We investigate the properties of the hydrodynamic flow around eccentric protoplanets and compare them with the often assumed case of a circular orbit. To this end, we perform a set of 3D hydrodynamic simulations of protoplanets with small eccentricities ($eleq 0.1$). We adopt an isothermal equation of state and concentrate resolution on the protoplanet to investigate flows down to the scale of the protoplanets circumplanetary disk (CPD). We find enhanced prograde rotation exterior to the CPD for low planet masses undergoing subsonic eccentric motion. If the eccentricity is made large enough to develop a bow shock, this trend reverses and rotation becomes increasingly retrograde. The instantaneous eccentric flow field is dramatically altered compared to circular orbits. Whereas the latter exhibit a generic pattern of polar inflow and midplane outflow, the flow geometry depends on orbital phase in the eccentric case. For even the modest eccentricities tested here, the dominant source of inflow can come from the midplane instead of the poles. We find that the amount of inflow and outflow increases for higher $e$ and lower protoplanet masses, thereby recycling more gas through the planets Bondi radius. These increased fluxes may increase the pebble accretion rate for eccentric planets up to several times that of the circular orbit rate. In response to eccentric motion, the structure and rotation of the planets bound CPD remains unchanged. Because the CPD regulates the eventual accretion of gas onto the planet, we predict little change to the gas accretion rates between eccentric and circular planets.
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