As discussed under "PET Coincidence Logic" on this website, the PET instrument command state was, for many years, set up so that penetrating events with guard-ring triggers would be counted in the PEN rate scaler, but not accepted into the pulse-height analysis (PHA) buffers for output in the telemetry stream. This resulted in overestimates of the true rates of PEN events, as in the following example: suppose that, in one six-second rate sampling period, 60 particles triggered detectors P1, P4, and P8 (and, of course, almost always P2-3 and P5-7 as well), which is the nominal definition of the PEN rate. Suppose further that 36 of these events have guard triggers as well, and 12 of the no-guard events are protons; suppose, moreover, that due to telemetry limitations (20 PHA events per second, from all buffers) only 6 PEN PHA events make it down to the ground in those 6 seconds. If the PET command state is such that the guard-triggered events are not allowed into the PHA stream, then those 6 PHA events would constitute an unbiased sample of the 24 no-guard-trigger events, not the 60 events that were counted in the PEN rate scaler; thus on average we would see 3 protons among the PHA events. If we (erroneously) assume, as I did in early analysis, that these are instead an unbiased sample of all 60 PEN-rate events, we would calculate a rate of 30 protons per six seconds, instead of the actual rate of 12 protons per six seconds! (This ignores PLIVE deadtime corrections, which would be the same in either case.)

There were two periods, 92357-93023 and 99014-99271, when all PEN events regardless of guard state were accepted into the RNG telemetry buffer (though in the former period they would have been counted in the PEN rate scaler and in the latter they would have been divided between the RNG and PEN scalers depending on whether or not, respectively, any guards had been triggered). To estimate the correction needed in periods when the guard-triggered PEN PHA events are not available, I calculated the ratio of the number of PEN events without guard triggerings to the total number of PEN events, as a function of B and L; in the example above, it would be 24/60 or 40%, which is the correction factor needed to pull our original estimate of 5 protons per second down to the actual value of 2 protons per second. The plots on this page show this correction under various conditions, as explained below each plot. The plots are color-scale "spectrograms" of this ratio or correction factor as a function of invariant latitude vs. magnitude of B; I used negative values for the invariant latitude for data south of the magnetic equator.

This plot is for the earlier period, covering all pitch angles. Note the general gradation from green toward yellow toward the poles (invariant latitude of -90 or +90 degrees) at the higher values of B, and the gradient between orange and blue toward the very lowest values of B (in the inner zone, mostly observed in the South Atlantic Anomaly with a little protrusion across the equator in a small range of invariant latitude). The purple background indicates regions of no data.

This plot is for the same time period, but restricted to times when the instrument was looking within ten degrees of perpendicular to the local magnetic field. In the "orbit-rate rotation" mode at the time, we did not look perpendicular to the field very much at all except near the equator, so there are large regions of no data. Nonetheless, the same gradation in the inner zone is visible, with roughly the same colors (slightly biased toward the high end of the color bar).

This is another plot for the same time period, but for times when the instrument was looking more than ten degrees away from perpendicular to the local magnetic field. The inner zone contains somewhat lower values than in the previous plot; breaking the data down into finer pitch-angle subsets (not shown here) demonstrates a distinct trend in this direction as pitch angles farther from 90 degrees are sampled. This is not surprising, since the pitch-angle distribution is peaked perpendicular to the magnetic field, and therefore a larger proportion of cross-cutting particles (that intersect the guard rings and trigger them) will result from tilting the instrument away from perpendicular to the field.

This is the same kind of plot, for the later of the two periods considered. The green-to-yellow gradation at higher B is about the same as before, but somewhat larger values are observed in the inner zone than in the earlier period. This is an artifact of the pointing mode, as will be shown in the next two plots.

This is a plot for the later period, restricted to times when the instrument was looking within ten degrees of perpendicular to the magnetic field. Note the biteout near the equator at the higher values of B; this is because MAST and PET were, during this time, turned off at low L away from the South Atlantic Anomaly. Comparing this plot with the one for the earlier period with near-perpendicular pitch angles, we see that the color scale in the inner zone is about the same in both these plots. Thus the apparent increase in values from the first period to the second in the plots for all pitch angles is due to the dominance of the earlier period by observations away from perpendicular, and the later period by observations in the inner zone near perpendicular to the field, coupled with the observation that the value of this ratio decreases as the instruments look away from the perpendicular direction.

This is the plot for the later period, for pitch angles more than ten degrees away from the field-perpendicular direction. Again, the high-B region looks about the same whichever direction is observed, but the inner zone shows lower values of the ratio away from than near perpendicular. The values in this plot appear higher than those in the inner zone away from perpendicular for the earlier period; again, this is due to a bias of the observed pitch angles toward perpendicular in the pointing mode of the later period (there is essentially no data more than about 40 degrees away from perpendicular in the later period, whereas there was plenty in the earlier period). Plots (not shown) that sample the same (finer) pitch-angle bins show about the same colors in the inner zone in both periods.

This plot shows the values that I will use to correct livetimes during the periods when we do not have PEN events with guard triggers in the PHA telemetry stream. This is symmetrical about the magnetic equator; at most values of B and L I use a smooth average of the data for B greater than about 0.24 Gauss, as a function of invariant latitude, while in the inner zone I adopt values from the sum of the two periods. I considered adding another dimension to correct for the pitch-angle variation in the inner zone; however, the statistics away from perpendicular to the field are rather poor in this region, as I noted above (the former period is short, and the latter period is in the "j-perp" attitude-control mode), so I don't know if I would trust the results to within 30% or so, which is about the size of the effect. Besides, the data that are of the most interest, being least susceptible to errors from convolution of the instrument response with the angular distribution, are those from nearly perpendicular to the field where the pitch-angle distribution is flat. (Certainly, those are the only data I've ever trusted enough to use in my analyses!) Thus the values in the above plot should serve us well.

One remaining concern I have is that there were no substantial solar energetic particle events during these two periods, or at least none with any significant flux at these very high energies (above 86 MeV for protons). Thus the application of the correction in this plot (mostly due to cosmic rays over the polar caps) to the large solar energetic particle events elsewhere in the data will rest on the assumption that the angular distribution for solar protons and cosmic-ray protons is about the same. From what little analysis I was able to do of the angular distribution over the poles, this is a pretty good approximation.

new 27 May 2000