to a DM halo mass of $\approx10^{8}M_{\sun}$ at $z\sim10$. In principle, this could be lower as the first stars are likely hosted within haloes with $M_{\rm halo}\approx 10^{6}$–$10^{7}$ $M_{\sun}$ [@Haiman:1996p2144; @Abel:2002p2149; @Bromm:2002p2153]. However, star formation within these haloes is likely inefficient (a few stars per halo) and can be quickly ($z>20$) suppressed by Lyman–Werner or other feedback processes well before the [EoR]{} [@Haiman:2000p2155; @Ricotti:2001p2160; @Haiman:2006p2169; @Mesinger:2006p2171; @Holzbauer:2012p2890; @Fialkov:2013p2903].

Here, we allow for a critical temperature threshold, $T^{\rm Feed}_{\rm vir}$, which can even be larger than $10^{4}$ K. Below $T^{\rm Feed}_{\rm vir}$ (but above $10^{4}$ K), haloes are still sufficiently large to produce low-mass galaxies; however, their potential wells are not deep enough to retain supernovae-driven outflows that quench star formation and their corresponding contribution to reionization [e.g. @Springel:2003p2176]. In this work, we allow $T^{\rm Feed}_{\rm vir}$ to vary within the range $T^{\rm Feed}_{\rm vir}\in[10^{4},2\times10^{5}]$ K, with the lower limit set by the atomic cooling threshold and the upper limit consistent with observed high-$z$ Lyman break galaxies (see for example Fig. \[fig:UVLum\]).

Likelihood statistic {#sec:likelihood}
--------------------

The offset of the 21 cm brightness temperature relative to the [CMB]{} temperature, $T_{\gamma}$ [e.g. @Furlanetto:2006p209], can be written as, $$\begin{aligned}
\delta T_{\rm b}(\nu) &=& 