Excitation temperature

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

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

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 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".^[1]

References

↑ Dickey, J. M.; Mebold, U.; Stanimirovic, S.; Staveley‐Smith, L. (2000). "Cold Atomic Gas in the Small Magellanic Cloud". The Astrophysical Journal 536 (2): 756. doi:10.1086/308953.

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