of binaries on these measures. Moreover, we quantify substructure by looking at the projected radial stellar density profile, by comparing projected azimuthal stellar density profiles and by determining Cartwright & Whitworth’s Q parameter. We find that only high degrees of substructure affect the projected radial density profile, whereas the projected azimuthal density profile is very sensitive to substructure. The Q parameter is also sensitive to substructure but its absolute value shows a dependence on the radial density gradient of the cluster and is strongly influenced by binaries. Thus, in terms of applicability and comparability for large sets of N‐body data, the mass function slope method and the azimuthal density profile method seem to be the best choices for quantifying the degree of mass segregation and substructure, respectively. The other methods are computationally too demanding to be practically feasible for large data sets.

We undertake a systematic analysis of the early (< 0.5 Myr) evolution of clustering and the stellar initial mass function in turbulent fragmentation simulations. These large scale simulations for the first time offer the opportunity for a statistical analysis of IMF variations and correlations between stellar properties and cluster richness. The typical evolutionary scenario involves star formation in small-n clusters which then progressively merge; the first stars to form are seeds of massive stars and achieve a headstart in mass acquisition. These massive seeds end up in the cores of clusters and a large fraction of new stars of lower mass is formed in the outer parts of the clusters. The resulting clusters are therefore mass segregated at an age of 0.5 Myr, although the signature of mass segregation is weakened during mergers. We find that the resulting IMF has a smaller exponent (alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters are truncated at masses only somewhat larger than the most massive stars (which depends on the richness of the cluster) and an universal upper mass limit of 150 Msun is ruled out. We also find that the simulations show signs of the IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars is suppressed in the integrated IMF compared to the IMF in individual clusters. We identify clusters through the use of a minimum spanning tree algorithm which allows easy comparison between observational survey data and the predictions of turbulent fragmentation models. In particular we present quantitative predictions regarding properties such as cluster morphology, degree of mass segregation, upper slope of the IMF and the relation between cluster richness and maximum stellar mass. [abridged]Comment: 21 Pages, 25 Figure