February 2, 2000

This note documents the current estimate of the systematic error associated with the Epoch 4 Sky_VLE predicted background, derived from data that went into the model. The systematic error is approximately 0.15 cts/s/2pcu in the 2-10 keV band for data selected from the front layer. This is approximately three times as large as the statistical error on a given data point.

The background data were accumulated from five different pointing directions (table 1). Data from all five directions were used in the construction of the model, and light curves were extracted from these data using the standard selection criteria for faint sources (table 2).

Table 1: Pointing Directions
Pointing Rates vs Bin number Residuals vs Time
1a,b 5.00 -67.00 pt1_plot1.ps pt1_plot2.ps
2a 60.00 +2.00 pt2_plot1.ps pt2_plot2.ps
3a 138.00 +15.00 pt3_plot1.ps pt3_plot2.ps
4a 235.00 +10.00 pt4_plot1.ps pt4_plot2.ps
5a 345.00 -18.00 pt5_plot1.ps pt5_plot2.ps

a Observed for several orbits every three weeks since 11/96
b Part of the twice daily campaign started in 4/98

Table 2: Selection Criteria
Criterion Description
(BKGD_THETAa < -70.0 or BKGD_THETA > 150.0) or TIME_SINCE_SAAb > 30.0 or TIME_SINCE_SAA < 0.0 Outside the South Atlantic Anomaly
PCUn_ON 0.5 PCUn fully on
ELV > 10.0 Angle between the satellite pointing direction and the Earth's horizon
OFFSET < 0.01 Angle between the satellite pointing direction and the nominal field of view
VpX1L, VpX1R < 6.25 Veto rate between the propane layer and the left/right halves of the Xenon layer
(VpX1L+VpX1R)/Q6c < 0.1 Normalized propane layer veto rate

a Longitude of the ascending node of the satellite's orbit
b Time since SAA passage
c Veto rate between six of the eight anode chains

Light curves are made available showing the observed rate (sky plus internal background), Ri, the model predicted rate, Mi, and the observed-model rate, Xi = Ri - Mi, for each of the five background pointing directions (column 4 in the above table). Time is not shown here as the data are taken from many orbits spread over many years. Instead, the x-axis is a running number of successive orbital bins rather than time. The statistical error for individual points is simply the Poisson error, i = Ri.

A second set of figures show the observed-model rate versus time for each background pointing direction (column 5).

For a particular light curves, the total variance is given by


where the individual data values are weighted by a factor


which includes both systematic and measurement errors. The latter is given by


and the derived systematic error is


Values of the standard deviation, average error, and derived systematic error are given for each of the five background pointing directions (table 3). The large values of systematic error are due, in part, to the occasional outlier, which may (or may not) be representative of those that will also occur in source data. We also calculate the systematic error excluding points greater than 7 from the mean (i.e. as for the Epoch 3 model). These values are also given (table 4).

Table 3: Systematic Errors
Pointing su < err > syst

1

 0.175 0.060 0.164

2

 0.195 0.065 0.184

3

 0.145 0.058 0.133

4

 0.122 0.056 0.108

5

 0.105 0.057 0.088

Table 4: Systematic Errors excuding Outliers
Pointing su < err > syst

1

 0.142 0.061 0.129

2

 0.161 0.066 0.147

3

 0.145 0.058 0.133

4

 0.122 0.056 0.108

5

 0.105 0.057 0.088