Last post we produced a parameter set for each spectra line. The method of \(\mathcal{X}^2\) is useful, but will produce this parameter set regardless of wether or not the data features an actual spectra line. There are more sophisticated methods that help filter out real spectra lines from statistical fluke. However, we are not implementing these, and must instead filter the spectra lines based on our intuition and a few criteria:
- The Doppler shift in the real spectral lines should be the same, although because of the noise we do not expect them to be perfectly identical.
- Real spectral lines tend to have lower values for the minimum flux than the statistical flukes.
- We will not necessarily find every spectral line of a gas (see the table below), finding a single spectral line is fine.
- Different spectral lines from the same gas will have the same temperature (although the gases can have varying temperatures. Again, noise is sure to give some variation here.
Armed with these criteria, we attempt to find out if the following values we calculated are valid, or if we need to throw them out.
| Element | \(F_{min}\) | \(\lambda\)[nm] | Temperature [K] | |V| [m/s] |
|---|---|---|---|---|
| O2 | 0.842 | 632 | 150.00 | 10000 |
| O2 | 0.874 | 690 | 149.99 | 10000 |
| O2 | 0.921 | 760 | 149.99 | 10000 |
| H2O | 0.795 | 720 | 449.99 | 10000 |
| H2O | 0.890 | 820 | 150.00 | 10000 |
| H2O | 0.921 | 940 | 449.99 | 10000 |
| CO2 | 0.842 | 1400 | 418.41 | 10000 |
| CO2 | 0.858 | 1600 | 149.99 | 10000 |
| CH4 | 0.890 | 1660 | 450.01 | 10000 |
| CH4 | 0.905 | 2200 | 150.00 | 10000 |
| CO | 0.953 | 2340 | 150.00 | 10000 |
| N2O | 0.905 | 2870 | 449.99 | 10000 |
We get several results for the same molecule, and we expect to! Some molecules have several spectral lines. As previously mentioned, we didn't manage to find the radial velocities, we just assumed an upper velocity 10 km/s, which is the value we will continue working with.
The green elements represent those we believe are in the atmosphere, and the red those we do not, while the one black value we are a bit unsure about. As we already decided that we have water in the atmosphere, we decided this was alright. We should remember that this is difficult to say for sure, based on these results. We still try our best to reason our way toward the best results:
Oxygen, O2:
For oxygen we measure three spectral lines, all with similar temperatures, velocities, and dips we consider deep enough.
However, the first plot has a dip at the opposite point of the other two, and as the shift is a result of the Doppler effect from the motion of the flux meter, this indicates that at 
least one dip may be caused by noise. It is unlikely that the data was measured while the flux meter was moving in two different directions, after all.
In order to decide which dip is caused by noise, we note that on the first plot, there is a dip in the noise where the dip in the Gaussian line is, which may indicate that this dip is caused by noise. This is 
further backed up by the fact that this is the only plot out of three with a negative position.
Finally, the last plot has a relatively high value for the minimum flux.
Ultimately we need to look at lines from other plots before we determine which lines are realistic. The temperatures are all similar values, but if they do not match with other realistic lines, then we do not have oxygen in the atmosphere.
Water, H2O: 
We have similar values for the temperatures for all plots except the middle one, which has a much lower temperature.
The first plot seems quite certain. This isn't just one line that jumped very far down, the noise moves with the curve! We have reason to believe that this line is real. 
Again, we have dips on opposite sides. Judging from the temperature, we have reason to believe the middle plot is simply noise, which also supports the suspicion that the first oxygen plot is also noise.
Judging from the previous observation that the dips on the positive side of the x-axis are correct, and looking at these plots, we judge that lines on the negative side of the x-axis are false.
The final plot also has a relatively high value for the flux, and may be noise, though this is hard to judge.
It seems that the dips should be on the positive side of the x-axis, and that the temperature should lie somewhere around 450 K.
It looks like we do have water in the atmosphere, but that we do not have oxygen, as all the temperature values for O2 were in the 150 K range.
Carbon dioxide, CO2:
Both lines are on the side of the x-axis we expect, albeit very far from each other. Judging from the temperature, we believe the last plot is false.
The line in the first plot is deep enough, and seems to follow the curve of the noise, rather than come from one high datapoint.
It seems as if we can conclude that we have carbon dioxide in the atmosphere!
Methane, CH4: 
The precence of methane indicates either possible signs of life or geological activity, so this one is exciting.
The first plot has a temperature we expect, but is on the wrong side of the x-axis. The second plot is on the right side of the x-axis, but has a temperature we do not expect. 
It seems as if we can conclude that there is no methane in the atmosphere. If we look at the plots closely, especially the final plot, the noise is very large in the area where the dip is, and this may be what caused it.
Carbon monoxide, CO:
The line here is very close to 1, but still possible. However, the temperature of the particle is too low, and so we decide that we do not have carbon monoxide in the atmosphere.
We again note that the noise is very large in the area where the dip is.
Nitrus oxide, N2O: 
This gas is commonly called laughing gas, and indicates possible signs of life.
The line here is on the positive side of the x-axis, and looks deep enough. The temperature is within the range we want it to be, and the absolute value of the particles velocity seems to be realistic.
We therefore conclude that we have nitrus oxide in the atmosphere! This bodes well for finding life on the planet, even if we didn't have any methane.
We will from this point on assume that the planets atmosphere consists of water, carbon dioxide, and nitrus oxide, and that the atmosphere has approximately the same amount of each one, meaning that the atmosphere is:
33.33 % H2O
33.33 % CO2
33.33 % N2O
We assume the atmosphere is uniform. In our case this means that we consider every point in the atmosphere to have the same amount of gas, 33.33 % of each.
We can then find the average molecular weight (the average mass of a molecule in the atmosphere), ?:
\(\mu=\sum\limits^N_{i=1}f_i\frac{m_{i}}{m_H}=\frac{1}{3}\frac{m_{H_2O}}{m_H}+\frac{1}{3}\frac{m_{CO_2}}{m_H}+\frac{1}{3}\frac{m_{N_2O}}{m_H}=12\) hydrogen masses
where we've used the relationship between the mass of the molecule and the mass of a hydrogen atom.
Next, we can use this information in order to develop a model of our atmosphere, which is very important when we want to land!