= Radiative relaxation time in a planetary atmosphere
{title2=$\tau_{\rm rad}$}
A column near <pressure> $p$ contains mass per area of order $p/g$. Linearizing its <blackbody> cooling around <temperature> $T$ gives the estimate
$$
\tau_{\rm rad}\sim\frac{c_pp}{4g\sigma_{\rm SB}T^3},
$$
where $c_p$ is <specific heat capacity at constant pressure>. This estimate omits details of wavelength-dependent <radiative transfer>, but captures faster relaxation in hotter and lower-pressure atmospheric layers.
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