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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 $H$.

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.

For an unclustered population of fully covering circular disc absorbers, the inverse mean free path is proper number density times mean projected area. A comoving number density must first be multiplied by $(1+z{)}^3$. The incidence then constrains the proper radius; covering factor and multiplicity of detectable lines can change the inference.

In the collisionless exosphere, an atom escapes if its outward trajectory has positive total mechanical energy. Neglect tides and stellar forces and use Newtonian gravity at exobase radius $r_e$:With thermal speed $v_{\mathrm{th}}=\sqrt{2k_B{T}_e/m}$, the Jeans escape parameter isA thermal distribution always has an escaping tail; Jeans escape is exponentially suppressed for ${\lambda }_e\gg 1$, with Jeans escape flux proportional to $(1+{\lambda }_e)e^{-{\lambda }_e}$. Efficient escape requires ${\lambda }_e$ of order a few or smaller, with an order-unity energetic estimate $k_B{T}_e\sim G{M}_{p}m/r_e$.

Assume a Neptune-like mass and radius, $r_e\simeq R_p$, and atomic hydrogen. Using the supplied rounded constants givesHenceUsing the mean kinetic energy $3k_{B}T/2$ instead gives an order-unity coefficient and $T\simeq 2.3\times 10^4\mathrm{K}$. An expanded exobase has weaker binding and lowers the estimate by $R_p/r_e$. A comet-like tail can also be shaped by radiation pressure and stellar-wind interactions; it does not by itself measure $T_e$ or prove that a hydrostatic Jeans model is valid. At ${\lambda }_e\sim 1$, $H/r_e\sim 1$ and hydrostatic equilibrium fails as a global description: substantial mass loss must usually be treated as hydrodynamic atmospheric escape.

The exobase is defined by mean free path $\ell \sim H$, not by a universal pressure. For a neutral hydrostatic gas with collision cross-section ${\sigma }_c$,For example, explicitly assuming ${\sigma }_c\sim 10^{-19}\text{–}10^{-20}{\mathrm{m}}^2$ gives $P_e\sim 2\times 10^{-7}\text{–}2\times 10^{-6}\mathrm{Pa}$, or $2\times 10^{-12}\text{–}2\times 10^{-11}\mathrm{bar}$. These are representative extremely dilute neutral-exobase pressures, with orders of magnitude varying with composition, cross-sections and expansion. The supplied constants contain no collision information, so they cannot uniquely determine an exobase pressure; ionization or a non-hydrostatic density profile changes this estimate.