the sink particles are on average more massive than their Pop.  III.1 counterparts since they have less competition for the available mass. (bottom) The combined mass function for the two simulations.](fig10a){height="2.5in"}

![\[fig:sinkmf32big\] (top) Mass functions for our two 1000 Pop.  III.2 clouds. As with the Pop.  III.1 data in Fig. \[fig:sinkmf\], we show the mass function after 100 of gas has been accreted by the sink particles. Due to the reduced fragmentation in these calculations, the sink particles are on average more massive than their Pop.  III.1 counterparts since they have less competition for the available mass. (bottom) The combined mass function for the two simulations.](fig10b){height="2.5in"}

![image](fig11a){width="2.5in"} ![image](fig11b){width="2.5in"}

![image](fig11c){width="2.5in"} ![image](fig11d){width="2.5in"}

![image](fig12a){width="3.5in"} ![image](fig12b){width="3.5in"}

Initial conditions {#sec:ics}
==================

Since the aim of this study is to investigate the fragmentation properties of primordial gas, we use initial conditions that allow us to perform a controlled numerical experiment. The clouds start as unstable Bonnor-Ebert (BE) spheres into which we inject a subsonic turbulent velocity field. The BE sphere is made by allowing a gravitationally stable cloud of gas to evolve under its own self-gravity until the system has settled into a stable, centrally condensed configuration. During this initial settling phase, the gas temperature is 