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 $0leq x_{mathrm{AGN}} < 1$ of the monochromatic luminosity at $lambda_0=$ 4020 AA. In addition to a set of fits for PL distributions $F_{ u} propto u^{-alpha}$ 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.
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