Re: spectrally weighted exposure maps

From: Casey Law (claw@head-cfa.harvard.edu)
Date: Wed Jun 13 2001 - 11:49:22 EDT


Hello All,
        This topic was (seemingly) covered in an April 4 email, in which I answered a
question posed by Ben Maughan. Cornelia Lang later followed up the issue in
her own work and found my answer on April 4th lacking. The three of us then
corresponded and found that my answer was indeed wrong. I'll summarize our
discussion for the benefit of the chandra-users crowd. I will also begin
revising the threads, help documents, etc. as appropriate.

        The original question posed by Ben, is summarized as follows: if one makes an
exposure map for a particular band (say 2-4 keV), using a spectral weighting
scheme, should the weights be calculated for the band in question, or should
one take a subset of a larger set of spectral weights (e.g. calculated for
0.5-10 keV)?
        My original (wrong) answer was this: since the weights (as calculated by the
spectrum.sl script) are normalized to one, the weighting of any two bands (say
for 2-4 keV and 8-10 keV) would be equal, that is, equal to one. Thus, the
effective area calculated over these two bands would be roughly equal, which
should not be true (the 2-3 keV band has a much higher effective area). This
reasoning is false since the weights are not the only factor in calculating the
effective area, obviously, but the weights are simply co-factors to the value
of the ARF at that energy.
        The correct answer is that *any* time you use spectral weights, the weights
should sum to one. If not, you will have rediculously small values for the
effective area (~10 cm^2), even over bands where the effective area should be
significant.
        I apoligize for any confusion this may have caused. If anyone has further
questions, please let me know.

                cheers,
                casey



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