= Temperature from a transmission-band amplitude
{title2=$T\simeq\frac{\mu m_ug\,\Delta D R_\star^2}{2k_BR_pN_H}$}
For a thin hydrostatic <isothermal atmosphere>, $\Delta D\simeq2R_pN_HH/R_\star^2$ and $H=k_BT/(\mu m_ug)$. Hence $T\simeq\mu m_ug\Delta D R_\star^2/(2k_BR_pN_H)$. A measured <exoplanet transmission spectrum> amplitude constrains $N_HH$, so gravity, mean molecular mass and the number $N_H$ of sampled <atmospheric scale heights> are additional inputs. In a clear fixed-composition model, $N_H\simeq\log(\kappa_{\rm band}/\kappa_{\rm cont})$; clouds or abundance gradients can change it.
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