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Predicting Ly$α$ Emission from Galaxies via Empirical Markers of Production and Escape in the KBSS

Ly$α$ emission is widely used to detect and confirm high-redshift galaxies and characterize the evolution of the intergalactic medium. However, many galaxies do not display Ly$α$ emission in typical spectroscopic observations, and intrinsic Ly$α$-emitters represent a potentially biased set of high-redshift galaxies. In this work, we analyze a set of 703 galaxies at $2\lesssim z\lesssim3$ with both Ly$α$ spectroscopy and measurements of other rest-frame ultraviolet and optical properties in order to develop an empirical model for Ly$α$ emission from galaxies and understand how the probability of Ly$α$ emission depends on other observables. We consider several empirical proxies for the efficiency of Ly$α$ photon production as well as the subsequent escape of these photons through their local interstellar medium. We find that the equivalent width of metal-line absorption and the O3 ratio of rest-frame optical nebular lines are advantageous empirical proxies for Ly$α$ escape and production, respectively. We develop a new quantity, $X_\mathrm{LIS}^\mathrm{O3}$, that combines these two properties into a single predictor of net Ly$α$ emission, which we find describes $\sim$90% of the observed variance in Ly$α$ equivalent width when accounting for our observational uncertainties. We also construct conditional probability distributions demonstrating that galaxy selection based on measurements of galaxy properties yield samples of galaxies with widely varying probabilities of net Ly$α$ emission. The application of the empirical models and probability distributions described here may be used to infer the selection biases of current galaxy surveys and evaluate the significance of high-redshift Ly$α$ (non-)detections in studies of reionization and the intergalactic medium.