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6 Background semi-annuli

  The same data as in Sect. 5 were used to create a set of spectra extracted from within two semi-annuli located 17' from the center of the FOV at positions diametrically opposite to the locations of the radioactive calibration sources (see Fig. 1). The location and sizes of the semi-annuli were carefully chosen to ensure that source "spill-over'' is only significant for bright sources, while the correction for mirror vignetting is kept as small as possible. The sum of the semi-annuli geometric areas is equal to that of the standard 8' radius source extraction region. Counts within the semi-annuli consist of both particle and internal background events (i.e., the NXB), sky background events, and any contribution from source photons that "spill-over'' into the semi-annuli. The effects of "spill-over'' are illustrated in Fig. 7 where the count rate in the semi-annuli, ${ C_{\rm ann}}$, is plotted against source count rate in the central 8' radius source extraction region, ${ C_{\rm src}}$. Extended sources such as supernova remnants and clusters of galaxies, observations where the target source is offset in the FOV, and pointings near the galactic center are excluded. The solid line shows the fit to the expected linear relation: ${ C_{\rm ann} = 0.0212 + 0.00212\, C_{\rm src}}$. This simple relation ignores the the energy dependence of "spill-over''. It indicates that "spill-over'' adds <10% to the semi-annuli background for on-axis source count rates <1 s-1.

  
\begin{figure}
{
\psfig {figure=ds1657f7.eps,width=8.8cm,angle=0}
}\end{figure} Figure 7: The dependence of the 0.1-10 keV background semi-annuli count rate on the source count rate in the central 8$^\prime$ radius extraction region. The solid line shows the best-fit model discussed in the text

The energy dependence of "spill-over'' was investigated by subtracting the count rates obtained with blank fields from each of the semi-annuli spectra and dividing the remaining counts by those of the source with the standard background subtracted. Figure 8 shows a polynomial fit (Table 3) to the ratio derived in this way as a function of energy. There are at least two effects which produce these additional counts in the background semi-annuli. At low-energies "spill-over'' is dominated by the poor detector spatial resolution (${\rm \propto Energy^{-0.5}}$), while at high-energies the mirror scattering wings dominate.

  
\begin{figure}
{
\psfig {figure=ds1657f8.eps,width=8.0cm,angle=-90}
}\end{figure} Figure 8: Ratio of additional counts in the background semi-annuli divided by source counts as a function of energy. The solid line shows the fifth-order polynomial fit given in Table 3


  
Table 3: Coefficients of the fifth-order polynomial fit to the ratio of additional counts in the background semi-annuli divided by source counts as a function of energy in keV. These coefficients can be used to correct counts extracted from the background semi-annuli for source contamination. a0 is the constant term

\begin{tabular}
{lccc} 
\hline\noalign{\smallskip}
${a_{n}}$\space & \multicolum...
 ..._{5}$\space & $+9.57\ 10^{-7}$\space \\ \noalign{\smallskip}
\hline\end{tabular}

The blank field exposures listed in Table 2 were also used to derive the offset correction factors which are shown in Fig. 9. Above 4 keV, where there are few sky background counts, the correction factors were derived by extrapolating results obtained from a Crab Nebula observation at an offset of 11$^\prime$.Multiplication of the NXB subtracted spectrum in the semi-annuli by these factors gives the predicted background spectrum in the central 8$^\prime$ radius source extraction region when the NXB is added. These correction factors are not simply the mirror vignetting function given in Conti et al. (1994) since, other factors such as an increase in PMT noise due to the lower signal levels off-axis and the position dependency of singularly reflected X-rays may contribute. The correction factors do not change significantly within the range of nominal target locations within the FOV of $\sim$2$^\prime$ (see Sect. 3). Correction factors have also been determined for extraction radii of 4$^\prime$ and 6$^\prime$. These may be obtained by scaling the values in Fig. 9, which are for an extraction radius of 8$^\prime$, by the ratio of extraction region areas. The ability to accurately derive these correction factors is limited by the low number of counts in the standard background exposure. As more LECS background fields become available, these correction factors will be updated.

  
\begin{figure}
{
\psfig {figure=ds1657f9.eps,width=8.0cm,angle=-90}
}\end{figure} Figure 9: Correction factors to be applied to a sky spectrum obtained from the background semi-annuli to give the predicted sky background in the standard 8$^\prime$ radius source extraction region

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