Pileup mod - Pseudo function for correcting pileup

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Pileup Correction Component

Introduction

pileup_mod attempts to correct for photons which lose energy in the detector at the same time (within 1 microsecond of each other). Photons that arrive within the 1 µs are counted as a single event with the energy of the photons summed. During high countrate time intervals of a flare this detector effect can distort the spectrum. This fit component attempts to fit pileup effects during these intervals, this allows a more accurate measure of physical parameters such as the Emission Measure and Temperature.

Parameters

pileup_mod - always returns a value of 0. Parameters are varied during fit and used in apply_drm method to add pileup effects to model on the fly.

Fitting with pileup_mod

Pileup causes a distortion of the RHESSI spectrum during high countrate time intervals of an event. RHESSI Spectra have a low energy peak. During high countrate time intervals it becomes likely that any two photons losing energy in the detector within 1µs will have the energy of a photon around the peak of the spectrum. This leads to a shoulder in the spectrum at around twice the value (in keV) of the low energy peak. There is some spread to the shoulder just as there is spread to the peak of spectrum due to smearing of counts during binning and other statistical variations. Below is a typical spectrum showing pileup.


A typical spectrum showing pileup at ~13keV

pileup_mod is a pseudo function. This means that the function does not return a value on its own. For instance if you add pileup_mod to your fit function setup GUI and attempt to plot the pileup_mod component alone no component will appear on the plot. Pileup only affects the other components of the model such as vth and thick target. The size of the pileup effect depends on the countrate. This means that pileup_mod will affect the spectrum differently even if all parameters are kept at the default values. We can take advantage of this by keeping the pileup_mod parameters fixed at their default values during the A0 and A1 attenuator states. When the countrate is low pileup will have very little effect on the model, but as it it increases pileup_mod will adjust the model to compensate for increasing pileup even though the parameters of the component are always fixed at the same value.

A good way to visualize the effect of pileup_mod is to look at the difference in a model without pileup_mod and one with pileup_mod inserted. In the below figure the parameters for the components vth, thick target, and drm_mod are the same in both panels. The only difference is pileup_mod has been added as a fit component in the lower panel. Note that no fit has been done, pileup_mod still has all parameters set to their default values.

A fit model without pileup_mod (top panel) and with pileup_mod added (bottom panel)

It is clear that pileup_mod has a significant effect on the model even before the fit. Note that the values of the parameters for the other components have not been changed. This is significant because it means that by accounting for the distortion in the spectrum due to pileup with it's own component the free parameters in the other components do not have to adjust to fit this detector artifact. This should give us values of the parameters that are closer to being independent of detector effects.

In most cases pileup_mod can be used with the rest of the fit function components with all of the values of its parameters set to their default values and fixed. Time Intervals where pileup is not an issue will see very little effect, time intervals with high count rates where pileup can become a problem will see a significant effect.

Synopsis

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