Robust active galactic nucleus and host-galaxy decomposition in optical spectral fitting

Unraveling the growth of supermassive black holes and their connection to host galaxies requires disentangling the active galactic nuclei (AGN) emission from that of the stellar populations in which they are embedded. When an AGN spectrum is observed at different activity phases, if the spectral decomposition properly recognizes the nuclear and stellar components, key physical properties — such as black hole mass, stellar mass, and stellar velocity dispersion — should remain consistent. These quantities are essential for scaling relations used to study the co-evolution of black holes and galaxies. We present a novel optical spectral-fitting approach that combines and to robustly decompose spectra into stellar and AGN components. We applied this technique to three Sloan Digital Sky Survey samples with repeated optical spectra of the same objects at złeq0. 55: 32 changing-look AGN in bright and dim states and 15 quasars and 15 galaxies with three single-epoch and one stacked spectrum each and spanning a range of signal-to-noise ratios. For comparison with the literature, we also used SDSS spectra and photometric data from AGN in the eFEDS field as well as Gemini and VLT observations of some of our selected changing-look AGN. This analysis enabled us to evaluate the reliability of stellar mass, velocity dispersion, and black hole mass measurements, especially in relation to the AGN-to-total continuum contribution (f_ pPXF PyQSOFit AGN). For host-derived properties, especially when f_ AGN <0. 8, our method yields consistent results. For single-epoch black hole mass estimates from Hα and Hβ, a 3σ confidence in the broad-line flux and full width at half maximum provides effective criteria for selecting reliable measurements. The reliability of our measurements was confirmed by their alignment with previously established scaling relations. Many changing-look AGN in our sample exhibit ``breathing'' broad-line regions, as determined from Hα analysis, while some deviate significantly, suggesting non-virialized systems across the spectral transition.