Emission Line Predictions for Mock Galaxy Catalogues: a New Differentiable and Empirical Mapping from DESI

Estimating the incompleteness of spectroscopic redshift training sets via mock galaxy catalogs is critical for characterizing photometric redshifts from LSST. Predicting the stellar continua of large mock galaxy catalogs is fairly well-understood, however, predicting emission lines with photoionization models remains difficult and computationally infeasible. We adopt an empirical approach for estimating the line strengths of strong optical emission lines using synthetic medium-band spectrophotometry of DESI Early Release data. Our method reproduces the observed emission line strength distributions and their distributions in the BPT diagram when accounting for observational uncertainties, demonstrating the utility of such a method.