  We report the results of a systematic search for ultra-faint Milky Way
satellite galaxies using data from the Dark Energy Survey (DES) and Pan-STARRS1
(PS1). Together, DES and PS1 provide multi-band photometry in
optical/near-infrared wavelengths over ~80% of the sky. Our search for
satellite galaxies targets ~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. While satellite galaxy searches have been performed independently on
DES and PS1 before, this is the first time that a self-consistent search is
performed across both data sets. We do not detect any new high-significance
satellite galaxy candidates, while recovering the majority of satellites
previously detected in surveys of comparable depth. 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.
