Fast and accurate Gaia-unWISE quasar mock catalogs from LPT and Eulerian bias

We present $100$ full-sky quasar spectrophotometric mock catalogs with smooth redshift evolution from $z=0$ to z~ 4, tailored to analyze the Gaia-unWISE Quasar Catalog (Quaia). In particular, we apply a novel hierarchical nonlocal nonlinear bias scheme (Hicobian) to dark matter fields generated through Augmented Lagrangian Perturbation Theory on the lightcone (WebON code), calibrating the free parameters of the bias model on Abacus quasar HOD mock catalogs tuned to reproduce DESI Early Data Release observations in real and redshift space. After having obtained such accurate spectroscopic catalogs, we inject in the mocks the observational effects characterizing the Quaia catalog: (i) spectrophotometric redshift uncertainties, (ii) the angular selection function, and (iii) the redshift number counts distribution. We assess the accuracy of our catalogs by validating a number of summary statistics: the full-sky QSO maps, the redshift uncertainty distributions as a function of redshift, the redshift $n(z)$ distribution, the angular power spectra and their normalized covariance matrices, and the angular two-point correlation functions. We find excellent agreement between these metrics from the mocks and from the Quaia catalog. We publicly release the mock catalogs to the community.