## 6. Discussion: why are the forbidden and fine-structure lines so important?
It seems to be a paradox: the permitted lines typically have radiative
transition probabilities 4 ... 10 orders of magnitudes larger than the
forbidden and fine-structure lines, but do not dominate the radiative
heating and cooling according to the results of this
paper In the following, we will briefly discuss the radiative cooling by spectral lines in two important limiting cases. We neglect bound-free transitions, which enables us to evaluate the bound-bound radiative heating/cooling rate either from Eq. (6) or, alternatively, from Eq. (12):
Eq. (26) states that the cooling rates of spectral lines are not at
all dependent on the number or the properties of the lines but do only
depend on the collisional properties of its carrier in this
case -
the cooling rates linearly depend on (roughly ), favouring abundant elements (e. g. C, N, O), -
most important contributions come from those *upper levels**u*which have (implying ). Therefore, the most efficient cooling lines are expected to be low-excitation lines in the infrared (e. g. at*µ*m for ).
Eq. (27) states that the line-cooling does not depend on the
density of the carrier, nor on the "strength" of the lines (the
Einstein coefficients
) -
the cooling rates depend linearly on , -
the cooling rates are roughly density-independent, which means that the cooling rate per mass decreases linearly with increasing density (hence, trace elements may be as important as abundant elements), -
the cooling rates depend linearly on the *number of lines*in the spectral region . The most efficient cooling lines in this case are therefore expected to lie in the optical spectral region (e. g. at nm for ).
In both considered limiting cases, the radiative cooling by spectral lines does not depend on the strength of the lines, e. g. permitted lines are in fact not favoured. In contrast, the other listed criteria (i. e. the number of lines in case 2 and especially the low excitation energy in case 1) in fact suggest that forbidden and fine-structure lines are more important in both limiting cases. © European Southern Observatory (ESO) 1999 Online publication: June 30, 1999 |