investigate how such conditions could affect the ‘standard’ picture of primordial star formation. In a Pop. III analogue of the studies on present-day star formation, we will look at how subsonic turbulence affects the collapse of marginally super-critical Bonnor-Ebert spheres, in an attempt to quantify the effects of turbulently induced fragmentation on the mass function of Pop. III stars. Central to this study will be the use of the sink particles to allow us to capture the evolution of the gas cloud beyond the collapse of the first region.

The paper is laid out in the following manner. Our modifications to the cosmological SPH code Gadget 2 [@springel05] are outlined in §\[sec:gadget2\] (with further details of the chemical networks and heating and cooling described in the Appendix). The initial conditions for this numerical experiment are described in §\[sec:ics\], including the definitions of Pop. III.1 and III.2 that are used in our study. The details of the fragmentation process seen in the simulations are discussed in §\[sec:frag\] and the long-term chemical and thermodynamical evolution of the infalling envelope are described in §\[sec:evol\]. We discuss the implications of this study for the initial mass function (IMF) of primordial stars in §\[sec:chat\], and 