Excitation temperature

The Excitation Temperature (T_ex) (often called the spin temperature for the 21 cm line) is defined for a population of particles via the Boltzmann factor. It satisfies

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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 thermodynamical equilibrium. The excitation temperature can even be negative for a system with inverted levels (such as a maser).