Title: 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.