  The tenuous atmospheres of the Galilean satellites are sourced from their
surfaces and produced by a combination of plasma-surface interactions and
thermal processes. Though thin, these atmospheres can be studied via their
auroral emissions, and most work to date has focused on their aurora at UV
wavelengths. Here we present the first detections of Ganymede's and Callisto's
optical aurorae, as well detections of new optical auroral lines at Europa,
based on observations of the targets over ten Jupiter eclipses from 1998 to
2021 with Keck/HIRES. We present measurements of OI emission at 6300/6364,
5577, 7774, and 8446 A and place upper limits on hydrogen at 6563 A. These
constitute the first detections of emissions at 7774 and 8446 A at a planetary
body other than Earth. The simultaneous measurement of multiple emission lines
provides robust constraints on atmospheric composition. We find that the
eclipse atmospheres of Europa and Ganymede are composed predominantly of O2
with average column densities of (4.1 \pm 0.1) x 10^{14} cm^{-2} and (4.7 \pm
0.1) x 10^{14} cm^{-2}, respectively. We find weak evidence for H2O in Europa's
bulk atmosphere at an H2O/O2 ratio of $\sim$0.25, and place only an upper limit
on H2O in Ganymede's bulk atmosphere, corresponding to H2O/O2 < 0.6. The column
density of O2 derived for Callisto is (4.0 \pm 0.9 x 10^{15} cm^{-2} for an
assumed electron density of 0.15 cm^{-3}, but electron properties at Callisto's
orbit are very poorly constrained.
