The cosmic shoreline: the evidence that escape determines which planets have atmospheres, and what this may mean for Proxima Centauri b

Abstract: The planets of the Solar System divide neatly between those with atmospheres and those without when arranged by insolation ($I$) and escape velocity ($v_{\mathrm{esc}}$). The dividing line goes as $I \propto v_{\mathrm{esc}}^4$. Exoplanets with reported masses and radii are shown to crowd against the extrapolation of the Solar System trend, making a metaphorical cosmic shoreline that unites all the planets. The $I \propto v_{\mathrm{esc}}^4$ relation may implicate thermal escape. We therefore address the general behavior of hydrodynamic thermal escape models ranging from Pluto to highly-irradiated Extrasolar Giant Planets (EGPs). Energy-limited escape is harder to test because copious XUV radiation is mostly a feature of young stars, and hence requires extrapolating to historic XUV fluences ($I_{\mathrm{xuv}}$) using proxies and power laws. An energy-limited shoreline should scale as $I_{\mathrm{xuv}} \propto v_{\mathrm{esc}}^3\sqrt{\rho}$, which differs distinctly from the apparent $I_{\mathrm{xuv}} \propto v_{\mathrm{esc}}^4$ relation. Energy-limited escape does provide good quantitative agreement to the highly irradiated EGPs. Diffusion-limited escape implies that no planet can lose more than 1% of its mass as H$2$. Impact erosion, to the extent that impact velocities $v{\mathrm{imp}}$ can be estimated for exoplanets, fits to a $v_{\mathrm{imp}} \approx 4\,-\,5\, v_{\mathrm{esc}}$ shoreline. The proportionality constant is consistent with what the collision of comet Shoemaker-Levy 9 showed us we should expect of modest impacts in deep atmospheres. With respect to the shoreline, Proxima Centauri b is on the metaphorical beach. Known hazards include its rapid energetic accretion, high impact velocities, its early life on the wrong side of the runaway greenhouse, and Proxima Centauri's XUV radiation. In its favor is a vast phase space of unknown unknowns.