![image](fig03b){height="3.4in"}

![image](fig04a){height="3.in"} ![image](fig04b){height="3.in"}

![image](fig04c){height="3.in"} ![image](fig04d){height="3.in"}

![\[fig:rhotevol\] Temperature as a function of number density for the Pop. III.1 (dark blue) and Pop. III.2 (light blue) $\Delta v_{\rm turb} = 0.1\,c_{\rm s}$ simulations. In both cases, the curves denote the state of the cloud at the point just before the formation of the sink particle. ](fig05a){height="3.0in"}

![image](fig06a){height="3.in"} ![image](fig06b){height="3.in"}

![\[fig:mdotcloud\] Accretion rates as a function of enclosed gas mass in the Pop. III.1 (upper lines; blue) and Pop. III.2 (lower lines; magenta) simulations, estimated as described in Section \[pop31\]. Note that the sharp decline in the accretion rates for enclosed masses close to the initial cloud mass is an artifact of our problem setup; we would not expect to see this in a realistic Pop. III halo.](fig07a){height="3.0in"}

![\[fig:tsf\] Time taken for the first sink particle to form in each simulation. For reference, the horizontal dashed line denotes the free-fall time of the clouds at their initial density.](fig08a){height="3.in"}

![image](fig09a){height="3.in"} ![image](fig09b){height="3.in"}

![\[fig:sinkmf32big\] (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, 