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The first observation of the Crab made in 1983 with the GSPC on EXOSAT indicated that the response of the detector as given by the pre-launch calculations and calibrations was incorrect. A large deficiency in counts below 4 keV was apparent along with a line feature in the spectrum around 4.78 keV. Effective areas as a function of energy were modified to give the correct fit to the Crab. In addition to these problems the absolute gain calibration as defined by two line features in the background, which had been ascribed to Lead L fluorescence, did not give the correct energy for the Sulphur line measured from Cas A. This suggested that these lines might not be Lead, but rather were from Bismuth, perhaps caused by the radio-active decay of a lead isotope.

Over the past few months a major effort has been made to obtain' a fuller understanding of the GSPC response. This has, in part, been helped by the performance of a long observation of the Crab made with the burst length discriminator set to give a maximum acceptance range. This discriminator is used to reduce the particle background, but also removes a small percentage of X-rays in an energy dependent way. Since the energy dependence of this process requires calibration, such an observation was essential in order to investigate the above problems. The appropriate observation of the Crab was made in February 1985.

Using data from this observation, considerable progress has been made. A number of uncertainties in critical detector parameters have come to light and make it possible to reproduce the Crab spectrum to within 2% without making arbitrary changes to the response. The following describes the various steps that were taken to resolve the problem of the GSPC calibration.

It should be stressed that calibration of the GSPC, a new instrument with a resolution approximately a factor of two better than that of a conventional proportional counter, presented new and unexpected problems. The improved resolution revealed many subtle effects that hitherto would have gone unnoticed in a proportional counter. In retrospect, the ground calibration fell short of what was required to fully model the nuances of the instrument response.

1. The Absolute Energy Calibration

A detailed study of the background spectrum has been made by P. de Korte. A spectrum taken in gain one is shown in Figure I. This reveals a number of line features that can be identified as resulting from three separate processes. First the two strong lines between channels 65 and 100 are the L alpha and beta lines from the fluorescence of lead in the collimator. A cursory glance at Figure 1 reveals that the L beta line is stronger than the alpha line, which is contrary to the expected branching ratio of 110:70. This is caused by a second line complex that overlaps the lead lines. The broad bump around channel 125 is a blend of the lead L gamma line and a Thorium L beta line at 16.2 keV, the latter resulting from the radioactive decay of residual plutonium in the Beryllium window. The K alpha Thorium line is at 12.9 keV and lies very close to the lead K beta line at 12.6 keV such that the upper of the two lead lines is a blend, which can be treated as a single line with a mean energy of 12.703 keV. The energy of the lead L alpha line is 10.541 keV.

The remaining line in the spectrum between channels 200 and 225 is identified with Xenon K alpha and arises from the escape photons of high energy background particle events that are captured by the detector walls. This line cannot be used as an absolute calibration standard since comparison with the energies of the lead lines gives an energy lower than the expected value of 29.67 keV, probably arising from the fact that the escape photons illuminate the whole detector. If the photons deposit their energy in the scintillation region or close to the detector walls then the total energy deposited will be less than that of a photon entering via the detector window. The apparent energy of this line appears to be 29.4 keV. For very bright sources where the lead lines are not visible it can be used to lock the gain. Otherwise the two lead lines should be used since they lie closer to the critical iron line region. It is recommended that the bump around 16 keV should not be used since it is too weak to accurately lock the gain. To summarize:

Lead L alpha = 10.541 keV

Lead L beta + Thorium L alpha = 12.703 keV

Xenon K feature = 29.4 keV

2. The Detector Gain

The line feature that appears around 4.78 keV in all X-ray spectra occurs because the gain of the detector increases above the LIII edge of the Xenon filling gas the reason being that the Xenon atoms do not completely de-excite after the initial ionisation process and a small amount of energy is not recorded in the detector. Above the LIII edge the final ionisation state of the Xenon atom increases. Measurements of this effect by Carlson et al. (1966, Phys.Rev. 151,41) for Xenon atoms in close to vacuum conditions confirm this, although the value of the gain jump predicted by the Carlson work is much larger than the 50 eV estimated from the Crab spectrum. This difference is most likely due to the fact that the Xenon in the GSPC is at a pressure of one atmosphere. There do not appear to be any major gain jumps across the first two L edges, although it is difficult to rule out small jumps of 10 eV or less.

There must be similar jumps in the gain across the other shells. While these are not relevant to the absolute gain calibration in the energy range that the GSPC is sensitive, they will cause the zero channel offset (as defined above the LIII edge) to be greater than 50 eV. The amount of this offset could not with any degree of confidence be determined from the pre-launch calibrations, but was estimated to be +150 eV from fitting to the Crab spectrum as described below.

In dealing with the gain jump in spectral fitting programs it is best to consider the problem in volts. The decrease in gain above the LIIIedge (at 4.78 keV) is equivalent to the volts generated by a photon above the edge being lower by 50 eV times the slope of the energy/volts curve (GP). Another way of thinking of this effect is that just above and below the edge a measured voltage corresponds to one of two possible energies. Since the absolute energy calibration of the detector is determined above the LIII edge all channel boundary definitions are referenced to the gain above the LIII edge.

The channel boundary convention is defined as follows:

E = (N-0.5).GP + 0 150

where N is the channel no. from 0 - 225 (as defined in FOTH) and E is the energy of the required channel. in this definition N=1.0 gives the centroid energy of the first channel. This applies to all gain modes. The value of GP should be determined for each observation from the measured position of the lead lines. GP is approximately 0.13 for gain 1.0 and 0.065 for gain 2.0.

If the source is too bright to determine accurately the position of the lead lines and the gain is 2.0 so that the Xenon feature is not available, then use the data from the proceeding slew to determine the gain. DO NOT use the following slew. This is because for thermal control of the CMA the 28 volt Al power lines (which drive the HT converters) to all the experiments are briefly switched off after an observation. The gain of the GSPC photomultiplier may change by several percent when high voltages are switched off and on. During long continuous observations the gain drifts by at most one gain 2.0 channel per 12 hours, and usually by less.

3. Loss to the Window

Part of the electron track created in the detector will be lost to the window before it has time to drift away. In general the total number of events for which this causes a significant decrease in the measured energy of the ionising event is confined to those which occur very close to the window. While this constitutes a small fraction of the total events registered it is still sufficient to cause a low energy tail to the gaussian distribution. Because the penetration depth of the photons is a very strong function of energy this effect is strongest at low energies and just above the L edge. Inoue et al. (1978, Nuc.Inst. Method, 157,295) have considered this problem in detail and give the following formula which gives the probability of a photon with energy El giving a measured energy in the detector of E (where E <E1):

f(E).dE = k.(1-E/E1 ) k-1 .dE

The parameter k depends on the diffusion coefficient, drift velocity density and mass absorption coefficient of the detector filling gas. For the EXOSAT GSPC, k has a value of 0.03 at 5.9 keV, determined by adjusting its value to reproduce the observed low energy tail to be consistent with the residual flux observed below the low energy cut-off of the window ( < 2keV). This value of k is insensitive to other uncertainties in the detector calibrations. It is comparable to that expected from the theoretical value and also with that found by the TENMA group from their pre-launch calibrations (Koyama et al. 1985, P.A.S.P. 36,659).

Appendix I contains a listing of a function PTAIL which returns the probability of measuring in a given energy interval DE centered on E a residual low energy tail from a photon with an initial energy E1. It should be noted that the above function becomes undetermined at E=E1. This is taken care of in PTAIL by integrating over the last milli-percent of the function up to E1. The resulting line profile should then be spread by the detector broadening function. In Figure 3 the expected profile of a line injected at a single energy is illustrated. The second peak is the escape peak. In the Observatory software to save computing time, the low energy tail is not included on the escape peak. This will not make any difference since the L-escape only represents < 3% of the total count rate above 4.78 keV.

4. The Beryllium Window Thickness

The pre-launch calculations assumed that the window had a constant thickness of 175 microns (the specified minimum). They, failed to take into account the fact that the window is dome shaped and that the projected thickness increases towards the edge of the dome (where most of the effective area is). Measurements on flight spare windows indicated that thicknesses varied between 175 and 220 microns, and the window thickness of the flight GSPC must at present be considered a free parameter (within reasonable limits).

5. Edge Effects

Towards the edge of the detector the electric field geometry becomes uncertain such that electron tracks may be deflected to the detector walls and not registered. This area of the detector is critical because it constitutes a large fraction of the total effective area. In addition at this point the conical shaped detector walls meet the dome shaped window ie. the total gas depth decreases to zero. This can cause a fairly large L edge to appear in the response because photons just below the edge have a higher probability of not being stopped than those just above it where the penetration depth is low.

The fitting procedure described below indicated a stronger L edge in the spectrum than would be expected. It could be removed to a large extent by adjusting the detector parameters to take into account the expected field geometry.

6. The Burst Length Efficiencies

Discrimination of events based on the rise time of the pulse generated (the burst length) can be used to increase the signal to noise ratio, by reducing the particle background counting rate. The optimum setting of the single channel analyser discriminator is a trade-off, between the reduction in background and the number of X-rays rejected and was established during the performance verification phase as channels 89-107.

This results in a loss of between 10 and up to 90% of the X-rays registered in the detector, with the fraction lost increasing rapidly below 5 keV. The burst length discrimination efficiency as a function of energy was determined during the February 1985 observation of the Crab by dividing the burst length discrimination 89-107 spectrum by the 'no-discrimination' spectrum. The data were smoothed and fit to a splined polynomial. The function GSAXE given in Appendix II returns for a given energy E, the fraction of X-rays that are not attenuated. The efficiencies are not well determined above ~15 keV because of limitations in the background subtraction. However there appears to be no major change in efficiency at higher energies and it is taken to be a constant. Also given are the efficiencies for the 89-104 setting used early in the PV phase.

These efficiencies should be applied AFTER the spreading by the detector response. Thus there will be only one set of effective areas for all burst length window settings. (In the earlier calibration the burst length efficiencies had been included in the initial effective areas because of uncertainties in deconvolving these from the other problems in the detector response).

7. Escape Fractions

A certain number of photons emitted by the Xenon ions as they de-excite will escape the detector and hence will cause a deficiency in the detected energy of precisely the energy of the fluorescent photon. The efficiency of this process for the L shell of Xenon is 3% at 5.1 keV, and decreases linearly to zero up to the K absorption edge. At the K edge this then increases to 58% and is kept constant. The edge energies are taken to be an average of the various sub-shells and are 5.1 keV (L) and 34.56 (K). Note the escape energy that must be subtracted is 4.33 keV and 30.49 keV respectively.

8. Systematic Uncertainties

The main limiting factor will always be the fact that the channel boundary widths are only known to 1%. This means that a systematic error of 1% of the total count rate should be added quadratically to the statistical error.

9. The Effective Areas and Zero Offset

The above considerations leave two unknowns in the detector parameters: 1) The average thickness of the window; 2) the energy offset of channel zero (when referenced to energies above 4.78 keV). The effect of varying the zero offset on fits to the Crab data without burst length discrimination was tested allowing the window thickness to be a free parameter. The Crab spectrum was assumed to have an energy index of 2.1 and a low energy cut-off of 3.5 x 10 21 H/cm2. Residuals from the fit using two different offsets of 50 eV and 250 eV are shown in Figure 3. The deviation from the fit in the lower channels around 2-3 keV strongly depends on the chosen offset. When 50 eV is used there is a strong excess of counts, whereas for 250 eV this becomes a deficit. In Figure 4 finer steps of varying offset are used. A reasonable fit to the data can be obtained for an offset of 150 eV with an uncertainty of at most 50 eV in total. This translates to plus or minus 25 eV at the iron line. The required window thickness was ~200 microns.

There are still some small (< 2%), systematic trends in the residuals left centered on 4.78 keV which can be attributed to edge effects in the detector. Since these are very difficult to model they were removed by fitting a polynomial to the response. The final residuals are shown in Figure 5 along with the original PHA spectrum. Also given is the best fit to the data obtained from the Crab using the 89-107 burst length setting. The final overall effective areas fall short of the pre-launch values by ~15%. This is ascribed to uncertainties in masking by the collimator support structures, edge effects in the detector and count rate independent dead time effects (see 10). It has been corrected by re-normalising the effective areas. In Appendix III the current set of effective areas is listed.

These calibrations were then applied to the data on Cas A. The energy of the Sulphur line is now consistent with that measured by the Einstein SSS. In the case of the various different Crab observations, the new calibrations all give in the 2-16 keV band (and where available the 2-30 keV band) a fit consistent with a slope of 2.10 + 0.03 and a column density of 3.5 + 1.5 x 1021 H/cm 2 .

10. Dead Time

The accumulation times for the Crab observations were corrected for data handling sampling effects using the formula:

f = Co/(-S-Log(1.0 - Co/S))

where Co is the observed count rate, and S is the sampling rate in Hz given by the workspace parameter No.2 of all GSPC OBC programs. The typical dead time is~0.7% for the background and ~5% for the Crab (gain 2.0).

Additional 2.5% dead time effects (ref. p.67) were not included for the Crab observations used to determine the GSPC effective areas. Since these are count rate independent they were taken into account during the re-normalisation of the effective areas to give the correct normalisation for the Crab spectrum. Only the sampling effect should be included when computing the dead time for spectral data. Note that the current CCF backgrounds are not dead time corrected.

11. Outstanding Issues

A self-consistent fit to the GSPC spectrum of the Crab can now be obtained up to a level of a few percent. Any remaining uncertainties are most likely caused by edge effects in the detector. The only improvement possible is in measuring the burst length discrimination efficiency as a function of energy. The current values become limited by uncertainties in the background subtraction, which may lead to systematic variations at around the one percent level. This is well within the quoted systematic uncertainties. A further set of observations of the Crab will soon be carried out to better determine this parameter. However for all purposes the current values are quite adequate and the difference will not be noticed except for the very brightest sources (> 1 Crab).

There have been reports of problems with subtracting the CCF background from recent data suggesting that the shape of the background is varying. This may be because there is either a long term evolution with time or a dependence with the absolute detector gain. A study of this problem is currently underway and it is likely that a time/gain dependent CCF background will be issued. In the meantime, users should compare the background obtained from the slew file with that from the CCF. If there are obvious discrepancies, in particular an excess or deficiency below channel 40 (gain 2.0), then two possible solutions exist. First if the slew is long enough, use this as the background. Otherwise, contact M. Gottwald for selection of a new background from an observation close to the one in question.

12. New GSPC Operating Procedures

Two changes to the operation of the GSPC have been made:

(1) The photomultiplier LED stimulations have been discontinued except for one made before and after the high voltage has been turned off. Experience has shown that the lead lines are quite adequate for measuring the gain stability and that stimulations have a perverse habit of being done when X-ray bursts or other interesting events occur.

(2) The standard gain mode is now gain 1.0. This is to accumulate a time history of the background in gain 1.0 and to ensure that any (cyclotron) line features in spectra above 15 keV are not missed. It should be noted that this will in no way impact on measurements of the iron line which in gain 2.0 was grossly oversampled (gain 1.0 gives 10 channels across a narrow iron line). The only justification for using. gain 2.0 is for studying the Sulphur line in bright supernova remnants, however no more observations of these objects (basically Cas A and Tycho) are presently planned. If a user still feels strongly that gain 2.0 is best then a background observation carried out in gain 2.0 will be assigned on the same orbit.

N.E. White
Fig 1 and Fig 2 the gspc background spectrum and response 
to a narrow line at 6 keV

Fig 3 residual from Crab fits for various detector offsets

Fig 4 same as figure 3 but with finer steps of varying offsets

Fig 5 final Crab fits and residuals

Appendix I

0001  FTN4,L              
0003  C
0004  C
0006  C          TAIL IN THE GSPC RESPONSE        NEW JUNE 85
0007  C          SEE INOUE ET AL (1978) NUCL. INST. METHODS, 157, 295.
0008  C
0009  C
0010        DATA IJ/ 1 /
0011        IF (IJ.EQ.0) G0 TO 1
0012        AKMN = 0.03
0013        IJ = 0
0014    1   PTAIL = 0.0
0015  C
0016  C
0017        EEL = ELINE/5.9
0018        IF (ELINE.GT.10.) EEL = 1.69
0019        AK = AKMN / (EEL)**2.66667
0020        IF(ELINE.LT.4.78) AK = AK*0.348
0021        IF(ELINE.LT.5.10) AK = AK*0.710
0022        IF(ELINE.LT.5.45) AK = AK*0.860
0023  C
0024  C
0025  C
0026  C
0027    9  IF (EOBS.GE.O.9999*ELINE) G0 TO 8
0029       RETURN
0030    8  PTAIL=(I.0-(EOBS-DE/2.0)/ELINE)-*AK
0031       RETURN
0032       END

Appendix II

0001 FTN4,L
0003 C
0004 C
0007 C 
0009 C                 1 89-107
0010 C                 2 89-104
0011 C
0012 C
0013       DIMENSION E(S).POLI ( 13).POL2(13)
0014	   DATA E/0.0,15.0,
0015 C
0016 C
0017 C
0018 C 89-107/WO: SPLINE FIT TO-8S +84 CRAB DATA
0019 C
0020       DATA POL1/, -0.1O5E-02,0.227E-04,0.I6OE-0I,
0021      *-0.122E-02 0.386E-04,0.578E-02,-0.630E-04,0.23SE-06,
0022      *0.129E-02,0.838E-04,-0.385E-05/
0023 C
0024 C
0025 C 89-1-04/WO
0026 C
0027       DATA POL2/0.322.0.184E-01,-0.969E-03.0.278E-04,0.153E-01
0028      *-0.133E-02,0.437E-04,0.543E-02,-0.36E-04.-O.197E-07,
0029      *0.270E-02,0.222E-04 -0.429E-O5/
0030 C
0031 C 
0032 C 
0033       DATA NMIN/12/,NMAX/100/
0034 C
0035 C
0036 C
0037       IF(IBL.NE.0)60 TO I
0038       GSAXE=1.0
0039       RETURN
0040       CONTINUE
0041       CHAN=(EIN-0.I5O)/0. 138792+0.5
0044       CHAN=CHAN-NMIN+I
0047       IF(GSAXE.GT.I.0-)GSAXE=I.0
0048       RETURN
0049       END

0001 FTN4,L 0002 SUBROUTINE SPLIN(P, E, N, EIN, VAL) 0003 DIMENSION P(l),E(l) 0004 VALP=P(l) 0005 VAL=VALP 0006 IF(EIN.LE.E(l))RETURN 0007 DO 88 IV=I,N0 0008 IF(EIR.GE.E(IV).AND.EIN.LT.E(IV+1))G0 TO 90 0009 EE=E(IV+I)-E(IV) 0010 VAL=VALP+POLY(P,EE,IV) 0011 88 VALP=VAL 0012 IF(EIN.GT.E(N+I))RETURN 0013 90 EE=EIN-E(IV) 0014 VAL=VALP+POLY(P,EE,IV) 0015 RETURN 0016 END 0017 FUNCTION POLY(P,EE,IV) 0018 DIMENSION P(1) 0019 IN=(IV-I)*3+1 0020 POLY=P(IN+l)*EE+P(IN+2)*EE*EE+P(IN+3)*EE*EE*EE 0021 RETURN 0022 END

Appendix III - GSPC Effective Areas

1 1.0000 .0000

2 1.1000 .0000

3 1.2000 .0001

4 1.3000 .0022

5 1.4000 .0170

6 1.5000 .0815

7 1.6000 .2757

8 1.7000 .7209

9 1.8000 1.6306

10 1.9000 3.1601

11 2.0000 5.4313     
12 2.1000 8.4935     
13 2.2000 12.3211    
14 2.3000 16.8275    
15 2.4000 21.8858    
16 2.5000 27.3496    
17 2.6000 33.0705    
16 2.7000 38.9102    
19 2.8000 44.7474    
20 2.9000 56.4815    
21 3.0000 56.0329    
22 3.1000 61.3419    
23 3.2000 66.3661    
24 3.3000 71.0789    
25 3.4000 75.4660    
26 3.5OOO 79.5236    
27 3.6000 83.2557    
28 3.7000 66.6728    
29 3.8000 89.7899    
30 3.9000 92.6256    
31 4.0000 95.2011    
32 4.1000 97.5389    
33 4.2000 99.6629    
34 4.3000 101.5972   
35 4.4000 103.3663   
36 4.5000 104.9942   

37 4.6000 107.5619

38 4.7000 111.6849

39 4.8000 121.0973

40 4.9000 122.6857

41 5.0000 119.4384

42 5.1000 121.7029

43 5.2000 122.8926

44 5.3000 123.9889

45 5.4000 124.9976

46 5.5000 126.3690

47 5.6000 127.2448

48 5.7000 128.0493

49 5.8000 128.7864

50 6.3000 131.5941

51 6.8000 133.2057

52 7.3000 133.8900

53 7.8000 133.8328

54 8.3000 133.1673

55 8.8000 131.9922

56 9.3000 130.3839

57 9.8000 128.4043

58 10.3000 126.4752

59 10.8000 124.5567
60 11.3000 122.4343
61 11.8000 120.1254   
62 12.3000 117.6462
63 12.8000 115.0128
64 13.3000 112.2418
65 13.8000 109.3504
66 14.3000 106.3563
67 14.8000 103.2782
68 15.3000 100.1353
69 16.3000 93.7318
70 17.3000 87.2949
71 18.3000 80.9571
72 19.3000 74.8260
73 20.3000 68.9814
74 25.3000 45.1878
75 30.3000 29.8375
76 35.3000 78.1392
77 40.3000 64.3952
78 45.3000 52.6245
79 50.3000 42.9379
80 55.3000 35.1340    
81 60.3000 28.9043
82 65.3000 23.9414
83 70.3000 19.9784
84 75.3000 16.7982

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