Constraint on the location of the emitting region r in centimeters, defined as the distance from the SMBH, as a function of the bulk Lorentz factor Γ. The red exclusion region represents the opacity constraint, the blue exclusion region represents the collimation constraint, and the orange exclusion region represents the cooling constraint, the last two computed for τ_var = 6 h. Dashed lines show how the constraints change assuming τ_var = 2 h. The white regions indicate the allowed part of the parameter space. The vertical black lines represents the estimated locations of the BLR r_BLR and of the dust torus r_torus. The green star identifies the parameters of the EIC solution discussed in Sect. 3.2 and plotted in Fig. 5.