Analysis of XSM, RHESSI, and GOES observations of the flare on 26 April 2004, starting at 02:30 UT. The light curves are shown below.
As before, I did thermal fits to the XSM and RHESSI spectra with the iron and iron-nickel line complexes represented by Gaussians with a FWHM of 0.1 keV in the photon spectrum. In all cases for consistency, I used the Mewe atomic data base rather than the new Chianti data base. This will presumably give emission measures that are too high but they should be consistent for all three data sets. Below, I plot the time histories of the temperature, emission measure, and continuum flux at 6.7 keV determined from the best fit function for each of the three instruments.
We see that the XSM and GOES temperatures are in remarkable agreement, generally better than 1 MK, particularly early in the XSM operating period. Both are consistently higher than GOES temperatures by 3 - 4 MK. This is probably because GOES is sampling lower energies than were used for both the XSM and RHESSI fits.
The comparison of the emission measures is more problematic since the emission measure depends on the temperature used for the fit. Thus, the higher GOES values may just reflect the lower temperatures seen with GOES.
The more significant comparison is the continuum flux at 6.7 keV. Here we see that XSM is consistently about a factor of 2 - 3 higher than GOES with RHESSI somewhere in between. We interpret the higher values seen with RHESSI as compared to GOES as the result of the multi-temperature nature of the emitting plasma. RHESSI sees the higher temperature component whereas GOES sees more of the lower temperature component. This is also reflected in the higher temperatures derived from the XSM and RHESSI observations
XSM is giving a photon flux at 6.7 keV that is significantly
higher than both GOES and RHESSI. Since I used Richard's program to input XSM
data into OSPEX, this implies that there is something wrong with the conversion
factors he is using. The remarkable agreement in the temperatures implies that
the problem is a constant multiplicative factor, largely independent of energy.
Below, I show a comparison of the fluxes at 6.7 keV but with the XSM
points divided by a factor of 2. I would guess the correct value should be
closer to 2.0 to give better agreement with RHESSI results or 6.0 to give better
agreement with GOES. Given the argument about the multi-thermal nature of the
plasma, I would expect better agreement between XSM and RHESSI than between XSM
and GOES so I would predict that the factor, when found, will be closer to 2.0.
Mikko provided us with energy fluxes between 6 and 8 keV that he determined from the XSM measured count rate spectrum for this same flare. They are plotted as a function of time in the following figure - the small blue plus signs.
I have also included on this plot (the solid blue line) the energy fluxes I obtain from the same XSM data analyzed using OSPEX as described above. We get remarkably good agreement near the peak of the flare from 02:40 to 02:43 UT giving some confidence that we are using the same normalization factors to get from the count rate to the photon energy spectrum. I have plotted the ratio of the two curves in blue in the following plot.
I suggest that the deviation that shows up after ~02:44 UT is caused by our different handling of the very hard spectrum seen at higher energies. I have removed it as a background by extrapolating the fitted spectrum above 8 keV down into the 6 - 8 keV range, thus obtaining a lower energy flux. Mikko presumably did not subtract this background component and hence got the higher energy flux. The effect of this high energy tail on the XSM spectrum can be seen in the XSM light curves shown above.
Comparison with the energy flux derived from the RHESSI data and shown in the above light-curve figure in red still shows the factor of ~3 disagreement with XSM that we saw before. The ratio of the two is shown in black as a function of time in the above plot. As before, however, the factor is nearly constant if we compare the XSM and RHESSI fluxes both computed using OSPEX. Comparison between RHESSI and XSM fluxes calculated by Mikko shows a larger difference after ~02:44 UT, again suggesting the different approach to the hard tail on the XSM spectrum.
The agreement between my calculations of the energy flux between 6 and 8 keV from XSM data using OSPEX and Mikko's energy flux vales from 02:40 to 02:44 UT suggests to me that we are both using the same calibration factors to compute the XSM count rates to photon fluxes. The deviation after that time can be attributed to the different handling of the high energy tail in the XSM spectrum that cannot be a true indication of the solar flare spectrum. I still see factor of ~3 difference between the XSM and RHESSI energy fluxes that remains unexplained.