 Atmospheric scale height

The atmospheric scale height measures how quickly pressure decreases upward. In an isothermal ideal gas with nearly constant gravitational acceleration, hydrostatic equilibrium givesHere $k_B$ is the Boltzmann constant, $T$ the temperature, $\mu m_H$ the mean particle mass, and $g$ the gravitational acceleration. Rising by one atmospheric scale height reduces pressure and number density by a factor $e$. Hotter, lighter gas has a larger atmospheric scale height; stronger gravity compresses it.

For a thin exoplanet atmosphere, a feature spanning $N_H$ such heights contributes roughly $2R_p{N}_{H}H/R_{\star }^2$ to the exoplanet transit depth. This explains why light molecular hydrogen-rich envelopes are favourable for transit spectroscopy. It is the atmospheric application of the general scale height.