Planting a Lyman alpha forest on AbacusSummit

The full-shape correlations of the Lyman alpha (Ly$\alpha$) forest contain a wealth of cosmological information through the Alcock-Paczy\'{n}ski effect. However, these measurements are challenging to model without robustly testing and verifying the theoretical framework used for analyzing them. Here, we leverage the accuracy and volume of the $N$-body simulation suite \textsc{AbacusSummit} to generate high-resolution Ly$\alpha$ skewers and quasi-stellar object (QSO) catalogs. One of the main goals of our mocks is to aid in the full-shape Ly$\alpha$ analysis planned by the Dark Energy Spectroscopic Instrument (DESI) team. We provide optical depth skewers for six of the fiducial cosmology base-resolution simulations ($L_{\rm box} = 2\,h^{-1}{\rm Gpc}$, $N = 6912^3$) at $z = 2.5$. We adopt a simple recipe based on the Fluctuating Gunn-Peterson Approximation (FGPA) for constructing these skewers from the matter density in an $N$-body simulation and calibrate it against the 1D and 3D Ly$\alpha$ power spectra extracted from the hydrodynamical simulation IllustrisTNG (TNG; $L_{\rm box} = 205\,h^{-1}{\rm Mpc}$, $N = 2500^3$). As an important application, we study the non-linear broadening of the baryon acoustic oscillation (BAO) peak and show the cross-correlation between DESI-like QSOs and our Ly$\alpha$ forest skewers. We find differences on small scales between the Kaiser approximation prediction and our mock measurements of the Ly$\alpha$$\times$QSO cross-correlation, which would be important to account for in upcoming analyses. The \textsc{AbacusSummit} Ly$\alpha$ forest mocks open up the possibility for improved modelling of cross correlations between Ly$\alpha$ and cosmic microwave background (CMB) lensing and Ly$\alpha$ and QSOs, and for forecasts of the 3-point Ly$\alpha$ correlation function. Our catalogues and skewers are publicly available on Globus.