The evolution of galaxies appears linked to the growth of supermassive black holes (SMBH), as evidenced by empirical scale relations between hosts' large-scale properties and the mass of their central black holes. This co-evolutionary scenario suggests that all galaxies experience nuclear activity — active phases during which the black hole accretes material from the host galaxy and grows. At the same time, feedback from active galactic nuclei (AGN) impacts the general properties of their host galaxies, either enhancing or quenching star formation and controlling the gas cooling processes.

The characterization of AGN and their host galaxies provides key constraints and valuable insights into this model. Integral field spectroscopic (IFS) observations of type I AGN are particularly well-suited for exploring the co-growth scenario. Data cubes from IFS enable the estimation of both the properties of the host galaxy and the mass of the central SMBH through the application of the single-epoch virial method.

However, hosts are generally strongly outshined by their central bright AGN, and studying their properties/parameters (e.g. luminosity, stellar velocity dispersion) requires an accurate removal of the AGN emission. In this context, a comprehensive understanding of the point-spread function (PSF) across the entire spectral range (3D-PSF) of the IFS data becomes crucial for AGN-host spectra deblending.

The broad component of the type I AGN emission lines serves as a basis for generating a PSF image, supporting the PSF characterization at a reference narrow-band filter. To recover the 3D-PSF, the parametrized PSF is extended to distinct wavelengths taking advantage of the well-characterized behaviour of the atmospheric turbulence with wavelength. Each slice is then scaled to the AGN flux at each wavelength, a flux determined by fitting the spectrum obtained from a 2 arcsec radius circular aperture from the IFS data cube. This procedure provides the pure-AGN data cube as observed by the instrument in the absence of any host contribution, allowing the easy removal of the AGN contribution from the host-galaxy spectra.

In this presentation, we explain our innovative deblending method and showcase its efficacy through the application on MUSE observations of three type I AGN—specifically, NGC7469, MRK1044, and MRK926.