A method for following fragmentation simulations further in time using smoothed particle hydrodynamics (SPH) is presented. In a normal SPH simulation of the collapse and fragmentation of a molecular cloud, high-density regions of gas that form protostars are represented by many particles with small separations. These high-density regions require small time steps, limiting the time for which the simulation can be followed. Thus, the end result of the fragmentation can never be de nitively ascertained, and comparisons between cloud fragmentation calculations and the observed characteristics of stellar systems cannot be made.In this paper, each high-density region is replaced by a single, non-gaseous particle, with appropriate boundary conditions, which contains all the mass in the region and accretes any infalling mass. This enables the evolution of the cloud and the resulting protostars to be followed for many orbits or until most of the original cloud mass has been accreted.The Boss & Bodenheimer standard isothermal test case for the fragmentation of an interstellar cloud is used as an example for the technique. It is found that the binary protostellar system that forms initially does not merge, but instead forms a multiple system. The collapse is followed to 4 initial cloud free-fall times when approximately 80 per cent of the original mass of the cloud has been accreted by the protostars, or surrounds them in discs, and the remainder of the material has been expelled out to the radius of the initial cloud by the binary.

We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large‐scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly‐dynamic and chaotic process. Star formation occurs in localized bursts within the cloud via the fragmentation both of dense molecular cloud cores and of massive circumstellar discs. Star–disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. We find that the observed statistical properties of stars are a natural consequence of star formation in such a dynamical environment. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation (≈5 Jupiter masses). The initial mass function is consistent with a Salpeter slope (Γ=−1.35) above 0.5 M⊙, a roughly flat distribution (Γ= 0) in the range 0.006–0.5 M⊙, and a sharp cut‐off below ≈0.005 M⊙. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low‐mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations ≲10 au) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 au due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium cluster and implies that most stars and brown dwarfs do not form large planetary systems.

We investigate the physics of gas accretion in young stellar clusters. Accretion in clusters is a dynamic phenomenon as both the stars and the gas respond to the same gravitational potential. Accretion rates are highly non‐uniform with stars nearer the centre of the cluster, where gas densities are higher, accreting more than others. This competitive accretion naturally results in both initial mass segregation and a spectrum of stellar masses. Accretion in gas‐dominated clusters is well modelled using a tidal‐lobe radius instead of the commonly used Bondi–Hoyle accretion radius. This works as both the stellar and gas velocities are under the influence of the same gravitational potential and are thus comparable. The low relative velocity which results means that Rtidal

Recent surveys of star forming regions have shown that most stars, and probably all massive stars, are born in dense stellar clusters. The mechanism by which a molecular cloud fragments to form several hundred to thousands of individual stars has remained elusive. Here, we use a numerical simulation to follow the fragmentation of a turbulent molecular cloud and the subsequent formation and early evolution of a stellar cluster containing more than 400 stars. We show that the stellar cluster forms through the hierarchical fragmentation of a turbulent molecular cloud. This leads to the formation of many small subclusters which interact and merge to form the final stellar cluster. The hierarchical nature of the cluster formation has serious implications in terms of the properties of the new-born stars. The higher number-density of stars in subclusters, compared to a more uniform distribution arising from a monolithic formation, results in closer and more frequent dynamical interactions. Such close interactions can truncate circumstellar discs, harden existing binaries, and potentially liberate a population of planets. We estimate that at least one-third of all stars, and most massive stars, suffer such disruptive interactions.Comment: 6 pages, 4 figures, accepted for publication in MNRAS. Version including hi-res colour postscript figure available at http://star-www.st-and.ac.uk/~sgv/ps/clufhier.ps.g

We present a model for the formation of massive (M≳10 M⊙) stars through accretion‐induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate‐mass stars that have formed through accretion on to low‐mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.