The minimum mass for opacity-limited fragmentation in turbulent cloud cores

We present a new analysis of the minimum mass for star formation, based on opacity-limited fragmentation. Our analysis differs from the standard one, which considers hierarchical fragmentation of a 3D medium, and yields M-MIN similar to 0.007 to 0.010 M-. for Population I star formation. Instead we analyse the more realistic situation in which there is one-shot fragmentation of a shock-compressed layer, of the sort which arises in turbulent star-forming clouds. In this situation, M-MIN can be smaller than 0.003 M-.. Our analysis is more stringent than the standard one in that ( a) it requires fragments to have condensation timescales shorter than all competing mass scales, and (b) it takes into acount that a fragment grows by accretion whilst it is condensing out, and therefore has to radiate away the energy dissipated in the associated accretion shock ( in addition to the PdV work done by internal compression). It also accords with the recent detection, in young star clusters, of free-floating star-like objects having masses as low as 0.003 M-..