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{{refimprove|date=November 2006}}
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The '''Excitation Temperature''' (<math>T_{\rm ex}</math>) is defined for a population of particles via the [[Boltzmann factor]]. It satisfies
 
:<math>
\frac{n_{\rm u}}{n_{\rm l}} = \frac{g_{\rm u}}{g_{\rm l}} \exp{(-\frac{\Delta E}{k T_{\rm ex}})},
</math>
 
where ''n<sub>u</sub>'' and ''n<sub>l</sub>'' represent the number of particles in an upper (''e.g.'' excited) and lower (''e.g.'' ground) state, and ''g<sub>u</sub>'' and ''g<sub>l</sub>'' 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]]).
 
In observations of the [[21 cm line]], the apparent value of the excitation temperature is often called the "spin temperature".<ref>{{cite doi | 10.1086/308953}}</ref>
 
==References==
 
{{reflist}}
 
{{DEFAULTSORT:Spin Temperature}}
[[Category:Temperature]]
 
 
{{Physics-stub}}

Latest revision as of 20:46, 6 December 2014

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