Atmospheric ion escape and solar wind deposition as a function of planetary radius

ABSTRACT We explore the ability of an unmagnetized planet to retain an atmosphere as a function of its radius. We use a particle-in-cell hybrid code to simulate the global plasma interaction of unmagnetized terrestrial planets at 1 au under average solar wind conditions. We vary the radius of the planet $(R_\mathrm{ p})$ from Mars-sized ($3390 \ \mathrm{km}$) to super-Earth-sized ($9390 \ \mathrm{km}$). We inject hydrogen and oxygen ion outflows from the ionosphere and quantify how the ion escape, recirculation, solar wind deposition, and net atmospheric mass flux vary as a function of planetary radius. We find that as the radius and the corresponding ionospheric outflow rate are varied, the fraction of outflowing $\mathrm{ H^+}$ that escapes remains at $15.5\pm 1.0{{\ \rm per\, cent}}$, while the rest recirculates back towards the planet. The fraction of produced $\mathrm{ O^+}$ that escapes from a Mars-sized planet is $27\pm 1{{\ \rm per\, cent}}$, and decreases to $7\pm 1{{\ \rm per\, cent}}$ for super-Earth, suggesting that smaller planets are less able to retain heavy ions. We find, however, that larger planets have lower solar wind deposition fractions because their bow shocks are at greater distances from the surface of the planet. The ionospheric outflow rate at which mass deposition is equal to mass escape is found to be proportional to $R_\mathrm{ p}^2$. Lastly, we propose that the bulk gyration of the solar wind at the induced magnetosphere can lead to differential escape trajectories of light and heavy ions.