Electron cooling by carbon monoxide in the atmospheres of Mars and Venus
© Campbell et al. 2008
Received: 15 November 2007
Accepted: 04 February 2008
Published: 04 February 2008
Electron cooling, in which free electrons lose energy to vibrational excitation of gases, has been identified as a significant process in the atmospheres of Mars and Venus for electron impact on CO2. This process does not appear to have been evaluated for CO, although the density of CO exceeds that of CO2 in the upper atmospheres of these planets. In this paper electron cooling rates for CO are calculated and compared with existing rates for CO2. It is found that electron cooling by CO becomes more significant than by CO2 above altitudes of about 300 km on Mars and about 168 km on Venus. The sensitivity of the calculated cooling rates to different measurements of the integral cross sections for electron-impact vibrational excitation of CO is also investigated.
PACS Codes: 34.80.Gs, 96.12.Jt
Morrison and Greene  identified electron cooling by electron impact excitation of CO2 as an important energy transfer process in the atmospheres of Mars and Venus. They presented electron energy loss rates (i.e. cooling rates per unit electron and molecule density) as a function of electron temperature. The rate was calculated at each temperature by averaging over the electron energy distribution, assumed to be Maxwellian. These rates can be multiplied by the electron and CO2 densities to give the electron cooling rates in an actual atmosphere. Strangeway  used the electron energy loss rates of Morrison and Greene in modeling the ionosphere of Venus.
Measurements have been made of the densities of CO2 and CO in the atmospheres of Mars and Venus. Laboratory measurements have been made of the integral cross sections for vibrational excitation of CO by low-energy electrons. Hence it is now possible to assess the extent of electron cooling by CO, relative to that by CO2. In this paper we review the available data for the cross sections and atmospheric parameters, then use them to calculate electron cooling rates in the atmospheres of both planets. It is found that electron cooling by CO is greater than by CO2 above altitudes of 300 km on Mars and above 168 km on Venus.
The sensitivity of the results to different available cross sections is also investigated. At heights where cooling by CO is significant compared to that of CO2, differences of up to 35% arise from using different cross-section sets for CO. At lower altitudes, where the cooling by CO is much smaller than that of CO2, the differences due to different cross-section sets are much larger. While this is not of any great consequence in the calculation of cooling rates, it is expected to be important in predictions of infrared emissions by CO.
Results and discussion
Electron impact vibrational excitation of CO
Integral cross sections for electron impact vibrational excitation of CO (0 → ν') were measured by Schulz  for ν' = 1 – 8 and by Ehrhardt et al.  for ν = 1 – 7. Schulz did not give absolute values for individual vibrational levels, but it can be deduced by analysis of the presented graphs that Schulz measured a maximum cross section for 0 → 1 of 3.6 × 10-16 cm2 at 1.75 eV. Schulz suggested that this could be in error by a factor of 2. Ehrhardt et al. deduced a maximum cross section for 0 → 1 of 3.5 × 10-16 cm2 at ~1.83 eV. Subsequent measurements for 0 → 1 excitation were reviewed by Brunger and Buckman , including absolute measurements by Gibson et al.  which give a cross section of 4.874 × 10-16 cm2 at 1.91 eV. Recently Poparić et al.  made measurements for ν' = 1 – 10, but normalised to the data of Gibson. et al. Hence there is only one recent measurement of the absolute integral cross section, which is ~35% higher than earlier values.
Atmospheric parameters of Mars and Venus have been measured by various spacecraft since 1976. The measurements required to calculate electron cooling rates are the electron temperature and the densities of CO2, CO and for the free electrons.
Electron energy transfer rates
The transfer rates due to rotational excitation (J = 0 → 1), calculated using the cross sections presented by Randell et al. , are also shown in figure 8. These rates are small compared to the 0 → 1 vibrational excitations, except at very low electron temperatures.
Calculation of cooling rates
The cooling rates due to the rotational excitation J = 0 → 1 in CO are also shown in figure 9. They are not significant relative to those of CO2 at any height and so are not considered further.
The cooling rates due to CO(0 → 1) are substantially less than those for CO2 below ~280 km, but are greater above 300 km. The cooling rates due to CO(0 → ν', ν' = 2 – 10) are much smaller again at the lower altitudes but exceed those of CO2 at altitudes above ~310 km. At the heights where the CO cooling is significant, there is little difference between the rates for 0 → 1 excitation for the two different cross-section sets, as expected given their similarity at higher temperatures. For excitation to higher levels the cooling rates are about 35% higher for the cross sections of Poparić et al., consistent with their higher values for the cross sections. As both of these comparisons are dependent on the same normalisation to the values of Gibson et al, it would be useful if another independent measurement of the absolute cross sections for CO could be made.
The cross sections of Allan lead to higher cooling rates in the altitude range 100–156 km for the 0 → 1 excitation and below ~168 km for the higher levels (ν' = 2 – 10). As at these heights the CO cooling rates are insignificant compared to those of CO2, these differences are inconsequential as far as calculations of cooling rates are concerned. However, as the infrared emissions due to radiative decay following excitation are related to the excitation rate, the differences are worth noting in case the infrared emissions from CO can be measured with sufficient sensitivity. In this case it would be useful to resolve the differences at low energy between the measurements of Allan and those of Poparić et al.
Electron cooling rates due to CO in the atmospheres of Mars and Venus have been calculated using two sets of electron impact cross sections for vibrational excitation. It was found that above ~300 km in the atmosphere of Mars and above ~168 km in the atmosphere of Venus, the cooling rates due to CO(0 → 1) exceed the total rate for all excitations of CO2. In each case at a slightly greater height the cooling rate due to electron-impact excitation to the higher vibrational levels of CO is also greater than for all levels of CO2. At the heights where the cooling rate due to CO is significant, there are differences of up to ~35% between the rates calculated with the two different cross-section sets, so more definitive values of the absolute CO cross sections would be useful for accurate modeling of cooling rates. There are much larger differences between the cooling rates calculated with the different cross section sets at altitudes with lower electron temperatures. While these differences are of no concern for the calculation of electron cooling rates, which are dominated by CO2 at these altitudes, they would make a difference to the calculated CO infrared emissions. In this case it would be useful to resolve the differences between experimental measurements of the CO cross sections at low energy.
This work was supported by the Australian Research Council.
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