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 3-D medium, and yields $M_{{}_{\mathrm{M}\mathrm{I}\mathrm{N}}}\sim 0.007\mathrm{t}\mathrm{o}0.010M_{\odot }$ 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, $M_{{}_{\mathrm{M}\mathrm{I}\mathrm{N}}}$ can be smaller than $0.003M_{\odot }$. 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 has to radiate away the energy dissipated in the associated accretion shock. It also accords with the recent detection, in young star clusters, of free-floating star-like objects having masses as low as $0.003{\mathrm{M}}_{\odot }$.