Few topics in astronomy initiate such vigorous discussion as whether or not the initial mass function (IMF) of stars is universal, or instead sensitive to the initial conditions of star formation. The distinction is of critical importance: the IMF influences most of the observable properties of stellar populations and galaxies, and detecting variations in the IMF could provide deep insights into the process by which stars form. In this review, we take a critical look at the case for IMF variations, with a view towards whether other explanations are sufficient given the evidence. Studies of the field, local young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a "universal" IMF: a power-law of Salpeter index (Γ = 1.35) above a few solar masses, and a log normal or shallower power-law (Γ ∼ 0 − 0.25) between a few tenths and a few solar masses (ignoring the effects of unresolved binaries). The shape and universality of the IMF at the stellar-substellar boundary is still under investigation and uncertainties remain large, but most observations are consistent with a IMF that declines (Γ < −0.5) well below the hydrogen burning limit. Observations of resolved stellar populations and the integrated properties of most galaxies are also consistent with a "universal IMF", suggesting no gross variations in the IMF over much of cosmic time. There are indications of "non-standard" IMFs in specific local and extragalactic environments, which clearly warrant further study. Nonetheless, there is no clear evidence that the IMF varies strongly and systematically as a function of initial conditions after the first few generations of stars. We close with suggestions for future work that might uncover more subtle IMF variations than those that could be discerned to date.

We present a global study of low‐mass, young stellar object (YSO) surface densities (Σ) in nearby (<500 pc) star‐forming regions based on a comprehensive collection of Spitzer Space Telescope surveys. We show that the distribution of YSO surface densities in the solar neighbourhood is a smooth distribution, being adequately described by a lognormal function from a few to 103 YSOs pc−2, with a peak at ∼22 stars pc−2 and a dispersion of . We do not find evidence for multiple discrete modes of star formation (e.g. clustered and distributed). Comparing the observed surface density distribution to previously reported surface density threshold definitions of clusters, we find that the fraction of stars in clusters is crucially dependent on the adopted definitions, ranging from 40 to 90 per cent. However, we find that only a low fraction (<26 per cent) of stars are formed in dense environments where their formation/evolution (along with their circumstellar discs and/or planets) may be affected by the close proximity of their low‐mass neighbours.

We examine the luminosity and dynamical mass estimates for young massive stellar clusters. For many young (<50 Myr) clusters, the luminosity and dynamical mass estimates differ by a significant amount. We explain this as being due to many young clusters being out of virial equilibrium (which is assumed in dynamical mass estimates) because the clusters are undergoing violent relaxation after expelling gas not used in star formation. We show that, if we assume that luminous mass estimates are correct (for a standard IMF), at least 50 per cent of young clusters for which dynamical masses are known are likely to be destroyed within a few 10s Myr of their formation. Even clusters which will retain a bound core may lose a large fraction of their stellar mass. We also show that the core radius and other structural parameters change significantly during the violent relaxation that follows gas expulsion and that they should be considered instantaneous values only, not necessarily reflecting the final state of the cluster. In particular we note that the increasing core radii observed in young LMC/SMC clusters can be well explained as an effect of rapid gas loss.Comment: 8 pages, 5 figures. MNRAS, in pres

Abstract. We present a simple analytical description of the disruption of star clusters in a tidal field. The cluster disruption time, defined as t dis = {dln M/dt} −1 , depends on the mass M of the cluster as t dis = t 0 (M/M ) γ with γ = 0.62 for clusters in a tidal field, as shown by empirical studies of cluster samples in different galaxies and by N-body simulations. Using this simple description we derive an analytic expression for the way in which the mass of a cluster decreases with time due to stellar evolution and disruption. The result agrees very well with those of detailed N-body simulations for clusters in the tidal field of our galaxy. The analytic expression can be used to predict the mass and age histograms of surviving clusters for any cluster initial mass function and any cluster formation history. The method is applied to explain the age distribution of the open clusters in the solar neighbourhood within 600 pc, based on a new cluster sample that appears to be unbiased within a distance of about 1 kpc. From a comparison between the observed and predicted age distributions in the age range between 10 Myr to 3 Gyr we find the following results: (1) The disruption time of a 10 4 M cluster in the solar neighbourhood is about 1.3 ± 0.5 Gyr. This is a factor of 5 shorter than that derived from N-body simulations of clusters in the tidal field of the galaxy. Possible reasons for this discrepancy are discussed. (2) The present star formation rate in bound clusters within 600 pc of the Sun is 5.9 ± 0.8 × 10 2 M Myr −1 , which corresponds to a surface star formation rate of bound clusters of 5.2 ± 0.7 × 10 −10 M yr −1 pc −2 . (3) The age distribution of open clusters shows a bump between 0.26 and 0.6 Gyr when the cluster formation rate was 2.5 times higher than before and after. (4) The present star formation rate in bound clusters is about half that derived from the study of embedded clusters. The difference suggests that about half of the clusters in the solar neighbourhood become unbound within about 10 Myr. (5) The most massive clusters within 600 pc had an initial mass of about 3 × 10 4 M . This is in agreement with the statistically expected value based on a cluster initial mass function with a slope of −2, even if the physical upper mass limit for cluster formation is as high as 10 6 M .

We further the recent discussion on the relation between the star formation rate (SFR) of a galaxy and the luminosity of its brightest star cluster (SFR versus MbrightestV). We first show that the observed trend of SFR versus MbrightestV is due to the brightest cluster in a galaxy being preferentially young (≤15 Myr – for a constant SFR) and hence a good tracer of the current SFR, although we give notable exceptions to this rule. Archival Hubble Space Telescope (HST) imaging of high‐SFR galaxies, as well as additional galaxies/clusters from the literature, is used to further confirm the observed trend. Using a series of Monte Carlo simulations, we show that a pure power‐law mass function with index α= 2 is ruled out by the current data. Instead, we find that a Schechter function (i.e. a power law with an exponential truncation at the high‐mass end) provides an excellent fit to the data. Additionally, these simulations show that bound cluster formation (in M⊙ yr−1) represents only ∼8±3 per cent of the total star formation within a galaxy, independent of the SFR. From this, we conclude that there is only a single mode of cluster formation which operates over at least 6 orders of magnitude in the SFR. We provide a simple model of star/cluster formation feedback within dwarf galaxies (and star‐forming complexes within spirals) which highlights the strong impact that a massive cluster can have on its surroundings. Using this relation, we can extrapolate backwards in time in order to estimate the peak SFR of major merger galaxies, such as NGC 7252, 1316 and 3610. The derived SFRs for these galaxies are between a few hundred and a few thousand solar masses per year. The inferred far‐infrared luminosity of the galaxies, from the extrapolated SFR, places them well within the range of ultraluminous infrared galaxies (ULIRGs) and for NGC 7252 within the hyperluminous infrared galaxy (HLIRG) regime. Thus, we provide evidence that these post‐merger galaxies passed through a ULIRG/HLIRG phase and are now evolving passively. Using the current and extrapolated past SFR of NGC 34, we infer that the ULIRG phase of this galaxy has lasted for at least 150 Myr.

Abstract. We use archival Hubble Space Telescope observations of broad-band images from the ultraviolet (F255W-filter) through the near infrared (NICMOS F160W-filter) to study the star cluster population of the interacting spiral galaxy M 51. We obtain age, mass, extinction, and effective radius estimates for 1152 star clusters in a region of ∼7.3 × 8.1 kpc centered on the nucleus and extending into the outer spiral arms. In this paper we present the data set and exploit it to determine the age distribution and relationships among the fundamental parameters (i.e. age, mass, effective radius). We show the critical dependence of the age distribution on the sample selection, and confirm that using a constant mass cut-off, above which the sample is complete for the entire age range of interest, is essential. In particular, in this sample we are complete only for masses above 5 × 10 4 M for the last 1 Gyr. Using this dataset we find: i) that the cluster formation rate seems to have had a large increase ∼50−70 Myr ago, which is coincident with the suggested second passage of its companion, NGC 5195; ii) a large number of extremely young (<10 Myr) star clusters, which we interpret as a population of unbound clusters of which a large majority will disrupt within the next ∼10 Myr; and iii) that the distribution of cluster sizes can be well approximated by a power-law with exponent, −η = −2.2 ± 0.2, which is very similar to that of Galactic globular clusters, indicating that cluster disruption is largely independent of cluster radius. In addition, we have used this dataset to search for correlations among the derived parameters. In particular, we do not find any strong trends between the age and mass, mass and effective radius, nor between the galactocentric distance and effective radius. There is, however, a strong correlation between the age of a cluster and its extinction, with younger clusters being more heavily reddened than older clusters.

Globular clusters (GCs), once thought to be well approximated as simple stellar populations (i.e. all stars having the same age and chemical abundance), are now known to host a variety of anomalies, such as multiple discrete (or spreads in) populations in colour-magnitude diagrams and abundance variations in light elements (e.g. Na, O, Al). Multiple models have been put forward to explain the observed anomalies, although all have serious shortcomings (e.g. requiring a non-standard initial mass function of stars and GCs to have been initially 10-100 times more massive than observed today). These models also do not agree with observations of massive stellar clusters forming today, which do not display significant age spreads nor have gas/dust within the cluster. Here we present a model for the formation of GCs, where low-mass pre-main-sequence stars accrete enriched material released from interacting massive binary and rapidly rotating stars on to their circumstellar discs, and ultimately on to the young stars. As was shown in previous studies, the accreted material matches the unusual abundances and patterns observed in GCs. The proposed model does not require multiple generations of star formation, conforms to the known properties of massive clusters forming today and solves the 'mass budget problem' without requiring GCs to have been significantly more massive at birth. Potential caveats to the model as well as model predictions are discussed.

A significant number of intermediate age clusters (1–2 Gyr) in the Magellanic Clouds appear to have multiple stellar populations within them, derived from bimodal or extended main‐sequence turn‐offs. If this is interpreted as an age spread, the multiple populations are separated by a few hundred million years, which would call into question the long‐held notion that clusters are simple stellar populations. Here, we show that stellar rotation in stars with masses between 1.2 and 1.7 M⊙ can mimic the effect of a double or multiple population, whereas in actuality only a single population exists. The two main causes of the spread near the turn‐off are the effects of stellar rotation on the structure of the star and the inclination angle of the star relative to the observer. Both effects change the observed effective temperature, hence colour, and flux of the star. In order to match observations, the required rotation rates are 20–50 per cent of the critical rotation, which are consistent with observed rotation rates of similar mass stars in the Galaxy. We provide scaling relations which can be applied to non‐rotating isochrones in order to mimic the effects of rotation. Finally, we note that rotation is unlikely to be the cause of the multiple stellar populations observed in old globular clusters, as low‐mass stars (<1 M⊙) are not expected to be rapid rotators.