Derivation of characteristic energy and energy flux
Our Belgian colleagues in Liege have provided modeling results which predict the response of the IMAGE FUV instruments to specific electron and proton energy inputs. We can use these tables and reverse the process, estimating characteristic energy and total energy flux from the auroral measurements of WIC and S13.
The proton aurora is important as well, since precipitating protons create secondaries, which can be efficient in creating OI and N2-LBH emissions. We cannot be absolutely sure of the energy of the precipitation, but we hope to derive this at least locally at Poker using the FPI which obtained measurements during the Jan 21 substorm.
The process is as follows.
0) Remap all images to geographic coordinates.
For this work, I do no co-registration of images. I am counting on the pointing information to be correct, and have 'done stars' for this time to tune the pointing values. The mapping is a one-to-one process, where every image pixel is mapped to a geographic grid with .5x.5 resolution in lat and lon. The result is a fairly robust representation of the initial image, and only minimal interpolation is necessary after the inital mapping is performed.
1) Correct WIC for change in gain.
Late in 2000, after the study by Harald , J-C, and Benoit, the high voltage of the WIC camera was increased by 25 Volts. This resulted in an increase in the instrument gain and response. Rough estimates from dayglow observations (stars would be good as well) indicate a 35-45 % increase in instrument sensitivity. The WIC response is therefore reduced by 40% before any further calculations are made, so that we may use the values provided by Jean-Claude.
2) Estimate contribution of protons to SI-13 and WIC response.
We have estimates for LBH produced by protons at 3 characteristic energies: 2, 8, and 25 keV. The total LBH brightness in Rayleighs for 1 erg/cm^2/sec of proton precipitation each of those energies is 2250., 2900., and 3110., respectively. We use a quadratic interpolation/extrapolation for energies not at these discrete levels. Since we have not yet fully analyzed the ground based proton measurements (and don't have any such measurement globally) we assume a proton characteristic energy between 5-8 keV for the rest of this work.
Incidentally, for 1 erg of electron precipitation in the energy ranges of 0.5, 1, 5, and 25 keV, it is predicted that you will have 1920, 2390, 2320, and 1010 Rayleighs, respectively. Note that these drop off much more quickly with energy, as the electrons get deeper in the atmosphere than protons. Therefore, the O2 attenuation is greater.
The resultant response of WIC to these emissions generated by 1 erg/cm^2/sec of precipitating protons is 401, 510, and 538 A-D Units, respectively. Electron aurorae result in 344, 427, 346, and 95.4 A-D units for the respective characteristic energies. If you know a little about the count rates observed by WIC, you can see that many aurora are much greater than 1 erg. Knowing a little about the aurora, you see that most of the WIC counts are probably due to electrons, except possibly in some particular cases.
The proton aurora also shows up in SI-12, of course, and gives us these count rates for the energies noted above : 28.9,26.9, and 16.0 counts. The response of SI-12 to the aurora is often in the 20-50 count range, so you see that the proton aurora is often just about 1-2 ergs/cm^2. We assume a 5 keV proton aurora which means about 27 counts/erg/cm^2/sec. The next step is to calculate the proton energy flux from the observed brightness, or in computerese.
eflux=observed_s12_cts/predict_1erg_s12_cts
With that, and the assumed characteristic energy, you can predict the amount of LBH produced by the proton aurora, and subtract that from the WIC channel.
predict_proton_wic=predict_1erg_wic * eflux * 1 ; 1 is 1 erg^-1
This process is followed for SI-13 as well, to calculate predict_proton_s13.or rather the proton auroral effects that should be observed in the SI-13 channel. Both the WIC and SI-13 images are then corrected, which should allow one to consider the images as observations of the true electron aurora. Increasing the proton energy results in a greater correction to both channels.
3) Calculate the ratio of WIC to S13.
J-C provides the following table for ratios of WIC to S13 counts for
electron aurorae:
| <E> | WIC/S13 |
| 0.50 | 34.14 |
| 1.00 | 52.49 |
| 5.00 | 85.28 |
| 25.0 | 132.49 |
That is a pretty impressive spread in the ratios. IMAGE FUV is better than originally thought at doing energy calculations! So we remove the background bias of 400 A-D units in WIC, and calculate the ratio. At this point, wherever S13 counts are less than 10, I discard the values. S13 has excellent counting statistics, but we should put a lid on the uncertainties at 30% or so. At this point, we have an estimate of <E>. Great!
4) Calculate total energy flux from WIC.
With the estimate of energy flux from step 3, we go back to the WIC image, corrected for gain, protons, and bias, and estimate from the brightness of the image the total energy flux.
5) Sources of Error.
There are several things that may be sources of error.
A) The atmosphere. I believe at substorm onset there is good reason
to think that MSIS will provide something that closely resembles the actual
atmosphere. 20 minutes into the storm, this may no longer be the case over
Alaska, as the O/N2 ratios can really start to be affected. This will affect
the ratio of WIC/S13 to some extent.
The 60 keV spots well after the substorm are a little hard to believe.
As well as the 30 ergs/sec/cm^2 of electron precipitation everywhere.
B) The aurora. The spectra are hardly ever as simple as one would hope. The results of this work, without FAST flying right overhead, are always approximations. And as you know, FAST never flies right overhead.
C) Extrapolation. Even correcting the WIC response for protons, it is clear that the ratio can easily be twice as great as 132, the maximum calculated by the Liege group. I have extrapolated from here with what I think is a reasonable curve fit.
D) Energy Flux. Given that I have to extrapolate beyond 25 keV, there is significant uncertanty here. I provided a constraining WIC count rate of 20 at outlandish number of 300 keV, but the 3rd order fit I did went less than zero. So for now I am using a linear interpolation. Simulations at higher energies are needed to really do this right, at least up to 100 keV. Whether or not you think these energies are realistic, the calculated ratios indicate that they are necessary.
E) Altitude. I have not changed anything in the Belgian's numbers to account for the fact that these brightnesses are for electrons/protons at 600 km. The geometric factor of 20% should be applied at some point, but first we need to decide if this is right so far.
6) Good parts.
You could not ask for a better substorm over a proton camera at Poker.
The pointing is as good as it can be. Harald's fuview has plenty of
star markers to do the right thing. For this, the azimuth, co-elevation
and roll for the 3 instruments is as follows:
| Instrument | Azimuth | co-elevation | roll |
| SI-12 | 42.74 | -1.70 | -1.85 |
| WIC | 43.19 | 0.3 | -1.85 |
| SI-13 | 43.10 | -1.45 | -1.85 |
Thomas Immel - SSL, UCB.
