Left panel: correlation of the theoretical Λ_CII function (Equation (C11)) vs. n _H. The ∝ n _H and ﹩\propto {n}_{{\rm{H}}}^{2}﹩ relations are plotted for comparison. Right panel: theoretical vs. simulation C II cooling. The red solid line is the y = x function to guide the eye. As can be seen, the majority of the Λ_CII function is well reproduced following the analytical expressions discussed in Appendix C.