Stellar encounters involving massive stars in young clusters

We model collisions between pre-main-sequence stars using a smoothed particle hydrodynamics method. Assuming that all collisions lead to simple mergers, we use derived merger cross-sections to calculate the time-scale to make a 50-M-circle dot star by collisions within the core of a stellar cluster as a function of stellar number density. We show that a 50-M-circle dot star may be produced in this manner within 106 yr beginning with a cluster core of 200 1-M-circle dot stars within a radius of 0.0025 pc. Encounters between one high-mass star and one low-mass star tend to result in the tidal shredding of the latter, producing a massive disc around the former. This disc spreads viscously and provided a much larger target than any star for subsequent collisions. If a star strikes the disc, it is likely to be captured, and so forms a binary with the other star. Subsequent encounters between the binary and single stars lead either to exchanges or to the formation of merged objects. The inclusion of this effect leads to a significant reduction in the time taken to produce a 50-M-circle dot star. We also consider the role played by primordial binaries. We show that the time-scale required to produce a 50-M-circle dot star decreases with increasing binary fraction. We find that the number of primordial binaries is reduced by encounters. The core of a cluster must therefore contain a very high binary fraction initially if a large fraction of the massive stars are to be contained within binaries when the 50-M-circle dot star is produced.