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=2pt PCARMF v2.1.2

Keith Jahoda

April 17, 1997.

This memo describes briefly PCARMF v2.1.2, which is intended to be distributed as part of ftools v3.7. I highlight differences from previous versions and provide examples of the performance of these matrices. I also provide information on how to get the tools to generate these matrices, and provide the raw matrices from which any combination can be created.

Changes from previous versions

There are several substantial improvements in this version of the matrix generator. These are

1) New energy to channel coefficients for all detectors, all layers, all epochs. The supported model is 3, which first translates energy of the photon into number of secondary electrons, and then allows a quadratic fit for channel number as a function of number of electrons. The x-axis (number of electrons) is renormalized to be tex2html_wrap_inline178 energy for convenience for plotting inside xspec. The translation between photon energy and number of thermal electrons is non linear, and provides a natural way to account for the non linearities in the energy to channel relationship at the Xenon absorption edges. The details of this transformation will be described in greater length elsewhere.

2) The lower end of the energy scale has been fixed by requiring that the energy of the Cas-A Fe line be 6.59 keV (front layer), and by minimizing chi-squared on 2.5-50 keV fits to the Crab spectrum on the second and third layers. The second condition has the effect of pegging the energy scale at the Xenon L-edge at 4.78 keV. The results for the second and third layers can be seen in the results shown for the Crab spectrum where the counts observed below 5 keV are due to the small transmission window below the L edge.

3) Matrices for lld_code=63 (i.e. all layers) are now explicitly the sum of lld_code=3 + 12 + 48 (I.e. the sum of the matrices for the first, second, and third layers). Previously the total response was an approximation to this; adding the individual layer matrices automatically gets the weighting of the three layers correctly in an energy dependent way.

4) Propane matrices are now supported, nad are individually generated for each PCU to account for the different gains. The normalization of propane response to xenon response is unexpected (i.e. not 1). Users are advised to let the normalization of the propane layer float relative to other layers for the time being. An example is shown in the results section.

5) There are no defaults for the scale_hack parameter, although the code still exists. This allows an ad hoc correction to the effective areas, but the user must supply his own corrections. (This means that version 2.1.2 of pcarmf will not work with the version of pcarsp released in ftools 3.6.1. An alternate script which must be edited to fit individual observations is given at the end of this document.)

6) Non standard keywords having to do with response matrix parameters are now written out as history keywords (and survive through MARFRMF). This should make comparing different versions of the matrices earsier.

The rest of this memo gives some representative results from the Crab, Cas A, and discusses the propane layer efficiency.

Results from the Crab

The goal of this section is to provide representative comparisons of the matrices at different high voltage settings, in different layers within the same detector, between individual detectors, and across all detectors and layers.

Figure 1 compares the first layer of PCU 0 for Crab (nebula plus pulsar) data from the In Orbit Checkout period and the "epoch 3" high voltage setting (i.e. all data taken after April 14, 1996). The data have been fit to a single power law with the interstellar absorption fixed at tex2html_wrap_inline180 .

  figure22
Figure 1: In Orbit checkout and epoch 3 comparison

An xspec format summary of the fit is given below. Note that I have allowed an arbitrary overall normalization between the two data sets ( tex2html_wrap_inline182 ). The best fit power law index and normalization are 2.17 and 12.2, both of which seem slightly high compared to literature values. However, the derived 2 - 10 keV flux is tex2html_wrap_inline184 which is within two percent of the flux derived from the values adopted by Zombeck (index 2.05 and normalization 10.0) and Schattenberg and Canizares (index 2.1 and norm 10.9). The agreement is in fact too good, since I have not accounted for deadtime (known to be tex2html_wrap_inline186 for the Crab. In this (and all subsequent cases) the ancilliary response files are generated assuming that the open area of each detector is tex2html_wrap_inline188 . This is corrected only for the individual pointing offsets from the science axis.

XSPEC> sh all
 12:21:02 15-Apr-97
 Auto-saving is done after every command.
 Fit statistic in use is Chi-Squared
 Minimization technique is Lev-Marq
 Weighting method is standard
 Convergence criterion =     1.0000000000000D-02
 Querying enabled
 Prefit-renorming enabled
 Solar abundance table is angr

 Information for file   1
  belonging to plot group   1, data group   1
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr1_hv5.pha
  Background file  :bg_p0lr1_hv5.pha
  No current correction
  Response (RMF) file    : p0_l1_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     5 to    89
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2071.    +/- 1.6153     cts/s
  Model predicted rate :    2071.

 Information for file   2
  belonging to plot group   2, data group   2
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr1_hv7.pha
  Background file  :bg_p0lr1_hv7.pha
  No current correction
  Response (RMF) file    : p0_l1_e1.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     7 to   105
  File integration time     416.0
     and effective area     1.000
  File observed count rate     2210.    +/- 2.3134     cts/s
  Model predicted rate :    2209.

  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.000     frozen            1
    2    2    2   powerlaw   PhoIndex            2.174     +/-  0.1380E-02   1
    3    3    2   powerlaw   norm                12.18     +/-  0.3103E-01   1
    4    4    3   wabs       nH       10^22     0.3000     frozen            1
    5    5    4   constant   factor              1.029     +/-  0.1343E-02   2
    6    2    5   powerlaw   PhoIndex            2.174     = par   2         2
    7    3    5   powerlaw   norm                12.18     = par   3         2
    8    4    6   wabs       nH       10^22     0.3000     = par   4         2
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      668.0139     using   184 PHA bins.
 Reduced chi-squared =      3.690685
XSPEC> flux
 Model flux   3.725     photons ( 2.3502E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  1
 Model flux   3.833     photons ( 2.4184E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  2
XSPEC> log none

Figure 2 shows a similar fit but here the different data sets come from the three layers of PCU 0 during the third epoch. The power law index is constrained to be the same in each layer but the relative normalization remains a free parameter. (That a relative normalization is needed indicates that there is still room for improvement in the matrices for the inner layers; not shown is the fact that the current matrices give slightly different values for the power las index if the second or third layers are fit individually)

  figure31
Figure 2: Comparison of the 3 layers in PCU 0, epoch 3

Logging to file: e3_l123.log
XSPEC> sh all
 12:24:43 15-Apr-97
 Auto-saving is done after every command.
 Fit statistic in use is Chi-Squared
 Minimization technique is Lev-Marq
 Weighting method is standard
 Convergence criterion =     1.0000000000000D-02
 Querying enabled
 Prefit-renorming enabled
 Solar abundance table is angr

 Information for file   1
  belonging to plot group   1, data group   1
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr1_hv5.pha
  Background file  :bg_p0lr1_hv5.pha
  No current correction
  Response (RMF) file    : p0_l1_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     5 to    89
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2071.    +/- 1.6153     cts/s
  Model predicted rate :    2071.

 Information for file   2
  belonging to plot group   2, data group   2
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr2_hv5.pha
  Background file  :bg_p0lr2_hv5.pha
  No current correction
  Response (RMF) file    : p0_l2_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     4 to    88
  File integration time     800.0
     and effective area     1.000
  File observed count rate     210.6    +/-0.52550     cts/s
  Model predicted rate :    210.0

 Information for file   3
  belonging to plot group   3, data group   3
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr3_hv5.pha
  Background file  :bg_p0lr3_hv5.pha
  No current correction
  Response (RMF) file    : p0_l3_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     4 to    88
  File integration time     800.0
     and effective area     1.000
  File observed count rate     93.54    +/-0.36019     cts/s
  Model predicted rate :    92.91

  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.000     frozen            1
    2    2    2   powerlaw   PhoIndex            2.178     +/-  0.1625E-02   1
    3    3    2   powerlaw   norm                12.26     +/-  0.3627E-01   1
    4    4    3   wabs       nH       10^22     0.3000     frozen            1
    5    5    4   constant   factor              1.022     +/-  0.2844E-02   2
    6    2    5   powerlaw   PhoIndex            2.178     = par   2         2
    7    3    5   powerlaw   norm                12.26     = par   3         2
    8    4    6   wabs       nH       10^22     0.3000     = par   4         2
    9    6    7   constant   factor              1.008     +/-  0.4204E-02   3
   10    2    8   powerlaw   PhoIndex            2.178     = par   2         3
   11    3    8   powerlaw   norm                12.26     = par   3         3
   12    4    9   wabs       nH       10^22     0.3000     = par   4         3
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      1146.454     using   255 PHA bins.
 Reduced chi-squared =      4.567546
XSPEC> flux
 Model flux   3.732     photons ( 2.3528E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  1
 Lower range     2.00     reset by matrix bound to     2.46
 Model flux   2.900     photons ( 2.0802E-08 ergs)cm**-2 s**-1 (  2.456- 10.000) DtSet :  2
 Lower range     2.00     reset by matrix bound to     2.99
 Model flux   2.151     photons ( 1.7446E-08 ergs)cm**-2 s**-1 (  2.992- 10.000) DtSet :  3
XSPEC> log none

Figure 3 shows joint fits to the first layer of each of the five individual detectors. The relative normalization is within a few percent in all cases (the maximum deviation is tex2html_wrap_inline190 ). The photon index for all 5 detectors is 2.18, which is very similar to the values obtained above for PCU 0 only.

  figure38
Figure 3: Comparison of the first layer in 5 PCUs, epoch 3

Logging to file: e3_p01234.log
XSPEC> sh all
 12:31:43 15-Apr-97
 Auto-saving is done after every command.
 Fit statistic in use is Chi-Squared
 Minimization technique is Lev-Marq
 Weighting method is standard
 Convergence criterion =     1.0000000000000D-02
 Querying enabled
 Prefit-renorming enabled
 Solar abundance table is angr

 Information for file   1
  belonging to plot group   1, data group   1
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr1_hv5.pha
  Background file  :bg_p0lr1_hv5.pha
  No current correction
  Response (RMF) file    : p0_l1_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     5 to    89
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2071.    +/- 1.6153     cts/s
  Model predicted rate :    2070.

 Information for file   2
  belonging to plot group   2, data group   2
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p1lr1_hv5.pha
  Background file  :bg_p1lr1_hv5.pha
  No current correction
  Response (RMF) file    : p1_l1_e3.rsp
  Auxiliary (ARF) file    : p1.arf
  XSPEC filter : NONE
  Noticed channels     5 to    91
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2087.    +/- 1.6217     cts/s
  Model predicted rate :    2086.

 Information for file   3
  belonging to plot group   3, data group   3
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p2lr1_hv5.pha
  Background file  :bg_p2lr1_hv5.pha
  No current correction
  Response (RMF) file    : p2_l1_e3.rsp
  Auxiliary (ARF) file    : p2.arf
  XSPEC filter : NONE
  Noticed channels     5 to    89
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2082.    +/- 1.6199     cts/s
  Model predicted rate :    2081.

 Information for file   4
  belonging to plot group   4, data group   4
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p3lr1_hv5.pha
  Background file  :bg_p3lr1_hv5.pha
  No current correction
  Response (RMF) file    : p3_l1_e3.rsp
  Auxiliary (ARF) file    : p3.arf
  XSPEC filter : NONE
  Noticed channels     5 to    92
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2085.    +/- 1.6205     cts/s
  Model predicted rate :    2083.

 Information for file   5
  belonging to plot group   5, data group   5
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p4lr1_hv5.pha
  Background file  :bg_p4lr1_hv5.pha
  No current correction
  Response (RMF) file    : p4_l1_e3.rsp
  Auxiliary (ARF) file    : p4.arf
  XSPEC filter : NONE
  Noticed channels     4 to    86
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2049.    +/- 1.6069     cts/s
  Model predicted rate :    2048.

  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.007     +/-   45.20       1
    2    2    2   powerlaw   PhoIndex            2.185     +/-  0.7787E-03   1
    3    3    2   powerlaw   norm                12.31     +/-   552.7       1
    4    4    3   wabs       nH       10^22     0.3000     frozen            1
    5    5    4   constant   factor              1.036     +/-   46.47       2
    6    2    5   powerlaw   PhoIndex            2.185     = par   2         2
    7    3    5   powerlaw   norm                12.31     = par   3         2
    8    4    6   wabs       nH       10^22     0.3000     = par   4         2
    9    6    7   constant   factor              1.013     +/-   45.42       3
   10    2    8   powerlaw   PhoIndex            2.185     = par   2         3
   11    3    8   powerlaw   norm                12.31     = par   3         3
   12    4    9   wabs       nH       10^22     0.3000     = par   4         3
   13    7   10   constant   factor             0.9898     +/-   44.40       4
   14    2   11   powerlaw   PhoIndex            2.185     = par   2         4
   15    3   11   powerlaw   norm                12.31     = par   3         4
   16    4   12   wabs       nH       10^22     0.3000     = par   4         4
   17    8   13   constant   factor              1.028     +/-   46.11       5
   18    2   14   powerlaw   PhoIndex            2.185     = par   2         5
   19    3   14   powerlaw   norm                12.31     = par   3         5
   20    4   15   wabs       nH       10^22     0.3000     = par   4         5
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      3808.307     using   428 PHA bins.
 Reduced chi-squared =      9.045860
XSPEC> flux 2 10
 Model flux   3.744     photons ( 2.3572E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  1
 Model flux   3.849     photons ( 2.4234E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  2
 Model flux   3.763     photons ( 2.3690E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  3
 Model flux   3.678     photons ( 2.3158E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  4
 Model flux   3.819     photons ( 2.4046E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  5
XSPEC> data 1:1-3 p0lr1_hv5 p0lr2_hv5 p0lr3_hv5 2:4-6 p1lr1_hv5 p1lr2_hv5 p1lr3_hv ...
The value, 9, of upper limit of file no. range is outside the allowed range (1,7):/
The value, 12, of upper limit of file no. range is outside the allowed range (1,10):

Figure 4 shows a fit to all 5 detectors and all 3 layers in each detector. Seven relative normalizations are allowed, one each for each PCU and one each for the seond and third layers relative to the first. The results are quite similar to those already shown. The largest deviation in the ratio of data/model occur for the second and third layers near 2 keV and near 5 keV. The efficiency of the second and third layers is very low here, down by three orders of magnitude from the peak response on layer 2 and more than four orders of magnitude on layer 3. The log file omits the information about the associated files. The relative normalizations are within a few percent and the power law index is 2.19.

  figure45
Figure 4: Comparison of all layers, all PCUs, epoch 3

  mo = constant[1]*constant[2]( ( powerlaw[3] )wabs[4] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]*constant[2]( ( powerlaw[3] )wabs[4] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.000     frozen            1
    2    2    2   constant   factor              1.000     frozen            1
    3    3    3   powerlaw   PhoIndex            2.189     +/-  0.7210E-03   1
    4    4    3   powerlaw   norm                12.51     +/-  0.1830E-01   1
    5    5    4   wabs       nH       10^22     0.3000     frozen            1
    6    1    5   constant   factor              1.000     = par   1         2
    7    6    6   constant   factor              1.024     +/-  0.1283E-02   2
    8    3    7   powerlaw   PhoIndex            2.189     = par   3         2
    9    4    7   powerlaw   norm                12.51     = par   4         2
   10    5    8   wabs       nH       10^22     0.3000     = par   5         2
   11    1    9   constant   factor              1.000     = par   1         3
   12    7   10   constant   factor              1.012     +/-  0.1900E-02   3
   13    3   11   powerlaw   PhoIndex            2.189     = par   3         3
   14    4   11   powerlaw   norm                12.51     = par   4         3
   15    5   12   wabs       nH       10^22     0.3000     = par   5         3
   16    8   13   constant   factor              1.025     +/-  0.1057E-02   4
   17    2   14   constant   factor              1.000     = par   2         4
   18    3   15   powerlaw   PhoIndex            2.189     = par   3         4
   19    4   15   powerlaw   norm                12.51     = par   4         4
   20    5   16   wabs       nH       10^22     0.3000     = par   5         4
   21    8   17   constant   factor              1.025     = par  16         5
   22    6   18   constant   factor              1.024     = par   7         5
   23    3   19   powerlaw   PhoIndex            2.189     = par   3         5
   24    4   19   powerlaw   norm                12.51     = par   4         5
   25    5   20   wabs       nH       10^22     0.3000     = par   5         5
   26    8   21   constant   factor              1.025     = par  16         6
   27    7   22   constant   factor              1.012     = par  12         6
   28    3   23   powerlaw   PhoIndex            2.189     = par   3         6
   29    4   23   powerlaw   norm                12.51     = par   4         6
   30    5   24   wabs       nH       10^22     0.3000     = par   5         6
   31    9   25   constant   factor              1.004     +/-  0.1035E-02   7
   32    2   26   constant   factor              1.000     = par   2         7
   33    3   27   powerlaw   PhoIndex            2.189     = par   3         7
   34    4   27   powerlaw   norm                12.51     = par   4         7
   35    5   28   wabs       nH       10^22     0.3000     = par   5         7
   36    9   29   constant   factor              1.004     = par  31         8
   37    6   30   constant   factor              1.024     = par   7         8
   38    3   31   powerlaw   PhoIndex            2.189     = par   3         8
   39    4   31   powerlaw   norm                12.51     = par   4         8
   40    5   32   wabs       nH       10^22     0.3000     = par   5         8
   41    9   33   constant   factor              1.004     = par  31         9
   42    7   34   constant   factor              1.012     = par  12         9
   43    3   35   powerlaw   PhoIndex            2.189     = par   3         9
   44    4   35   powerlaw   norm                12.51     = par   4         9
   45    5   36   wabs       nH       10^22     0.3000     = par   5         9
   46   10   37   constant   factor             0.9854     +/-  0.1016E-02  10
   47    2   38   constant   factor              1.000     = par   2        10
   48    3   39   powerlaw   PhoIndex            2.189     = par   3        10
   49    4   39   powerlaw   norm                12.51     = par   4        10
   50    5   40   wabs       nH       10^22     0.3000     = par   5        10
   51   10   41   constant   factor             0.9854     = par  46        11
   52    6   42   constant   factor              1.024     = par   7        11
   53    3   43   powerlaw   PhoIndex            2.189     = par   3        11
   54    4   43   powerlaw   norm                12.51     = par   4        11
   55    5   44   wabs       nH       10^22     0.3000     = par   5        11
   56   10   45   constant   factor             0.9854     = par  46        12
   57    7   46   constant   factor              1.012     = par  12        12
   58    3   47   powerlaw   PhoIndex            2.189     = par   3        12
   59    4   47   powerlaw   norm                12.51     = par   4        12
   60    5   48   wabs       nH       10^22     0.3000     = par   5        12
   61   11   49   constant   factor              1.018     +/-  0.1055E-02  13
   62    2   50   constant   factor              1.000     = par   2        13
   63    3   51   powerlaw   PhoIndex            2.189     = par   3        13
   64    4   51   powerlaw   norm                12.51     = par   4        13
   65    5   52   wabs       nH       10^22     0.3000     = par   5        13
   66   11   53   constant   factor              1.018     = par  61        14
   67    6   54   constant   factor              1.024     = par   7        14
   68    3   55   powerlaw   PhoIndex            2.189     = par   3        14
   69    4   55   powerlaw   norm                12.51     = par   4        14
   70    5   56   wabs       nH       10^22     0.3000     = par   5        14
   71   11   57   constant   factor              1.018     = par  61        15
   72    7   58   constant   factor              1.012     = par  12        15
   73    3   59   powerlaw   PhoIndex            2.189     = par   3        15
   74    4   59   powerlaw   norm                12.51     = par   4        15
   75    5   60   wabs       nH       10^22     0.3000     = par   5        15
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      7863.804     using  1284 PHA bins.
 Reduced chi-squared =      6.162856
XSPEC> flux 2 10
 Model flux   3.755     photons ( 2.3617E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  1
 Lower range     2.00     reset by matrix bound to     2.46
 Model flux   2.917     photons ( 2.0893E-08 ergs)cm**-2 s**-1 (  2.456- 10.000) DtSet :  2
 Lower range     2.00     reset by matrix bound to     2.99
 Model flux   2.164     photons ( 1.7533E-08 ergs)cm**-2 s**-1 (  2.992- 10.000) DtSet :  3
 Model flux   3.849     photons ( 2.4207E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  4
 Lower range     2.00     reset by matrix bound to     2.52
 Model flux   2.879     photons ( 2.0973E-08 ergs)cm**-2 s**-1 (  2.523- 10.000) DtSet :  5
 Lower range     2.00     reset by matrix bound to     2.99
 Model flux   2.218     photons ( 1.7971E-08 ergs)cm**-2 s**-1 (  2.992- 10.000) DtSet :  6
 Model flux   3.769     photons ( 2.3709E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  7
 Lower range     2.00     reset by matrix bound to     2.46
 Model flux   2.929     photons ( 2.0974E-08 ergs)cm**-2 s**-1 (  2.456- 10.000) DtSet :  8
 Lower range     2.00     reset by matrix bound to     2.99
 Model flux   2.173     photons ( 1.7601E-08 ergs)cm**-2 s**-1 (  2.992- 10.000) DtSet :  9
 Model flux   3.700     photons ( 2.3273E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet : 10
 Lower range     2.00     reset by matrix bound to     2.50
 Model flux   2.803     photons ( 2.0304E-08 ergs)cm**-2 s**-1 (  2.501- 10.000) DtSet : 11
 Lower range     2.00     reset by matrix bound to     3.01
 Model flux   2.109     photons ( 1.7163E-08 ergs)cm**-2 s**-1 (  3.014- 10.000) DtSet : 12
 Model flux   3.821     photons ( 2.4033E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet : 13
 Lower range     2.00     reset by matrix bound to     2.48
 Model flux   2.931     photons ( 2.1113E-08 ergs)cm**-2 s**-1 (  2.478- 10.000) DtSet : 14
 Lower range     2.00     reset by matrix bound to     2.99
 Model flux   2.202     photons ( 1.7842E-08 ergs)cm**-2 s**-1 (  2.992- 10.000) DtSet : 15
XSPEC> log none

Finally, figure 5 shows a simultaneous fit to pcu 0, propane and layer 1. The relative normalization of the propane layer is 0.65, which suggests that there is room for substantial improvement here. Nonetheless, the propane layer matrices may be suitable ( caveat emptor) for tracking changes at the lowest energies. Including the propane layer in the fit has a modest effect on the best fit index which has moved dow to 2.17.

  figure53
Figure 5: Comparison of the propane and layer1 in PCU 0, epoch 3

Logging to file: p0_l1pr.log
XSPEC> sh all
 11:13:46 16-Apr-97
 Auto-saving is done after every command.
 Fit statistic in use is Chi-Squared
 Minimization technique is Lev-Marq
 Weighting method is standard
 Convergence criterion =     1.0000000000000D-02
 Querying enabled
 Prefit-renorming enabled
 Solar abundance table is angr

 Information for file   1
  belonging to plot group   1, data group   1
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0lr1_hv5.pha
  Background file  :bg_p0lr1_hv5.pha
  No current correction
  Response (RMF) file    : p0_l1_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     5 to    89
  File integration time     800.0
     and effective area     1.000
  File observed count rate     2071.    +/- 1.6153     cts/s
  Model predicted rate :    2071.

 Information for file   2
  belonging to plot group   2, data group   2
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: p0pr.pha
  No current background
  No current correction
  Response (RMF) file    : p0_l4_e3.rsp
  Auxiliary (ARF) file    : p0.arf
  XSPEC filter : NONE
  Noticed channels     3 to    18
  File integration time     912.0
     and effective area     1.000
  File observed count rate     465.9    +/-0.71475     cts/s
  Model predicted rate :    464.2

  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]( ( powerlaw[2] )wabs[3] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.000     frozen            1
    2    2    2   powerlaw   PhoIndex            2.169     +/-  0.1669E-02   1
    3    3    2   powerlaw   norm                12.06     +/-  0.3667E-01   1
    4    4    3   wabs       nH       10^22     0.3000     frozen            1
    5    5    4   constant   factor             0.6583     +/-  0.1464E-02   2
    6    2    5   powerlaw   PhoIndex            2.169     = par   2         2
    7    3    5   powerlaw   norm                12.06     = par   3         2
    8    4    6   wabs       nH       10^22     0.3000     = par   4         2
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      1981.125     using   101 PHA bins.
 Reduced chi-squared =      20.21557
XSPEC> flux 2 10
 Model flux   3.716     photons ( 2.3467E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  1
 Model flux   2.443     photons ( 1.5405E-08 ergs)cm**-2 s**-1 (  2.000- 10.000) DtSet :  2
XSPEC> flux 1 5
 Lower range     1.00     reset by matrix bound to     1.79
 Model flux   3.407     photons ( 1.5584E-08 ergs)cm**-2 s**-1 (  1.786-  5.000) DtSet :  1
 Model flux   4.502     photons ( 1.5129E-08 ergs)cm**-2 s**-1 (  1.000-  5.000) DtSet :  2
XSPEC> log none

Results from Cas-A

Figure 6 shows data from the first layer fit to a power law plus Fe line. The fit value of the line is 6.58 keV. The line has been fit simultaneously to all five detectors. There is less data for detectors 3 and 4 as these detectors were off for part of the interval which was accumulated. Note that the energy of the Cas A Fe line was one of the inputs to the energy scale of these matrices, so this result cannot be directly compared with other values. Remaining structure in the ratio plot is due to inaccuracies in the width of the energy response or the lack of a sufficiently detailed continuum model. The parameters of the fit are also summarized.

  figure61
Figure 6: Fits to the Cas A Fe line, front layer of all 5 detectors.

Logging to file: casa.log
XSPEC> sh all
 10:14:32 17-Apr-97
 Auto-saving is done after every command.
 Fit statistic in use is Chi-Squared
 Minimization technique is Lev-Marq
 Weighting method is standard
 Convergence criterion =     1.0000000000000D-02
 Querying enabled
 Prefit-renorming enabled
 Solar abundance table is angr

 Information for file   1
  belonging to plot group   1, data group   1
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: casa_p0lr1.pha
  No current background
  No current correction
  Response (RMF) file    : p0lr1_hv5.rsp
  Auxiliary (ARF) file    : none
  XSPEC filter : NONE
  Noticed channels    10 to    19
  File integration time     4112.
     and effective area     1.000
  File observed count rate     33.31    +/-9.00065E-02 cts/s
  Model predicted rate :    33.29

 Information for file   2
  belonging to plot group   2, data group   2
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: casa_p1lr1.pha
  No current background
  No current correction
  Response (RMF) file    : p1lr1_hv5.rsp
  Auxiliary (ARF) file    : none
  XSPEC filter : NONE
  Noticed channels    11 to    19
  File integration time     4112.
     and effective area     1.000
  File observed count rate     28.94    +/-8.38983E-02 cts/s
  Model predicted rate :    28.94

 Information for file   3
  belonging to plot group   3, data group   3
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: casa_p2lr1.pha
  No current background
  No current correction
  Response (RMF) file    : p2lr1_hv5.rsp
  Auxiliary (ARF) file    : none
  XSPEC filter : NONE
  Noticed channels    10 to    19
  File integration time     4112.
     and effective area     1.000
  File observed count rate     33.27    +/-8.99496E-02 cts/s
  Model predicted rate :    33.25

 Information for file   4
  belonging to plot group   4, data group   4
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: casa_p3lr1.pha
  No current background
  No current correction
  Response (RMF) file    : p3lr1_hv5.rsp
  Auxiliary (ARF) file    : none
  XSPEC filter : NONE
  Noticed channels    11 to    21
  File integration time     4112.
     and effective area     1.000
  File observed count rate     16.77    +/-6.38666E-02 cts/s
  Model predicted rate :    16.77

 Information for file   5
  belonging to plot group   5, data group   5
 telescope = XTE , instrument = PCA , channel type = PHA
  Current data file: casa_p4lr1.pha
  No current background
  No current correction
  Response (RMF) file    : p4lr1_hv5.rsp
  Auxiliary (ARF) file    : none
  XSPEC filter : NONE
  Noticed channels    10 to    18
  File integration time     4112.
     and effective area     1.000
  File observed count rate     14.28    +/-5.89300E-02 cts/s
  Model predicted rate :    14.26

  mo = constant[1]( powerlaw[2] + gaussian[3] )
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
  mo = constant[1]( powerlaw[2] + gaussian[3] )
  Model Fit Model Component  Parameter  Unit     Value                    Data
  par   par comp                                                          group
    1    1    1   constant   factor              1.000     frozen            1
    2    2    2   powerlaw   PhoIndex            2.758     +/-  0.1014E-01   1
    3    3    2   powerlaw   norm                1.094     +/-  0.1968E-01   1
    4    4    3   gaussian   LineE    keV        6.582     +/-  0.3397E-02   1
    5    5    3   gaussian   Sigma    keV           0.     frozen            1
    6    6    3   gaussian   norm               4.1565E-03 +/-  0.4864E-04   1
    7    7    4   constant   factor              1.037     +/-  0.4120E-02   2
    8    2    5   powerlaw   PhoIndex            2.758     = par   2         2
    9    3    5   powerlaw   norm                1.094     = par   3         2
   10    4    6   gaussian   LineE    keV        6.582     = par   4         2
   11    5    6   gaussian   Sigma    keV           0.     = par   5         2
   12    6    6   gaussian   norm               4.1565E-03 = par   6         2
   13    8    7   constant   factor              1.004     +/-  0.3839E-02   3
   14    2    8   powerlaw   PhoIndex            2.758     = par   2         3
   15    3    8   powerlaw   norm                1.094     = par   3         3
   16    4    9   gaussian   LineE    keV        6.582     = par   4         3
   17    5    9   gaussian   Sigma    keV           0.     = par   5         3
   18    6    9   gaussian   norm               4.1565E-03 = par   6         3
   19    9   10   constant   factor             0.4927     +/-  0.2301E-02   4
   20    2   11   powerlaw   PhoIndex            2.758     = par   2         4
   21    3   11   powerlaw   norm                1.094     = par   3         4
   22    4   12   gaussian   LineE    keV        6.582     = par   4         4
   23    5   12   gaussian   Sigma    keV           0.     = par   5         4
   24    6   12   gaussian   norm               4.1565E-03 = par   6         4
   25   10   13   constant   factor             0.4852     +/-  0.2398E-02   5
   26    2   14   powerlaw   PhoIndex            2.758     = par   2         5
   27    3   14   powerlaw   norm                1.094     = par   3         5
   28    4   15   gaussian   LineE    keV        6.582     = par   4         5
   29    5   15   gaussian   Sigma    keV           0.     = par   5         5
   30    6   15   gaussian   norm               4.1565E-03 = par   6         5
  ---------------------------------------------------------------------------
  ---------------------------------------------------------------------------
 Chi-Squared =      354.4485     using    49 PHA bins.
 Reduced chi-squared =      8.645085
XSPEC> eqw 3
 Additive group equiv width for model 3 (gaussian): 688. eV
 Additive group equiv width for model 6 (gaussian): 688. eV
 Additive group equiv width for model 9 (gaussian): 688. eV
 Additive group equiv width for model 12 (gaussian): 688. eV
 Additive group equiv width for model 15 (gaussian): 688. eV
XSPEC> log none

Propane efficiency

The propane layer is filled with proapne at an approximate pressure of 800 torr. Additionally it is known that during ground operations some xenon leaked out of the main volume into the propane volume. The amount of xenon in each propane volume is a parameter in the construction of the matrices. At the present we treat this value as a constant (i.e. there is no time dependance). The xenon does contribute appreciable opacity, particularly above the Xenon L edge, and therefore has an effect on the estimated efficiency in the main detector volume. Figure 7 shows the relative efficiency of the propane and 3 xenon layers for PCU 0. The value of the propane layer (beyond background rejection) is that it has the potential to extend the sensitive energy range to substantially lower values.

  figure69
Figure 7: Relative efficiency of the propane and 3 xenon layers in PCU 0.

Figure 8 shows the relative efficiency which is derived from the propane and the xenon oresent in the propane layer. Propane dominates the opacity below the xenon L edge, while xenon dominates the opacity above the L edge. The question of the relative efficiency of the propane layer relative to the first xenon layer requires further study.

  figure76
Figure 8: Relative efficiency of the propane and xenon within the propane layer of PCU 0.




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Next: About this document

Keith Jahoda
Thu Apr 17 10:31:38 EDT 1997