Construction of the Damped Ly$α$ Absorber Catalog for DESI DR2 Ly$α$ BAO

We present the Damped Ly$α$ Toolkit for automated detection and characterization of Damped Ly$α$ absorbers (DLA) in quasar spectra. Our method uses quasar spectral templates with and without absorption from intervening DLAs to reconstruct observed quasar forest regions. The best-fitting model determines whether a DLA is present while estimating the redshift and HI column density. With an optimized quality cut on detection significance ($Δχ_{r}^2>0.03$), the technique achieves an estimated 80% purity and 79% completeness when evaluated on simulated spectra with S/N~$>2$ that are free of broad absorption lines (BAL). We provide a catalog containing candidate DLAs from the DLA Toolkit detected in DESI DR1 quasar spectra, of which 21,719 were found in S/N~$>2$ spectra with predicted $\log_{10} (N_\texttt{HI}) > 20.3$ and detection significance $Δχ_{r}^2 >0.03$. We compare the Damped Ly$α$ Toolkit to two alternative DLA finders based on a convolutional neural network (CNN) and Gaussian process (GP) models. We present a strategy for combining these three techniques to produce a high-fidelity DLA catalog from DESI DR2 for the Ly$α$ forest baryon acoustic oscillation measurement. The combined catalog contains 41,152 candidate DLAs with $\log_{10} (N_\texttt{HI}) > 20.3$ from quasar spectra with S/N~$>2$. We estimate this sample to be approximately 85% pure and 79% complete when BAL quasars are excluded.