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 Å . 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 .