Star formation rate and SFE adopted for the FFB model as a function of halo mass and redshift (M_v, z). Left: SFR. Middle: Instantaneous SFE $ϵ\prime =\text{SFR}/(f_{\text{b}}{\dot{M}}_{\text{v}})$. Right: Integrated SFE ϵ​ = ​M_s/(f_bM_v). The SFR and the instantaneous SFE are interpolated across the FFB threshold of Eq. (2) (solid black curve), from the low SFE based on the standard UM model (B19) well below the threshold, to ϵ_max​ = ​1 well above the threshold. A smaller ϵ_max gives similar results but with correspondingly lower values for FFB galaxies. The colored area is limited to halos more abundant than 6σ peaks, with the halo masses of 2σ and 4σ peaks shown for reference (dashed lines). The integrated and instantaneous SFEs are extremely similar.