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Earth and Space Sciences · 术语表

什么是 Jeans escape; escape parameter？

又称： Jeans escape · escape parameter

Definition 27.5 University Earth and Space Sciences — Year 3 · 第 27 章 — Planetary Atmospheres and Habitability

Jeans escape is the loss to space of the particles of the Maxwell–Boltzmann tail that move upwards at the exobase faster than the escape velocity. The escape parameter of particles of mass $m$ at the exobase, of radius $r$ and temperature $T$ , on a planet of mass $M$ , is

\lambda = \frac{GMm}{kTr} = \frac{v_\mathrm{esc}^2}{u^2}, \qquad u = \sqrt{\frac{2kT}m},

the ratio of their gravitational binding energy to $kT$ , and also the square of the escape velocity over the most probable thermal speed $u$ .

(a) The escape parameter at the exobase against the mass of the particle, for Venus (290\, K), the Earth (1000\, K; dashed: 800 and 1600\, K, the range of the solar cycle), Mars (270\, K) and Titan (180\, K); below 2.5 (shaded) escape turns hydrodynamic. (b) The fraction (1 + )e- of the upward flux that escapes, with hydrogen, deuterium and helium at the Earth’s exobase; oxygen, at = 111, is far off the scale. — (a) The escape parameter at the exobase against the mass of the particle, for Venus ( $290\,\mathrm{K}$ ), the Earth ( $1000\,\mathrm{K}$ ; dashed: 800 and $1600\,\mathrm{K}$ , the range of the solar cycle), Mars ( $270\,\mathrm{K}$ ) and Titan ( $180\,\mathrm{K}$ ); below $\lambda \approx 2.5$ (shaded) escape turns hydrodynamic. (b) The fraction $(1 + \lambda)e^{-\lambda}$ of the upward flux that escapes, with hydrogen, deuterium and helium at the Earth’s exobase; oxygen, at $\lambda = 111$ , is far off the scale.

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