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Concept
Excitation temperature
Summary
In statistical mechanics, the excitation temperature (T_ex) is defined for a population of particles via the Boltzmann factor. It satisfies
where
nu is the number of particles in an upper (e.g. excited) state;
gu is the statistical weight of those upper-state particles;
nl is the number of particles in a lower (e.g. ground) state;
gl is the statistical weight of those lower-state particles;
exp is the exponential function;
k is the Boltzmann constant;
ΔE is the difference in energy between the upper and lower states.
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".
Official source
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