= Oxygen forbidden-line temperature diagnostic
{title2=$T_e\simeq32900\,{\rm K}/\ln(R/7.90)$}
For low-density gas with Maxwellian electrons, the excitation-energy difference between the ${}^1S_0$ and ${}^1D_2$ levels of doubly ionized oxygen makes $(I_{4959}+I_{5007})/I_{4363}$ temperature sensitive. A constant-collision-strength approximation is $R\simeq7.90e^{32900\,{\rm K}/T_e}$. Increasing temperature strengthens the higher-excitation auroral line and lowers $R$. Density, <extinction> and nonthermal electrons require separate treatment; the $5007/4959$ pair shares one upper level and is primarily a branching ratio rather than this thermometer.
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