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Astron. Astrophys. 343, 899-903 (1999)

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2. Investigation of systematic effects

The FGS photometric data had to be extracted from the Engineering-Subset-Data Files of the HST Data Archive at STScI in Baltimore, Maryland. First, datapoints not obtained in "Fine Lock Mode" of the FGS were eliminated. Second, the measurements were averaged over intervals of 10 seconds.

The resulting "raw" light curve of the third day of GS-75 is shown as a typical example in the top panel of Fig. 1 and the presence of systematic effects is obvious. The intensity modulation has two different characteristics. First, high peaks in the count rates, reaching extreme values, appear periodically but not in each orbit. These "spikes" can be identified as the influences from the South Atlantic Anomaly (SAA). The second type of modulation is characterized by changes synchronous to the HST orbit with a period of 96 minutes. The amplitude of this effect decreased during the HDF program. This effect can be explained by stray light contribution from the Earth.

[FIGURE] Fig. 1. Light curve of GS-75, third day of the HDF program. Top: raw data, middle: with correction for the South Atlantic Anomaly (SAA), bottom: residual light curve after SAA and stray light correction. Note the different scale for the top panel .

2.1. South Atlantic Anomaly (SAA)

In the Earth's southern hemisphere, near the east-coast of South America, a distortion of the terrestrial geomagnetic field exists. This region is called the South Atlantic Anomaly and its boundary at an altitude of 500 km ranges from -90 and +40 degrees in geographic longitude and from -50 and 0 degrees in latitude. As the spacecraft is exposed to high energy protons and electrons no astronomical or calibration observations are normally performed during passages through the SAA. However, in the transition zones to the SAA the FGS did measure already increased intensities before the PMTs were switched off. To map the influence of the SAA on the data we calculated the subsatellite position of the HST in geographic coordinates and indicated any positions for which the FGS count rate exceeded a given threshold (Fig. 2). An increase in count rates at the boundaries of the SAA is clearly visible, which is consistent with models in the literature (e.g. Zombeck 1992).

[FIGURE] Fig. 2. Map of the intensities measured for GS-75 above a chosen threshold as a function of the geographic position of the HST. An increased density of HST positions (points) for which the FGS countrate exceeded the threshold is clearly visible at the border of the South Atlantic Anomaly. When crossing this anomaly the FGS' were switched off.

As it was not possible to model reliably the boundary to the SAA we had to remove all "bad" data obtained within a heuristically determined trapezoidal shaped area (Fig. 2) from the photometric time series. The same figure also illustrates that the orbit of the HST approaches the southern auroral zone, as is evident from a slightly increased background level at the most negative latitudes. Furthermore, there is an indication for an area of slightly enhanced radiation just opposite to the SAA. The middle panel of Fig. 1 shows the data corrected for the SAA.

2.2. Contribution of stray light

A residual harmonic variation with the HST orbital period of 96 minutes and with a decreasing amplitude during the ten days remained in the data after the correction for effects due to the SAA. This effect can be explained as stray light coming from the illuminated Earth below the spacecraft. The brightness variations are a consequence of the changing aspect of the sunlit Earth relative to the spacecraft. Our result confirms the predictions (Petro 1995) for the contribution of background light in the Hubble Deep Field.

For a fuller analysis, the phase angle [FORMULA] between the Sun and the position of the HST was calculated according to simple spherical trigonometry:

[EQUATION]

with b and l the geographic latitude and longitude of the sun and the HST, respectively.

For [FORMULA] the HST is positioned right over the fully illuminated Earth, while at [FORMULA] the HST flies over "mid-night" sites, and the HST crosses the terminator at [FORMULA]. Hence, the contribution of scattered light from the Earth increases with decreasing phase angle [FORMULA]. As the orbit inclination of the HST is 28.5o and the orbital precession period is about 56d, the phase angle usually does not reach the extreme values of 0o and 180o.

To determine the amount of stray light correction, [FORMULA] was binned in intervals of 10o and the count rates were averaged over an observing period of 24h. A smaller size of the binning interval would potentially allow to better model possible details of the stray light function, but this advantage would be lost by the larger scatter of the average bin values due to less data points per (smaller) bin. Any high frequency pulsation would be smeared out with this procedure. The stray light effect is not symmetric around [FORMULA] (Fig. 3) because of the orientation of the optical axis of the HST. Therefore the stray light correction over the eastern hemisphere is different from the western hemisphere. An example for the procedure is shown in Fig. 1. For a given phase angle the correction was computed from a linear interpolation between appropriately chosen bins.

[FIGURE] Fig. 3a-d. Stray light Correction for GS-75 and the second day of the HDF program - a  stray light west, b  stray light east, c  uncorrected light curve with superposed stray light contribution computed from linear interpolations between appropriately chosen bins in panel a or b , respectively, d  stray light corrected light curve

2.3. Problems with FGS 2

In addition to the contribution of the SAA and the stray light contamination we found an error in the FGS 2 measurements. During an 11h time interval of the 10 days HDF program the count rates of both PMTs in the FGS 2 Y-axis dropped significantly, but the X-axis channels were not affected. For technical details, the meaning of X- and Y-axes, working principles, etc., see Holfeltz et al. (1995). As we add the counts of all four PMTs to a single photometric data point (see Paper I), the total intensity decreased by about 20%. The electronics of the Y-axis components recovered towards the end of the 11h period to the count rate observed before the interval. The origin of this effect presently is unknown and data points obtained during this time were excluded from the final analysis. No evidence for a similar behavior was found throughout the whole HDF program in the FGS3 (GS-54) data sets.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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