Forbidden emission line

A forbidden emission line is suppressed by the electric-dipole selection rules but can occur through weaker radiative channels such as magnetic-dipole or electric-quadrupole emission. Its relatively long-lived upper atomic level is vulnerable to collisional de-excitation in dense gas. Low-density astrophysical plasmas can therefore display strong forbidden-line emission even when laboratory dense sources do not.

For low-density gas with Maxwellian electrons, the excitation-energy difference between the ${}^1{S}_0$ and ${}^1{D}_2$ levels of doubly ionized oxygen makes $(I_{4959}+I_{5007})/I_{4363}$ temperature sensitive. A constant-collision-strength approximation is $R\simeq 7.90e^{32900\mathrm{K}/T_e}$. 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.