Atmospheric escape

Atmospheric escape removes gas from a planet through thermal motion, hydrodynamic outflow, photochemistry, and interactions with stellar radiation and plasma.

Nonthermal atmospheric escape supplies particle energy through processes other than the local thermal distribution. Examples include dissociation producing fast atoms, ion pickup by a stellar-wind electric field, and sputtering caused by impacting energetic particles. Radiation pressure can also accelerate material in an extended exosphere.

Jeans escape is collisionless atmospheric escape by particles in the high-speed tail of a thermal distribution at the exobase. The Jeans escape parameter $\lambda =GMm/(k_{B}T{r}_e)$ controls the exponential suppression, and the Jeans escape flux is proportional to $(1+\lambda )e^{-\lambda }$. There is no exact positive-temperature threshold below which the tail vanishes. For $\lambda$ of order a few or smaller, a purely hydrostatic tail model can fail and hydrodynamic atmospheric escape becomes important.

The exosphere is the dilute outer atmospheric region in which a particle can travel a substantial distance without a collision. Its lower boundary, the exobase, is near equality of the mean free path and the local atmospheric scale height. Escaping and gravitationally bound trajectories can coexist.

The exobase marks the transition between a collisional atmosphere and its exosphere. For a neutral, approximately hydrostatic ideal gas, take mean free path $\ell \simeq 1/(n{\sigma }_c)$ and atmospheric scale height $H=k_{B}T/(mg)$. The criterion $\ell \sim H$ givesAn order-one collision convention can change this coefficient. The pressure is not universal: the collision cross-section, composition, local gravity, and ionization must be specified. A strongly escaping, non-hydrostatic atmosphere requires an appropriate density-gradient length instead of a hydrostatic $H$.

For particles of mass $m$ at radius $r$ and temperature $T$, the Jeans escape parameter isLarge $\lambda$ gives weak tail escape, while order-unity $\lambda$ indicates hydrodynamic blow-off.

For exobase number density $n_e$ and $v_{\mathrm{th}}=\sqrt{2k_{B}T/m}$, the collisionless Jeans number flux is

Hydrodynamic atmospheric escape is a collisional transonic outflow in which bulk gas carries multiple species away. It replaces the hydrostatic Jeans-tail description when gravity is weak compared with thermal energy.

Energy-limited atmospheric escape equates a fraction $\eta$ of absorbed high-energy stellar power to the gravitational work needed to remove gas. Ignoring tidal and cooling corrections gives $\dot{M}=\eta \pi R_{\mathrm{EUV}}^2{F}_{\mathrm{EUV}}{R}_p/(G{M}_p)$.