Orbital evolution of eccentric perturbers under dynamical friction: crossing the sound barrier

In a gaseous medium, dynamical friction (DF) reaches a maximum when the orbital speed of a (point-like) perturber moving on a circular orbit is close to the sound speed. Therefore, in a quasi-steady state, eccentric orbits of perturbers approaching the sound barrier (from below) should rapidly circularize as they experience the strongest drag at pericenter passage. To investigate this effect, we extend the solution of Desjacques et al. 2022 for circular DF in a uniform gaseous medium to eccentric Keplerian orbits. We derive an approximation to the steady-state DF force, which is valid for eccentricities as high as $e=0.9$ in a limited range of Mach number around the transition to supersonic regime. We validate our analytical result with 3-dimensional simulations of the gas density response. Although gaseous DF generally dissipates orbital energy, we find that it can be directed along the motion of the perturber near pericenter passage when the eccentricity is $e\gtrsim 0.9$. We apply our results to compute the long-time evolution of the orbital parameters. Most trajectories tend to circularize as the perturber moves into the supersonic regime. However, orbits with eccentricities $e\gtrsim 0.8$ below the sound barrier experience a slight increase in eccentricity as they loose orbital energy. Possible extensions to our analytical approach are also discussed.