Solution (source code)

= Solution

Three physically distinct mechanisms are as follows.

* <Jeans escape>: particles in the high-speed tail of the local thermal distribution escape collisionlessly from the <exobase>. The <Jeans escape parameter> determines the exponentially small tail fraction when binding is strong. Light atoms escape more readily at fixed <temperature>.
* <Hydrodynamic atmospheric escape>: stellar extreme-ultraviolet or X-ray heating raises atmospheric <pressure> and drives an expanding bulk wind. A sufficiently strong wind entrains heavier species. An approximate <energy-limited atmospheric escape> estimate equates useful absorbed power to gravitational work, $\dot M\sim\eta\pi R_{\rm abs}^2F_{\rm XUV}R_p/(GM_p)$, but radiative losses, recombination and tides can invalidate this scaling.
* <Nonthermal atmospheric escape>: photodissociation or charge exchange produces fast atoms, while stellar-wind ion pickup and sputtering transfer energy to ions or neutrals independently of the local gas <temperature>. Magnetic geometry and stellar activity affect these channels. <Radiation pressure> can accelerate escaping neutral <hydrogen> into a tail.

\b[Thermal-tail escape, a bulk hydrodynamic wind, and nonthermal particle energization are three distinct channels; a detected tail need not distinguish them alone.] <Jeans escape> and <hydrodynamic atmospheric escape> are both thermal mechanisms in the broad sense, but have different distribution functions and dynamical assumptions.