Black body flux for different temperatures (upper panel) and BH masses (lower panel). For L₂, T-indep. in the upper panel, $F_{{\lambda }_{\mathrm{obs}}}\propto A_{\mathrm{em}}\propto L_2\propto M_{\mathrm{BH}}^{-1/6}$, which means the BH mass only changes the normalization of the flux because T is fixed. For L₂, T-dep. in the lower panel, F_λobs has a non-trivial dependence on M_BH and $T\propto M_{\mathrm{BH}}^{-3/8}$, which means the normalization and peak of the flux are coupled through the BH mass. For the top panel, we assumed a BH mass of 10⁶ M_⊙. In the bottom panel, we chose the BH masses such that each line color matches the temperature of the fixed-temperature models. For both panels, we assumed a redshift of z = 1.