ME CALIBRATION AND UPDATES TO THE CCF
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
1. Xenon Resolution Function
The spectral distribution function for Ar is unchanged. For Xe it is now given by:
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)
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. 184.108.40.206):
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. 220.127.116.11):
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
The following gives the gain parameters calculated using the Observatory Interactive Analysis system. For Detector D: