Analysis of RHESSI Variance

The model countrates (shown in red) and the observed countrates are shown below. (countrates in ms^-1)

For detectors 6-9 and countrates 0.25-0.85 ms^-1, the histograms are shown below. The predicted Poisson distribution with mean equal to the model mean FMEAN is shown in red. The histograms are normalized to unity at countrates of 0.

For detectors 3-6 and countrates of 0.25-0.85 ms^-1, the histograms are shown below. The predicted Poisson distribution with mean equal to the model mean FMEAN is shown in red.

The good agreement between the predicted Poisson distributions and the histograms of observed counts indicates that
 (a) the model is a good fit and
 (b) the countrates are Poisson distributed.

Additional tests were made by computing a simulated Poisson-distributed time series using the model countrates. This was done 15 times for each detector (3-9), so that the range of scatter could be seen in histograms. The seven plots below show histograms of the observed and simulated count rates with integer counts of 0 to 8.

In general, the histograms from the simulated counts (red) mimic the histograms of the observed counts (black), but there are notable differences:

• For all detectors there are more 0s than 1s, but the simulated counts have a higher proportion of 1s.
• Higher counts (>3) are more frequent in the observed time series than the simulated series..
• The differences become greater going into the tails of the distributions.
• The differences between the histograms are least for detector 5

• use of the fundamental without harmonics
• errors in calibration
• asymmetries in the sources
• time variability

Numerical experiments with the use of higher harmonics seem to give very nearly the same chisquare values for the fits, and the same results for the histograms described above.