 Doppler broadening

Doppler broadening is the spread of a spectral line caused by different line-of-sight emitter or absorber velocities. To first order in $v/c$, a rest-frame line at frequency ${\nu }_0$ is shifted by a magnitude ${\nu }_0|v_{\parallel }|/c$, with sign fixed by approach or recession.

For a nonrelativistic thermal gas of particles of mass $m$, a Maxwell velocity distribution gives a Gaussian line contribution with standard deviation ${\sigma }_{\nu }=({\nu }_0/c)\sqrt{k_{B}T/m}$. Its full width at half maximum is $2\sqrt{2\ln 2}{\sigma }_{\nu }$. The width can therefore constrain temperature when instrumental width, collisions and other motions are modeled. Doppler broadening is an ensemble distribution of frequency shifts, distinct from the finite-lifetime width of each emitter.