Excitation temperature
In statistical mechanics, the excitation temperature () is defined for a population of particles via the Boltzmann factor. It satisfies 

where 
 is the number of particles in an upper (e.g. excited) state;
 is the statistical weight of those upper-state particles;
 is the number of particles in a lower (e.g. ground) state;
 is the statistical weight of those lower-state particles;
 is the exponential function;
 is the Boltzmann constant;
 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".

References

Temperature