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 (

It has been known for a long time that the satellite galaxies of the Milky Way (MW) show a significant amount of phase‐space correlation, and they are distributed in a highly inclined disc of satellites (DoS). We have extended the previous studies on the DoS by analysing for the first time the orientations of streams of stars and gas, and the distributions of globular clusters within the halo of the MW. It is shown that the spatial distribution of MW globular clusters classified as young halo clusters (YH GC) is very similar to that of the DoS, while seven of the 14 analysed streams align with the DoS. The probability to find the observed clustering of streams is only 0.3 per cent when assuming isotropy. The MW thus is surrounded by a vast polar structure (VPOS) of subsystems (satellite galaxies, globular clusters and streams), spreading from Galactocentric distances as small as 10 kpc out to 250 kpc. These findings demonstrate that a near‐isotropic infall of cosmological substructure components on to the MW is essentially ruled out because a large number of infalling objects would have had to be highly correlated, to a degree not natural for dark matter substructures. The majority of satellites, streams and YH GCs had to be formed as a correlated population. This is possible in tidal tails consisting of material expelled from interacting galaxies. We discuss the tidal scenario for the formation of the VPOS, including successes and possible challenges. The potential consequences of the MW satellites being tidal dwarf galaxies are severe. If all the satellite galaxies and YH GCs have been formed in an encounter between the young MW and another gas‐rich galaxy about 10–11 Gyr ago, then the MW does not have any luminous dark matter substructures and the missing satellites problem becomes a catastrophic failure of the standard cosmological model.

Star-formation rates (SFRs) of galaxies are commonly calculated by converting the measured Hα luminosities (L Hα ) into current SFRs. This conversion is based on a constant initial mass function (IMF) independent of the total SFR. As recently recognised the maximum stellar mass in a star cluster is limited by the embedded total cluster mass and, in addition, the maximum embedded star cluster mass is constrained by the current SFR. The combination of these two relations leads to an integrated galaxial initial stellar mass function (IGIMF, the IMF for the whole galaxy) which is steeper in the high mass regime than the constant canonical IMF, and is dependent on the SFR of the galaxy. Consequently, the L Hα -SFR relation becomes non-linear and flattens for low SFRs. Especially

Massive stars can be efficiently ejected from their birth star clusters through encounters with other massive stars. We study how the dynamical ejection fraction of O star systems varies with the masses of very young star clusters, M ecl , by means of direct N-body calculations. We include diverse initial conditions by varying the half-mass radius, initial mass segregation, initial binary fraction, and orbital parameters of the massive binaries. The results show robustly that the ejection fraction of O star systems exhibits a maximum at a cluster mass offor all models, even though the number of ejected systems increases with cluster mass. We show that lower mass clusters) are the dominant sources for populating the Galactic field with O stars by dynamical ejections, considering the mass function of embedded clusters. About 15% (up to ≈38%, depending on the cluster models) of O stars of which a significant fraction are binaries, and which would have formed in a ≈10 Myr epoch of star formation in a distribution of embedded clusters, will be dynamically ejected to the field. Individual clusters may eject 100% of their original O star content. A large fraction of such O stars have velocities up to only 10 km s −1 . Synthesising a young star cluster mass function, it follows, given the stellar-dynamical results presented here, that the observed fractions of field and runaway O stars, and the binary fractions among them, can be well understood theoretically if all O stars form in embedded clusters.

It has been shown before that the high mass-to-light ratios of ultra compact dwarf galaxies (UCDs) can be explained if their stellar initial mass function (IMF) was top-heavy, i.e. that the IMF was skewed towards high mass stars. In this case, neutron stars and black holes would provide unseen mass in the UCDs. In order to test this scenario with an independent method, we use data on which fraction of UCDs has a bright X-ray source. These X-ray sources are interpreted as low-mass X-ray binaries (LMXBs), i.e. binaries where a neutron star accretes matter from an evolving low-mass star. We find that LMXBs are indeed up to 10 times more frequent in UCDs than expected if the IMF was invariant. The top-heavy IMF required to account for this overabundance is the same as needed to explain the unusually high mass-to-light ratios of UCDs and a top-heavy IMF appears to be the only simultaneous explanation for both findings. Furthermore, we show that the high rate of type II supernovae (SNII) in the star-burst galaxy Arp 220 suggests a top-heavy IMF in that system. This finding is consistent with the notion that star-burst galaxies are sites where UCDs are likely to be formed and that the IMF of UCDs is top-heavy. It is estimated that the IMF becomes top-heavy whenever the star formation rate per volume surpasses 0.1 M ⊙ yr −1 pc −3 in pc-scale regions.

The Orion Nebula cluster (ONC) appears to be unusual on two grounds: the observed constellation of the OB stars of the entire ONC and its Trapezium at its centre implies a time-scale problem given the age of the Trapezium, and an initial mass function (IMF) problem for the whole OB star population in the ONC. Given the estimated crossing time of the Trapezium, it ought to have totally dynamically decayed by now. Furthermore, by combining the lower limit of the ONC mass with a standard IMF it emerges that the ONC should have formed at least about 40 stars heavier than 5 M while only 10 are observed. Using the N-body experiments we (i) confirm the expected instability of the Trapezium and (ii) show that beginning with a compact OB-star configuration of about 40 stars both the number of observed OB stars after 1 Myr within 1 pc radius and a compact trapezium configuration can be reproduced. These two empirical constraints thus support our estimate of 40 initial OB stars in the cluster. Interestingly, a more-evolved version of the ONC resembles the Upper Scorpius OB association. The N-body experiments are performed with the new C-code CATENA by integrating the equations of motion using the chain-multiple-regularization method. In addition, we present a new numerical formulation of the IMF.

We introduce a new method to measure the dispersion of m max values of star clusters and show that the observed sample of m max is inconsistent with random sampling from an universal stellar initial mass function (IMF) at a 99.9% confidence level. The scatter seen in the m max -M ecl data can be mainly (76%) understood as being the result of observational uncertainties only. The scatter of m max values at a given M ecl are consistent with mostly measurement uncertainties such that the true (physical) scatter may be very small.Additionally, new data on the local star-formation regions Taurus-Auriga and L1641 in Orion make stochastically formed stellar populations rather unlikely. The data are however consistent with the local IGIMF (integrated galactic stellar initial mass function) theory according to which a stellar population is a sum of individual star-forming events each of which is described by well defined physical laws. Randomly sampled IMFs and henceforth scale-free star formation seems to be in contradiction to observed reality. 1 With 'form with a canonical IMF' it is meant that the form of the IMF of the star-forming region follows the canonical IMF but the upper mass limit is regulated by the mmax-M ecl relation. c 2013 RAS 2 C. Weidner et al.the canonical IMF. It should be pointed out here that the principal concept of the IGIMF -the galaxy-wide IMF (= IGIMF) of a galaxy is always the sum of all star-formation events within a galaxy -is in any case always true. The ingredients for the IGIMF as applied here are listed as follows:1. The IMF, ξ(m), within star clusters is assumed to be canonical (see Appendix B), 2. the CSFEs populate an embedded-cluster mass function (ECMF), which is assumed to be a power-law of the form, ξ ecl (M ecl ) = dN / dM ecl ∝ M −β ecl , 3. the relation between the most-massive star in a cluster, mmax, and the stellar mass of the embedded cluster, M ecl , 2006 Weidner et al. 2010), 4. the relation between the star-formation rate (SFR) of a galaxy and the most-massive young (< 10 Myr) star cluster, log 10 (M ecl,max ) = 0.746 × log 10 (SF R) + 4.93 .Uncertainties are only introduced by the details of star-formation. Properties like the slope of the embedded cluster mass function (ECMF) and its lower mass end (M ecl,min ) in dwarf galaxies or the top/bottom-heaviness of the IMF in the pc-scale star-formation events (Marks et al. 2012) are examples which need further studies. Therefore any models calculated within the IGIMF-theory contain uncertainties and can not be final. Conversely, it is possible to use observed relations and dependencies of galaxies to refine the understanding of the pc-scale star-formation events within the IGIMF-theory .However, the severity of the difference of the IGIMF to the underlying canonical IMF is strongly dependent on how stars form. Two extreme models can be discussed in the context of how stars should be sampled from the IMF. The first model, random sampling, assumes that the IMF is a probability density function. A star cluster is then an ens...

Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs > 10 M ⊙ yr −1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk-and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index β of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.