A B S T R A C TA universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation.In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M ( and near 0.08 M ( . Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter.Determinations of the power-law indices a are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Da < 0X5 between 0.1 and 1 M ( than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Me Ândez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.

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The distribution of stellar masses that form in one star-formation event in a given volume of space is called the initial mass function (IMF). The IMF has been estimated from low-mass brown dwarfs to very massive stars. Combining IMF estimates for different populations in which the stars can be observed individually unveils an extraordinary uniformity of the IMF. This general insight appears to hold for populations including present-day star formation in small molecular clouds, rich and dense massive star-clusters forming in giant clouds, through to ancient and metal-poor exotic stellar populations that may be dominated by dark matter. This apparent universality of the IMF is a challenge for star formation theory because elementary considerations suggest that the IMF ought to systematically vary with star-forming conditions.The physics of star formation determines the conversion of gas to stars. The outcome of star formation are stars with a range of masses. Astrophysicists refer to the distribution of stellar masses as the stellar initial mass function. Together with the time-modulation of the star-formation rate, the IMF dictates the evolution and fate of galaxies and star clusters. The evolution of a stellar system is driven by the relative initial numbers of brown dwarfs (BDs, < ∼ 0.072 M ) that do not fuse H to He, very low-mass stars (0.072 − 0.5 M ), low-mass stars (0.5−1 M ), intermediate-mass stars (1−8 M ) and massive stars (m > 8 M ). Non-luminous BDs through to dim low-mass stars remove gas from the interstellar medium (ISM), lockingup an increasing amount of the mass of galaxies over cosmological time scales. Intermediate and luminous but short-lived massive stars expel a large fraction of their mass when they die and thereby enrich the ISM with elements heavier than H and He. They heat the ISM through radiation, outflows, winds and supernovae (1, 2). It is therefore of much importance to quantify the relative numbers of stars in different mass ranges and to find systematic variations of the 1

We have carried out a large set of N‐body simulations studying the effect of residual‐gas expulsion on the survival rate, and final properties of star clusters. We have varied the star formation efficiency (SFE), gas expulsion time‐scale and strength of the external tidal field, obtaining a three‐dimensional grid of models which can be used to predict the evolution of individual star clusters or whole star cluster systems by interpolating between our runs. The complete data of these simulations are made available on the internet. Our simulations show that cluster sizes, bound mass fraction and velocity profile are strongly influenced by the details of the gas expulsion. Although star clusters can survive SFEs as low as 10 per cent if the tidal field is weak and the gas is removed only slowly, our simulations indicate that most star clusters are destroyed or suffer dramatic loss of stars during the gas removal phase. Surviving clusters have typically expanded by a factor of 3 or 4 due to gas removal, implying that star clusters formed more concentrated than as we see them today. Maximum expansion factors seen in our runs are around 10. If gas is removed on time‐scales smaller than the initial crossing time, star clusters acquire strongly radially anisotropic velocity dispersions outside their half‐mass radii. Observed velocity profiles of star clusters can therefore be used as a constraint on the physics of cluster formation.

Over the past years observations of young and populous star clusters have shown that the stellar initial mass function (IMF) appears to be an invariant featureless Salpeter power law with an exponent ¼ 2:35 for stars more massive than a few M . A consensus has also emerged that most, if not all, stars form in stellar groups and star clusters and that the mass function of young star clusters in the solar neighborhood and in interacting galaxies can be described, over the mass range of a few 10 to 10 7 M , as a power law with an exponent % 2. These two results imply that galactic-field IMFs for early-type stars cannot, under any circumstances, be a Salpeter power law, but that they must have a steeper exponent, field e2:8. This has important consequences for the distribution of stellar remnants and for the chemodynamical and photometric evolution of galaxies.

Direct N‐body calculations are presented of the formation of Galactic clusters using GasEx, which is a variant of the code Nbody6. The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 104 stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC‐like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic‐field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations. The results have wide implications, also for the formation of globular clusters and the Galactic‐field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star‐forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.

Abstract. We show that the shape of the observed distribution of Milky Way (MW) satellites is inconsistent with their being drawn from a cosmological sub-structure population with a confidence of 99.5 per cent. Most of the MW satellites therefore cannot be related to dark-matter dominated satellites.

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 (