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Incoming links: Nonthermal atmospheric escape
Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 315 4 b Solution Created 2026-10-03 Updated 2026-10-06
Four mechanisms are Jeans escape, hydrodynamic escape, Roche-lobe overflow and nonthermal atmospheric escape.
Jeans escape is loss from the high-speed tail of a nearly Maxwell-Boltzmann velocity distribution near the exobase. It is sensitive to the escape parameter and favors light species in a hot, weakly bound atmosphere.
Hydrodynamic escape occurs when strong XUV heating drives a bulk outflow, which can entrain heavier species. An illustrative energy-limited scale is when the absorption and planet radii are comparable; efficiency, radiative losses and recombination can invalidate that simple limit.
Roche-lobe overflow removes gas through the low effective-potential barrier toward the inner Lagrange point when the extended atmosphere approaches the Roche lobe. Tides can also assist a wind before actual overflow.
Nonthermal atmospheric escape includes ion pickup, sputtering, charge exchange and energetic photochemical products. Stellar-wind interactions and photoionization supply particles with escape energies not represented by the local thermal tail. These mechanisms can act together rather than constituting four mutually exclusive evolutionary states.
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 2 a ii Solution 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, , 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.