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ME CALIBRATION AND UPDATES TO THE CCF


Introduction

Changes in both format and content of the ME CCF have been introduced and are incorporated on FOTs produced from about the end of April 1985. Users can identify the new CCF by layout numbers of 5 and 3 for data types CB and SO respectively. The only other data type to have been changed is type SU.

These changes reflect recent work on both the Ar and Xe detector calibrations. Fitting the combined Ar and Xe half 1 spectra for the 1984 day 318 Crab Nebula observation using the Observatory Interactive Analysis System gives a chisq. of 141 for 148 degrees of freedom (Figure 1), with the column density fixed at 3x1021 atoms/cm2 and the power law slope at -2.1. 1% systematic uncertainties were included for both detectors. A normalisation figure of 9.53 and relative normalisation between the Ar and Xe detectors (a free parameter in the fitting) of 0.998 were determined. The improved Ar calibration results in residuals a factor of 2-4 smaller than in the previous calibration although the characteristic shape, a dip between 2-3 keV, is still present. For some unexplained reason detector E appears to give systematically larger residuals than the other detectors.

Changes to the Ar calibrations concern mainly the gain curves and their time dependence. The calibrations to date have assumed that the observed gain changes could be modeled as a change in the overall gain of each detector. Analysis of 6 Crab Nebula observations suggests that this is an oversimplification and that the amount of curvature, or non-linearity, is also time-dependent. To include this effect, the gain change parameters for both A1 and A2 are now included on the CCF.

The main change to the Xenon calibration is that an extra term has to be included in the Xenon resolution function, broadening the resolution by about 10% at 20 keV. This additional broadening, which was not present in the ground calibrations, is possibly caused by noise on the system power supplies. Its effect is expected to be considerably smaller for Ar. In addition there is evidence for a gradual decrease in overall gain of the Xe detectors, corresponding to a gain change of about 3.7% since launch. The change appears to be linear with time and occurs over the whole mission, except for detector A which exhibits an apparent change in gradient around 1984(85). Note that the Xe gain changes are in the opposite sense to Argon detector gain increases (ref. Express No.9, p.38).

Revised Record Layouts

Data Type CB

WordsContents
1-128 As before
129-144 Ar Fiducial or Reference Times dets A to H.
145-160 Start Time 1 of Applicability for A1 change
161-176 Start Time 1 of Applicability for A2 change
177-184 A1 Gain change/day (*E-4) at Times T1 to T2.
185-192 A2 Gain change/day (*E-5) at Times T1 to T2.
193-200 Amplifier Gain Settings at Fudicial Time
201-216 Start Time 2 of Applicability for A1 change
217-232 Start Time 2 of Applicability for A2 change
233-240 A1 Gain Change/day (*E-4) at Times T2
241-248 A2 Gain Change/day(*E-5) at Times T2
249-384 Currently Blank
385-504 As words 129-248 but for Xe except that the
units of the A1 and A2 change are E-7/day
505-768 Currently Blank
Note that if Start Time 2 = 0 then the Gain Change parameters for Time 1 apply at all times.
Data Type SD
WordsContents
1-128 Unchanged layout, Ar data
129-129 N1/0.01 for Xe Det. A Mode A
130-130 N2/0.01 for Xe Det. A Mode A
131-131 N3/1.E-4 for Xe Det. A Mode A
132-132 N4/1.E-5 for Xe Det. A Mode A
133-133 N5/0.01 for Xe Det. A Mode A
134-134 N6/0.01 for Xe Det. A Mode A
135-135 N7/1.E-4 for Xe Det. A Mode
136-136 N8/1.E-2 for Xe Det. A Mode
137-144 As above but for Mode B (The nominal)
145-160 As words 124-144 but for Det. B
161-176 As words 124-144 but for Det. C
177-192 As words 124-144 but for Det. D
193-208 As words 124-144 but for Det. E
209-224 As words 124-144 but for Det. F
225-240 As words 124-144 but for Det. G
241-256 As words 124-144 but for Det. H
How to use the Revised Calibrations
1. Xenon Resolution Function
The spectral distribution function for Ar is unchanged. For Xe it is now given by:

Del.V/V= SQRT (R2+(N8x2O/E)2)
where E is energy in keV and R the original Resolution. See the FOTH ch. 3.7.2.6, ie:

R=N1/10+N2/100/E+N3/l.E4xE+N4/l.E5xE2, E < N5/100
R=N6/100+N7/l.E4xE, E > N5/100

The values of N1 through N8 are given in the CCF record type SD.

2. Xenon Gain Coefficients
The Xe gain coefficients at time can be determined using the following relations where T2 is the start of applicability of the second set of gain change parameters, Tfud is the Fiducial time, DEL(T) the gain change per/day at time interval T, and A2 the gain coefficient.

DX = 0.0
IF (t.GT.T2.AND.T2.NE.0) then
  DX = (t-T2)*DEL(T2)
  t=T2
ENDIF
TX = t-T1
DG = TX*DEL(T1)+DX
A2 = A2/(DG*1.0)

A2 must be corrected for any difference in digital amplifier settings MAIN) between the observation time and the fiducial time (see Express No. 6, p.25). The values of DGAIN can be obtained from the Memory Load Commands in the observation directory.

GAIN = (DGAIN-200)*0.004+1.0
R = GAIN(t)/GAIN(Tfud)



and




A2 = A2/R


This relation differs from that given earlier for Ar since the Ar gain coefficients give channel boundaries for a given energy whereas the Xe coefficients give the reverse. The relation between energy and channel number (k between 1 and 128) is given by (FOTH Ch. 3.7.2.5):

E = A1/100+A2*K+A3*K2/l.E6+A4*K3/l.E8

Note that the Xe gain relation is actually linear since A1, A3 and A4 are all zero!

3. Argon Gain Coefficients
The CCF contains gain change parameters for coefficients A1 and A2. However rather than storing the values of A2 the values of A2real+ A1 * A4 are actually stored since these are easier to determine. The gain relation is unchanged as (FOTH Ch. 3.7.2.5):


mV = A1*(1.0-EXP(-A4*E))+A2*E*EXP(-A3*E)

However the-values of A2 stored on the CCF must first have the value of A4*A1 subtracted from them thus:


A2real = A2stored-A1*A4

Then the effect of the gain change with time can be calculated. Since T2=0 for all Ar detectors, the relation is:.


TX = T-Tfud
DG1 = TX*DEL1(T1)
DG2 = TX*DEL2(T1)

A1 = A1+DG1
A2real = A2real+DG2
A2 = A2real-A4*A1

Note that R has to be calculated as for Xe but is applied in the opposite sense since the gain coefficient relation is reversed. So finally:


A1 = A1*R

A2 = A2*R

Examples:

The following gives the gain parameters calculated using the Observatory Interactive Analysis system. For Detector D:


Date Ar/Xe DGAIN A1 A2 A3 A4
84/086 Ar 252 748.25 15.544 0.0 0.05
84/086 Xe 193 0.0 0.4139 0.0 0.0
85/087 Ar 209 889.75 7.787 0.0 0.05
85/087 Xe 193 0.0 0.4318 0.0 0.0

A.N. Parmar
A. Smith
Fig 1 spectra and residual described in text

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