Milky Way Satellite Census -- I. The Observational Selection Function for Milky Way Satellites in DES Y3 and Pan-STARRS DR1

We report the results of a systematic search for ultra-faint Milky Way satellite galaxies using data from the Dark Energy Survey and Pan-STARRS1. Our search covers ~25,000 deg$^2$ of the high-Galactic-latitude sky reaching a 10$\sigma$ point-source depth of $\gtrsim$ 22.5 mag in the $g$ and $r$ bands. We do not detect any new high-significance satellite galaxy candidates, and we characterize the sensitivity of our search using a large set of simulated satellites injected into the survey data. We use these simulations to derive both analytic and machine-learning models that accurately predict the detectability of Milky Way satellites as a function of their distance, size, luminosity, and location on the sky. To demonstrate the utility of this observational selection function, we calculate the luminosity function of Milky Way satellite galaxies assuming that the known population of satellite galaxies is representative of the underlying distribution. We provide access to our observational selection function to facilitate comparisons with cosmological models of galaxy formation and evolution.