Excitation temperature

The excitation temperature (${\displaystyle T_{\rm {ex}}}$) is defined for a population of particles via the Boltzmann factor. It satisfies

${\displaystyle {\frac {n_{\rm {u}}}{n_{\rm {l}}}}={\frac {g_{\rm {u}}}{g_{\rm {l}}}}\exp {(-{\frac {\Delta E}{kT_{\rm {ex}}}})},}$

where n_u and n_l represent the number of particles in an upper (e.g. excited) and lower (e.g. ground) state, and g_u and g_l their statistical weights respectively.

Thus the excitation temperature is the temperature at which we would expect to find a system with this ratio of level populations. However it has no actual physical meaning except when in local thermodynamic equilibrium. The excitation temperature can even be negative for a system with inverted levels (such as a maser).

In observations of the 21 cm line of hydrogen, the apparent value of the excitation temperature is often called the "spin temperature".[1]