Preliminary Definitions

First some definitions: by DTF (dead time fraction) I mean the fraction of time spent not collecting data due to dead time. With this definition, the corrected count rate C' is related to the detected count rate C by:

  C' = C/(1 - DTF)

  DTF = C * DT

Origin of PCA Deadtime

Since all events in the PCA cause deadtime, we have to make sure that all events are accounted for when we calculate the dead time. These fall into four main categories (in order of decreasing count rate for a bright observation):

1. Good Xenon Events: These are events which pass all the discriminators and anti-coincidence vetoes (all configurations include good xenon data - not just the "Good Xenon" configuration).

2. Coincident Events: These events are detected in more than one anode simultaneously. They are not included with the good xenon events since they are most likely due to particles.

3. Very Large Events (VLE): These are events above the upper discriminator. Like the coincident events, they are mostly due to particles.

4. Propane Events: Each PCU has a layer of propane in front of the xenon layers. Events detected in this layer are not included with the good xenon events.

By design, the two Standard PCA configurations contain all these events (all other configurations contain only good xenon events). Moreover, each event is counted only once, i.e. a good xenon event is not counted as a propane event nor as a coincident or VLE event. For the purpose of working out dead time, Standard-1 is better than Standard-2 because it has 0.125-second resolution as opposed to 16-second.

In the Standard-1 files themselves, the columns containing the count rates can be listed with the ftool flcol:

  > flcol standard1.fits
  ___Column_Names_________Formats______Dims______Units___
  Time                       D                   s
  XeCntPcu0                  1024I     (1024)    count
  XeCntPcu1                  1024I     (1024)    count
  XeCntPcu2                  1024I     (1024)    count
  XeCntPcu3                  1024I     (1024)    count
  XeCntPcu4                  1024I     (1024)    count
  RemainingCnt               1024I     (1024)    count
  VpCnt                      1024I     (1024)    count
  VLECnt                     1024I     (1024)    count
  CalX1LSpecPcu0             256I      (256)     count
  CalX1RSpecPcu0             256I      (256)     count
  .                          .         .         .
  .                          .         .         .
  .                          .         .         .

  XeCntPcu0-4      (Good xenon count rate in PCU0-4)
  VpCnt            (Propane layer count rate, all five PCU combined)
  VLECnt           (Very Large Event count rate, all five PCU combined)
  RemainingCnt     (Coincident events, all PCU combined)
  CalX1LSpec..     (Spectrum of the internal calibration source in the 
                    various PCU/anodes - does not contribute to dead
                    time)

Now the dead time per event is approximately 10 microseconds for good xenon, propane and coincident events, and 150 microseconds for VLE events. This means that the dead time fraction at time t for the whole PCA is the sum of the following terms:

  C(t)_XeCnt * 1.0E-05 / Non        DTF good xenon events

  C(t)_VpCnt * 1.0E-05 / Non        DTF for coincident events
          
  C(t)_RemainingCnt * 1.0E-05 / Non DTF for of propane events

  C(t)_VLECnt * 1.5E-04 / Non       DTF for  VLE in

At present, we do not have a purpose-built tool to implement this recipe. However, we can use the ftool fcalc to calculate the DTF from the XeCntPcu0-4, VpCnt, VLECnt and RemainingCnt columns.

How to Correct for PCA Deadtime in Spectra

Here's my revised recipe for correcting deadtime in PCA spectra. This time I've added a bit more explanation.

1. Extract your spectrum.

2. With the same time selection settings (GTI, timeint etc.), extract a second spectrum from the corresponding Standard-1 data. This time, however, use the following list of columns:

         XeCntPcu0
         XeCntPcu1
         XeCntPcu2
         XeCntPcu3
         XeCntPcu4
         RemainingCnt
         VpCnt
   

3. When the extraction is over, look at the screen output from the extractor and make a note of the count rate in the spectrum (which you can discard - it only had one bin anyway).

4. Repeat steps 2 & 3 but with the column VLECnt.

5. Calculate DTF, the dead time fraction:

         DTF = NonVLE_Countrate x 1.0E-5 + VLE_Countrate x 6.0E-5
   

   from which you get the deadtime correction factor, DCOR:

         DCOR = 1/(1-DTF)
   

6. In xspec, multiply the additive components in your model by the multiplicative "const" component - which you should set fixed at DCOR.

Notes:

You have to adjust the correction factor if you want the deadtime per PCU (be careful to divide DTF by the number of PCUs actually on).
• Deadtime is around 2 percent when the Good Xenon countrate is roughly 2000 counts/second (all PCU combined).

• Standard VLE window is assumed.