Thermal Doppler broadening
= Thermal Doppler broadening
If nonrelativistic emitters of mass $m$ have rest-frame angular frequency $\omega_0$, then the one-dimensional <Maxwell-Boltzmann velocity distribution> produces a Gaussian line with standard deviation
$$
\sigma_\omega=\frac{\omega_0}{c}\sqrt{\frac{k_BT}{m}}.
$$
Measuring the line width therefore determines the gas temperature when nonthermal broadening is negligible or separately modeled.