Drm mod - Pseudo function for fine tuning RHESSI DRM parameters

From RHESSI Wiki

Revision as of 00:30, 12 September 2009

Detector Response Matrix Modification

Introduction

drm_mod adjusts the detector response matrix on the fly as intervals are fit to account for changes in the detector resolution and gain. It can only be used with spectrum files for single detectors.

Parameters

drm_mod - always returns a value of 0. Parameters are varied during fit and used in apply_drm method to compute drm on the fly.

• a[0] - FWHM fraction
• a[1] - Gain offset
• a[2] - Blanket Coefficient - default is 1, multiplies xsec

Fitting with drm_mod

This function recalculates the RHESSI Detector Response Matrix (DRM) to account for distortion of the solar spectrum by detector effects that change over time. As stated, the DRM is recalculated for each fit interval when drm_mod is used as part of the model, however the new DRM does not include the complete list of possible interactions. For most cases the recalculated DRM is sufficient to account for detector interactions unless the the time interval being fit extends to high energies (above ~100keV). The drm_mod component is a pseudo function. This means that it does not return any value for the flux on its own. Trying to plot just the drm_mod component will show no result. Drm_mod effect shows up in the other components of the model. For instance plotting the variable thermal component (vth) of your model without drm_mod as part of your model will give a different result than plotting it using drm_mod in your model with the resolution, a[0], and the gain offset, a[2], as free parameters. The plot below shows vth without drm_mod (top panel), vth using drm_mod (middle panel), and an attempt at plotting drm_mod alone (bottom panel). Note the parameters for vth are the same in both plots but the shape of component is different in the top and middle panels due to the effect of drm_mod. Note as well that attempting to plot the drm_mod component alone yields no result, it only shows up in it's effect on vth (or any other component that may be present depending on the model used).

Vth plotted without using drm_mod (top panel). Vth plotted with drm_mod as part of the model (center panel). An attempt to plot drm_mod alone, note that no value is returned, the drm_mod component only shows up as an effect on other components.

To use drm_mod the spectrum files must be created for each detector individually. If parameters in the drm_mod fit component are allowed to vary during the fitting of a time interval the energy range being fit must include the Fe line at 6.7keV. The Fe line must also be visible above the thermal continuum for drm_mod to fit spectra properly.

The first parameter, a[0], changes the detector resolution. This parameter adjusts the bin size in energy (keV) of the model so it matches the data. It accomplishes this by adjusting the Full Width Half Mast (FWHM) fraction of the energy bin in the model. This is accomplished by adjusting the width of the energy bins in the model to match the energy bins in the data at the Fe line complex at approximately 6.7keV. In order to calibrate the small changes in the resolution and gain of the detector a fixed line needs to be used as a reference point, in the case of RHESSI we use the known Fe line. Note that the energy bins in the model are not changed, rather they are convolved with the Detector Response Matrix created by drm_mod to account for the resolution of the detectors along with other detector effects when going from the measured count rate spectrum to the photon spectrum. The default value of the parameter, a[0], is set to 1. This the generally accepted resolution of RHESSI in keV, hence without drm_mod the detector's are assumed to have a resolution of 1keV. In reality the resolution of each detector is slightly different and changes as a function of the time during the mission. In the relatively low energy domain where drm_mod adjusts the resolution is generally better than 1keV. In cases where drm_mod is used to fit the spectrum a value of a[0] between approximately ~.7keV and 1keV is expected. Any values outside of this range generally mean that the model being used is not correct for the data observed.

The second parameter, a[1], is the gain offset of the detector. This adjusts the model to fit the data by shifting the model in energy (keV). As with a[0], the FWHM fraction, the Fe line is used to measure the gain offset. Once again the gain offset is a detector effect that is taken into account in the Detector Response Matrix, the matrix recalculated by drm_mod. The gain offset is usually well determined. It generally only becomes necessary to use it as a fit parameter in regions of the flare where the count rate is high. As the count rate increases the gain will increase between 0.0keV and 0.3keV. There is no physical reason for the gain to be negative. The upper limit of approximately 0.3keV is arrived at by studies of the detectors during periods of high count rate. Once again if the gain offset, a[1], falls outside of these bounds when used as a free parameter the model should be reconsidered.

The third parameter, a[2], the measures the blanket coefficient. This varies the amount of attenuation at low energies due to the thermal blankets insulating the detectors. This parameter is always kept fixed. The effect is not well enough understood to let the value change.

The plots below show an example of using drm_mod. The first fit is done without using drm_mod. The second fit is done with everything identical to first except for the addition of drm_mod to the model.

A fit done without drm_mod along with the resulting residuals

The same fit as above with the addition of drm_mod along with the resulting residuals

A consequence of the use of drm_mod is a reduction in the reduced χ². Looking at the residuals for each fit, the largest contribution to the residuals without drm_mod was around the Fe line complex, exactly the area that drm_mod adjusts the resolution and gain offset to match the known Fe line. Perhaps the more important consequence of this is it's effect on the parameters of the other components of the fit. These parameters measure the physical properties of the event such as the Emission Measure and Temperature. Looking at the value of these parameters in vth, using drm_mod to calibrate the resolution and gain offset yields a 45% change in the emission measure and a 10% change in the temperature. Looking at the other parameters in the fit reveals that they have changed as well. This shows that using drm_mod correctly in the appropriate situations affects the values of the parameters measuring physical quantities, and should be considered when possible.

• drm_mod can only be used to fit spectra for single detectors, when detectors are combined to create spectrum files it cannot be used.
• drm_mod is only useful in cases where the Fe line in visible in the spectrum at 6.7keV because it uses this line to adjust the value of FWHM fraction, a[0], and the gain offset, a[1].
• The FWHM fraction,, a[0], should only vary between approximately 0.7keV and 1keV, any larger or smaller values indicate a problem with the model
• The gain offset, a[1], should only vary between 0keV and 0.3keV and should only be used in instances of high count rate.
• the blanket coefficient, a[2], should always be kept fixed at a value of 1.

Further Explanation of the drm_mod parameters

a[0], the first component is a measure of detector resolution. Resolution is the sum of a constant term (electronic resolution), a term proportional to the square root of energy (natural statistics of germanium electron/hole pairs), and a term proportional to energy (trapping).

The values of A, B, and C for each detector segment are read from a table of parameters vs dates (hessi_resol_vs_time.1000) and interpolated to the requested date. The units of the resolution are FWHM in keV of a gaussian line. The figure below shows the resolution for 21Apr2002 for an energy range of 3 – 160 keV, using the front segment of detector four.

THIS SECTION STILL UNDER CONSTRUCTION