The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

The possiblity of detection of ultracool dwarfs with the UKIRT Infrared Deep Sky Survey

We present predictions for the numbers of ultracool dwarfs in the Galactic disc population that could be detected by the WFCAM/UKIDSS Large Area Survey and Ultra Deep Survey. Simulated samples of objects are created with masses and ages drawn from different mass functions and birthrates. Each object is then given absolute magnitudes in different passbands based on empirically derived bolometric correction versus effective temperature relationships (or model predictions for Y dwarfs). These are then combined with simulated space positions, velocities and photometric errors to yield observables such as apparent magnitudes and proper motions. Such observables are then passed through the survey selection mechanism to yield histograms in colour. This technique also produces predictions for the proper motion histograms for ultracool dwarfs and estimated numbers for the as yet undetected Y dwarfs. Finally, it is shown that these techniques could be used to constrain the ultra-low-mass mass function and birthrate of the Galactic disc population.     

Star formation in unbound giant molecular clouds: the origin of OB associations?

We investigate the formation of star clusters in an unbound giant molecular cloud, where the supporting kinetic energy is twice as large as the cloud's self-gravity. This cloud manages to form a series of star clusters and disperse, all within roughly two crossing times (10 Myr), supporting recent claims that star formation is a rapid process. Simple assumptions about the nature of the star formation occurring in the clusters allows us to place an estimate for the star formation efficiency at about 5–10 per cent, consistent with observations. We also propose that unbound clouds can act as a mechanism for forming OB associations. The clusters that form in the cloud behave as OB subgroups. These clusters are naturally expanding from one another due to the unbound nature of the flows that create them. The properties of the cloud we present here are consistent with those of classic OB associations.     

The initial mass function of the rich young cluster NGC 1818 in the Large Magellanic Cloud

We use deep Hubble Space Telescope photometry of the rich, young (∼20- to 45-Myr old) star cluster NGC 1818 in the Large Magellanic Cloud to derive its stellar mass function (MF) down to  ∼0.15 M_⊙  . This represents the deepest robust MF thus far obtained for a stellar system in an extragalactic, low-metallicity  ([Fe/H]≃−0.4 dex)  environment. Combining our results with the published MF for masses above  1.0 M_⊙  , we obtain a complete present-day MF. This is a good representation of the cluster's initial MF (IMF), particularly at low masses, because our observations are centred on the cluster's uncrowded half-mass radius. Therefore, stellar and dynamical evolution of the cluster will not have affected the low-mass stars significantly. The NGC 1818 IMF is well described by both a lognormal and a broken power-law distribution with slopes of  Γ= 0.46 ± 0.10  and  Γ≃−1.35  (Salpeter-like) for masses in the range from 0.15 to  0.8 M_⊙  and greater than  0.8 M_⊙  , respectively. Within the uncertainties, the NGC 1818 IMF is fully consistent with both the Kroupa solar neighbourhood and the Chabrier lognormal mass distributions.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively.
We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system.
Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars.     

Binary stars and the fundamental initial mass function

We have carried out Monte Carlo simulations in which we generate a random pairing of objects drawn from a pre-assumed single-star power-law initial mass function (IMF), which we call the fundamental IMF. We show how the mass functions of primary stars and secondary stars and the mass function of the total mass of systems (if we could resolve them) differ from the underlying fundamental IMF for different slopes of this IMF. We also compare our results with the observed IMF, the binary frequency and the binary mass-ratio distributions for field stars and conclude that the fundamental IMF of subsolar mass stars could be steeper than is currently believed. In other words, the low-mass turn-over of the observed ('apparent') IMF could be spurious, if the main-sequence binary fraction of field stars is close to 100 per cent (perhaps owing to invisible companions).     

The low-mass initial mass function in the young cluster NGC 6611

NGC 6611 is the massive young cluster (2–3 Myr) that ionizes the Eagle Nebula. We present very deep photometric observations of the central region of NGC 6611 obtained with the Hubble Space Telescope and the following filters: ACS/WFC F775W and F850LP and NIC2 F110W and F160W, loosely equivalent to ground-based IZJH filters. This survey reaches down to   I ∼ 26 mag  . We construct the initial mass function (IMF) from  ∼1.5 M_⊙  well into the brown dwarf regime (down to  ∼0.02 M_⊙  ). We have detected 30–35 brown dwarf candidates in this sample. The low-mass IMF is combined with a higher-mass IMF constructed from the ground-based catalogue from Oliveira et al. We compare the final IMF with those of well-studied star-forming regions: we find that the IMF of NGC 6611 more closely resembles that of the low-mass star-forming region in Taurus than that of the more massive Orion Nebula Cluster. We conclude that there seems to be no severe environmental effect in the IMF due to the proximity of the massive stars in NGC 6611.     

Predicting the properties of binary stellar systems: the evolution of accreting protobinary systems

We investigate the formation of binary stellar systems. We consider a model where a 'seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs.
Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal-mass components and are more likely to have circumbinary discs than wider systems. Comparing our results with observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and 1/ r (e.g., Gaussian) with near-uniform rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extrasolar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation ≲10 au, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.