  Constraining the composition of super-Earth-to-sub-Neptune-size planets is a
priority to understand the processes of planetary formation and evolution. pi
Men c represents a unique target for the atmospheric and compositional
characterization of such planets because it is strongly irradiated and its bulk
density is consistent with abundant H2O. We searched for hydrogen from
photodissociating H2/H2O in pi Men c's upper atmosphere through H i Ly-alpha
transmission spectroscopy with the Hubble Space Telescope's STIS instrument,
but did not detect it. We set 1 (3) upper limits for the effective
planet-to-star size ratio RLy-alpha/Rearth=0.13 (0.24) and 0.12 (0.20) at
velocities [-215,-91] km/s and [+57,+180] km/s, respectively. We reconstructed
the stellar spectrum, and estimate that Men c receives about 1350 erg cm-2 s-1
of 5-912-Angstroms-energy, enough to cause rapid atmospheric escape. An
interesting scenario to explain the non-detection is that Men c's atmosphere is
dominated by H2O or other heavy molecules rather than H2/He. According to our
models, abundant oxygen results in less extended atmospheres, which transition
from neutral to ionized hydrogen closer to the planet. We compare our
non-detection to other detection attempts, and tentatively identify two
behaviors: planets with densities <2 g cm-3 (and likely hydrogen-dominated
atmospheres) result in H i Ly-alpha absorption, whereas planets with densities
>3 g cm-3 (and plausibly non-hydrogen-dominated atmospheres) do not result in
measurable absorption. Investigating a sample of strongly-irradiated
sub-Neptunes may provide some statistical confirmation if it is shown that they
do not generally develop extended atmospheres.
