On the emergent system mass function: the contest between accretion and fragmentation

We propose a new model for the evolution of a star cluster's system mass function (SMF). The model involves both turbulent fragmentation and competitive accretion. Turbulent fragmentation creates low-mass seed proto-systems (i.e. single and multiple protostars). Some of these low-mass seed proto-systems then grow by competitive accretion to produce the high-mass power-law tail of the SMF. Turbulent fragmentation is relatively inefficient, in the sense that the creation of low-mass seed proto-systems only consumes a fraction, similar to 23 per cent (at most similar to 50 per cent), of the mass available for star formation. The remaining mass is consumed by competitive accretion. Provided the accretion rate on to a proto-system is approximately proportional to its mass (dm/dt proportional to m), the SMF develops a power-law tail at high masses with the Salpeter slope (similar to-2.3). If the rate of supply of mass accelerates, the rate of proto-system formation also accelerates, as appears to be observed in many clusters. However, even if the rate of supply of mass decreases, or ceases and then resumes, the SMF evolves homologously, retaining the same overall shape, and the high-mass power-law tail simply extends to ever higher masses until the supply of gas runs out completely. The Chabrier SMF can be reproduced very accurately if the seed proto-systems have an approximately lognormal mass distribution with median mass similar to 0.11M(circle dot) and logarithmic standard deviation sigma(log10(M/M circle dot)) similar to 0.47).

Automated summary

The model proposed explains the evolution of a star cluster's SMF involving turbulent fragmentation and competitive accretion, where low-mass seed proto-systems grow into high-mass stars through accretion. The overall shape of the SMF remains consistent even with varying mass supply rates, with the high-mass tail extending as long as gas supply lasts.