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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-315/2/a/ii/solution

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Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 315 / 2 / a / ii / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-06

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, $\dot{M} \sim η π R_{abs}^{2} F_{XUV} R_{p} / (G M_{p})$ , 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.

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.

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