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Background Scale Calculation

Last modified Jan 27, 1997



Let's assume there are source spectral files which you want to combine,

displaymath139

and these files have the EXPOSURE values

displaymath141

and BACKSCAL values

displaymath143

respectively. These spectral files should have the unit COUNTS (not COUNTS/sec), as expected being produced with standard HEASARC software packages.

Corresponding background files are

displaymath145

which have the EXPOSURE values

displaymath147

and BACKSCAL values

displaymath149

respectively.

For each pair of the source and background spectral files, XSPEC calculates the following quantities (background subtracted spectra) to be fitted with models.

eqnarray13

From these quantities, one can make a single quantity,

displaymath151

  equation35

This is the quantity we should make to be fitted with models.

With mathpha, tex2html_wrap_inline153 can be summed with the option ``exposure=CALC" and ``backscal=NONE" (or ``backscal=1"), so that the combined spectrum has the EXPOSURE value tex2html_wrap_inline155 and the BACKSCAL value unity.

Let's put the weights for the background spectra to combine with tex2html_wrap_inline157 and the BACKSCAL value for the combined background spectrum tex2html_wrap_inline159 . With the option ``exposure=CALC", the EXPOSURE of the combined background spectrum will be

displaymath161

By properly choosing tex2html_wrap_inline157 , as shown below, this can be made equal to the desirable EXPOSURE value,

displaymath165

So we have,

  equation55

Consequently if the combined background spectrum thus made is subtracted from the combined source spectrum, XSPEC calculates the quantity,

displaymath151

  equation60

The values (1) and (3) should agree. Hence we have,

  eqnarray69

Equation (2) and equations (4) can be solved for tex2html_wrap_inline159 and tex2html_wrap_inline171 . Then finally, we get,

eqnarray96

These are the values you need to ensure the correct amount of background subtraction.



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Ken Ebisawa
Mon Jan 27 18:48:05 EST 1997


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