  Protoplanets are able to accrete primordial atmospheres when embedded in the
gaseous protoplanetary disk. The formation and structure of the
proto-atmosphere are subject to the planet--disk environment and orbital
effects. Especially, when planets are on eccentric orbits, their relative
velocities to the gas can exceed the sound speed. The planets generate
atmosphere-stripping bow shocks. We investigate the proto-atmospheres on
low-mass planets with eccentric orbits with radiation-hydrodynamics
simulations. A 2D radiative model of the proto-atmosphere is established with
tabulated opacities for the gas and dust. The solutions reveal large-scale gas
recycling inside a bow shock structure. The atmospheres on eccentric planets
are typically three to four orders of magnitude less massive than those of
planets with circular orbits. Overall, however, a supersonic environment is
favorable for planets to keep an early stable atmosphere, rather than harmful,
due to the steady gas supply through the recycling flow. We also quantitatively
explore how such atmospheres are affected by the relative velocity of the
planet to the gas, the planet mass, and the background gas density. Our
time-dependent simulations track the orbital evolution of the proto-atmosphere
with the planet--disk parameters changing throughout the orbit. Atmospheric
properties show oscillatory patterns as the planet travels on an eccentric
orbit, with a lag in phase. To sum up, low-mass eccentric planets can retain
small proto-atmospheres despite the stripping effects of bow shocks. The
atmospheres are always connected to and interacting with the disk gas. These
findings provide important insights into the impacts of migration and
scattering on planetary proto-atmospheres.
