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.
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