Exclusion redshifts for various models of quasar heating. In each panel the solid lines show ﹩z_{\mathrm{ex}\,}﹩ such that ﹩\langle N_{S}( z_{\mathrm{ex}\,},\ M) \rangle =1﹩, while the dashed lines correspond (top to bottom) to z‐values such that ﹩f_{S}( z,\ M) =1-\mathrm{exp}\,[ -\langle N_{S}( z,\ M) \rangle ] =0.25﹩, 0.5, 0.75, and 0.9. The panels are labeled by their assumed ﹩\epsilon _{k}﹩‐values, and in all cases ﹩F=1﹩.