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The thermal optical depth increases inward, so an atmospheric thermal inversion requires $dT/d\tau <0$. Differentiating the semi-grey irradiated atmosphere profile givesTherefore the inversion criterion with intrinsic planetary flux isAn inverted layer exists at the top precisely whenFor $T_{\mathrm{int}}>0$, it extends overprovided the logarithm is positive. Otherwise the profile has no inverted interval. For a strongly irradiated hot Jupiter, $T_{\mathrm{int}}\ll T_{\mathrm{irr}}$ and the threshold is approximately $\gamma >1$; the intrinsic flux eventually restores an inward-increasing temperature at greater depth.

Large visible absorption opacity deposits stellar heat high in the exoplanet atmosphere. Gas-phase titanium monoxide and vanadium monoxide are candidate absorbers in sufficiently hot layers. An atmospheric cold trap or other condensate loss can remove them, while sufficiently high temperature and vigorous mixing can help keep them in the gas. The condition concerns absorbing opacity: highly reflective scattering alone does not deposit the required heat.

Four mechanisms that can produce disequilibrium chemistry in an exoplanet atmosphere are:

The exoplanet transport and photochemical examples follow kinetic atmosphere calculations and models including horizontal transport; the condensate example is examined in cold-trap calculations.