February 22, 2000

This note documents the current estimate of the systematic error in the Epoch 3 faint source (L7_240) model background for different energy bands. Below 10 keV, the systematic error is approximately 0.15 cts/s/3pcu, or 2% of the background count rate, and is three times as large as the statistical error on a given data point. Above 10 keV, the systematic error is at least 0.1 cts/s/3pcu, or 0.5% of the background rate, and is twice as large as the statistical error.

The background data are accumulated from five different pointing directions (table 1). Data from three out of every four obsids were used in the construction of the model. Below 10 keV, where the statistical uncertainty in each data point is much smaller than the systematic error, light curves were extracted from the data that did not go into the construction of the model. However, above 10 keV, the systematic error is comparable to the statistical error, even when the data are binned coarsely. Therefore, to improve the signal to noise, light curves were extracted from all the data above 10 keV. From an extrapolation of the HEAO-1 results, spatial fluctuations in the Cosmic X-ray Background (CXB) are expected to contribute approximately ±0.4 cts/s/3pcu in the 2-10 keV band. Therefore, below 10 keV, the spatial fluctuation in each pointing direction has been subtracted prior to estimating the systematic error (errors estimates without subtracting the spatial fluctuation are also given; they should be regarded as a strong upper limit). The standard selection criteria for faint sources was used in the extraction of the light curves (table 2).

Table 1: Pointing Directions

1a,b 5.00 -67.00
2a 60.00 +2.00
3a 138.00 +15.00
4a 235.00 +10.00
5a 345.00 -18.00

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-model rate , Xi , for the different energy bands (column 2 in table 3). The statistical error for individual points is simply the Poisson error, i = R i , where Ri is the observed rate (sky plus internal background). For a particular light curve, 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

The standard deviation, average error, and derived systematic error are given for each energy band (table 3), with the values of systematic error quoted as cts/s, cts/s/ch, and as a percentage of the observed rate (sky plus internal background).

Table 3: Systematic Errors

Energy Band Residuals vs
su < err > syst
% bkgd rate

2-6 keVa

2-6.jpg 0.137 0.030 0.134 0.011 2%

2-6 keV

2-6.jpg 0.217 0.030 0.215 0.018 3%

6-10 keVa

6-10.jpg 0.048 0.025 0.042 3.8E-3 1%

6-10 keV

6-10.jpg 0.110 0.025 0.107 9.7E-3 2.2%

10-15 keV

10-15.jpg 0.023 0.011 0.021 1.5E-3 0.6%

15-20 keV

15-20.jpg 0.017 0.010 0.013 1.0E-3 0.5%

20-30 keV

20-30.jpg 0.048 0.013 0.046 3.5E-3 0.8%

30-50 keV

30-50.jpg 0.042 0.015 0.039 1.5E-3 0.5%

a Corrected for spatial fluctuations in the CXB