underpredict the number density of $L_\mathrm{X}\approx10^{43.5-44.5}$[$\mathrm{erg\;s^{-1}}$]{} AGNs, and the observed faint-end slope is somewhat flatter than our prediction.

Model B {#sec:modelB}
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In our second model (B), we adopt a more realistic scaling relation between the SMBH mass, [${\mathcal{M}_\mathrm{bh}}$]{}, and host stellar mass, [${\mathcal{M}_*}$]{}, that allows for intrinsic scatter in the relationship. We adopt an intrinsic scatter of 0.38 dex, consistent with measurements of the local relationship between spheroid stellar mass, $\mathcal{M}_\mathrm{spheroid}$, and [${\mathcal{M}_\mathrm{bh}}$]{} by @Bennert11b. This work used updated dynamical [${\mathcal{M}_\mathrm{bh}}$]{} estimates from @Gultekin09 for a sample of 18 local elliptical and S0 galaxies; spheroid stellar masses were estimated using the $J$, $H$ and $K$ magnitudes measured by @Marconi03 and the @Auger09 Bayesian stellar mass estimation code. We note that the @Bennert11b relationship was measured using the spheroid (bulge) stellar masses, but we assume that the same intrinsic scatter can be applied to the total stellar mass - SMBH mass relationship.

In model B we assume this 0.38 dex scatter in the [${\mathcal{M}_\mathrm{bh}}$]{}-[${\mathcal{M}_*}$]{} relationship to convert between $\lambda$ and Eddington ratio, applying a sharp cutoff in the probability of a galaxy hosting an AGN above the Eddington limit. The scatter in [${\mathcal{M}_\mathrm{bh}}$]{}-[${\mathcal{M}_*}$]{} results in a much softer cutoff in 