  Various lines of evidence suggest that the cores of a large portion of
early-type galaxies (ETGs) are virtually evacuated of warm ionised gas. This
implies that the Lyman-continuum (LyC) radiation produced by an assumed active
galactic nucleus (AGN) can escape from the nuclei of these systems without
being locally reprocessed into nebular emission, which would prevent their
reliable spectroscopic classification as Seyfert galaxies with standard
diagnostic emission-line ratios. The spectral energy distribution (SED) of
these ETGs would then lack nebular emission and be essentially composed of an
old stellar component and the featureless power-law (PL) continuum from the
AGN. A question that arises in this context is whether the AGN component can be
detected with current spectral population synthesis in the optical,
specifically, whether these techniques effectively place an AGN detection
threshold in LyC-leaking galaxies. To quantitatively address this question, we
took a combined approach that involves spectral fitting with STARLIGHT of
synthetic SEDs composed of stellar emission that characterises a 10 Gyr old ETG
and an AGN power-law component that contributes a fraction $0\leq
x_{\mathrm{AGN}} < 1$ of the monochromatic luminosity at $\lambda_0=$ 4020 \AA.
In addition to a set of fits for PL distributions $F_{\nu} \propto
\nu^{-\alpha}$ with the canonical $\alpha=1.5$, we used a base of multiple PLs
with $0.5 \leq \alpha \leq 2$ for a grid of synthetic SEDs with a
signal-to-noise ratio of 5-$10^3$. Our analysis indicates an effective AGN
detection threshold at $x_{\mathrm{AGN}}\simeq 0.26$, which suggests that a
considerable fraction of ETGs hosting significant accretion-powered nuclear
activity may be missing in the AGN demographics.
