Narrow-band imaging surveys allow the study of the spectral characteristics of galaxies without the need of performing their spectroscopic follow-up. In this work, we forward-model the Physics of the Accelerating Universe Survey (PAUS) narrow-band data. The aim is to improve the constraints on the spectral coefficients used to create the galaxy spectral energy distributions (SED) of the galaxy population model in Tortorelli et al. 2020. In that work, the model parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) data using Approximate Bayesian Computation (ABC). This led to stringent constraints on the B-band galaxy luminosity function parameters, but left the spectral coefficients only broadly constrained. To address that, we perform an ABC inference using CFHTLS and PAUS data. This is the first time our approach combining forward-modelling and ABC is applied simultaneously to multiple datasets. We test the results of the ABC inference by comparing the narrow-band magnitudes of the observed and simulated galaxies using Principal Component Analysis, finding a very good agreement. Furthermore, we prove the scientific potential of the constrained galaxy population model to provide realistic stellar population properties by measuring them with the SED fitting code CIGALE. We use CFHTLS broad-band and PAUS narrow-band photometry for a flux-limited ($mathrm{i}<22.5$) sample of galaxies spanning the redshift range $mathrm{0<z<1.0}$. We find that properties like stellar masses, star-formation rates, mass-weighted stellar ages and metallicities are in agreement within errors between observations and simulations. Overall, this work shows the ability of our galaxy population model to correctly forward-model a complex dataset such as PAUS and the ability to reproduce the diversity of galaxy properties at the redshift range spanned by CFHTLS and PAUS.
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